Global motion estimation and modeling for accurate global motion compensation for efficient video processing or coding

[0001] Embodiments generally relate to global motion estimation. More particularly, embodiments relate to technology that provides accurate global motion compensation in order to improve video processing efficiency.

[0002] Numerous previous approaches have attempted to improve estimation of global motion by a variety of approaches to achieve better global motion compensation and thus enable higher coding efficiency.

[0003] For instance a group of techniques have tried to improve robustness by filtering the often noisy motion field that is typically available from block motion estimation and used as first step in global motion estimation. Another group of techniques have tried to improve global motion compensated prediction by using pixel based motion or model adaptively (e.g., in a specialized case of panoramas) or higher order motion models. Another group of techniques have tried to improve global motion estimation quality by using better estimation accuracy, an improved framework, or by using variable block size motion. Another group of techniques have tried to get better coding efficiency at low bit cost by improving model efficiency. A still further group of techniques have tried to address the issue of complexity or performance.

[0038] As described above, numerous previous approaches have attempted to improve estimation of global motion by a variety of approaches to achieve better global motion compensation and thus enable higher coding efficiency.

[0039] However, while several schemes have managed to progress the state-of-the art, the actual achieved gains have been limited or have considerably fallen short of their objectives. What has been missing so far is a comprehensive approach for improving global motion estimation, compensation, and parameter coding problem. The implementations described herein represents such a solution to the existing failures of the existing state-of-the art, which include: low robustness or reliability in consistently and accurately measuring global motion; insufficiently accurate measured estimate of global motion; computed global motion estimate resulting in poor global motion compensated frame and thus poor global motion compensated prediction error; insufficient gain from use of global motion, even in scenes with global motion; high bit cost of coding global motion parameters; high computational complexity of algorithms; and low adaptively/high failure rates for complex content and noisy content.

[0040] As will be described in greater detail below, implementations described herein may provide a solution to the technical problem of significantly improving, in video scenes with global motion, the quality of global motion estimation, the accuracy of global motion compensation, and the efficiency of global motion parameters coding—in both, a robust and a complexity-bounded manner.

[0041] In some implementations, a highly adaptive and accurate approach may be used to address the problem of estimation and compensation of global motion in video scenes. The solution may be content adaptive as it uses adaptive modeling of motion using best of multiple models that are used to estimate global motion. Further, global motion estimation parameters may themselves be computed using one of the two optimization based approaches depending on the selected global motion model. Using estimated global motion parameters, compensation of global motion may be performed using interpolation filters that are adaptive to nature of the content. Further, the global motion parameters may be encoded using a highly adaptive approach that either uses a codebook or a context based differential coding approach for efficient bits representation. The aforementioned improvements in global motion estimation/compensation may be achieved under the constraint of keeping complexity to as low as possible. Overall, the implementations presented herein present an adaptive and efficient approach for accurate representation of global motion for efficient video coding.

[0042] For example, the solutions described herein may estimate global motion within a video sequence with an improved motion filtering and selection technique for calculation of global motion models, calculating multiple global motion models for a number of different parametric models per frame. From computed global motion models, a determination and selection may be made of the best global motion model and the best sub-pel interpolation filter per frame for performing global motion compensation. The computed global motion model parameters may then be efficiently encoded using a combination of codebook and differential encoding techniques that allow for compact representation for efficient video coding.

[0043] Accordingly, some implementations described below present a fast, robust, novel, accurate, and efficient method for performing global motion estimation and compensation in video scenes with global motion. For example, some implementations described below represent a significant step forward in state-of-the-art, and may be applicable to variety of applications including improved long term prediction, motion compensated filtering, frame-rate conversion, and compression efficiency of lossy/lossless video, scalable video, and multi-viewpoint/360 degree video. This tool may be expected to be a candidate for integration in future video standards, although it should also be possible to integrate this tool in extensions of current and upcoming standards such as H.264, H.265, AOM AV1, or H.266, for example.

[0044] FIG. 1 is an illustrative block diagram of an example global motion analyzer system 100, arranged in accordance with at least some implementations of the present disclosure. In various implementations, example global motion analyzer system 100 may include a video scene analyzer 102 (e.g., Video Scene Analyzer and Frame Buffer), a local block based motion field estimator 104 (e.g., Local (e.g., Block) Motion Field Estimator), a local motion filed noise reduction filter 106 (e.g., Local Motion Field Noise Reduction Filter), a multiple global motion estimator and modeler 108 (e.g., Multiple Global Motion Estimator and Modeler), an adaptive global motion compensator 110 (e.g., Adaptive Global Motion Compensator), a global motion model parameter and headers entropy coder 112 (e.g., Entropy Coder Global Motion Parameters and Headers), the like, and/or combinations thereof. For example, some of the individual components of global motion analyzer system 100 may not be utilized in all embodiments. In one such example, video scene analyzer 102 may be utilized in some implementations or eliminated in other implementations.

[0045] As illustrated, FIG. 1 shows a high level conceptual diagram of global motion analyzer system 100 including aggregated building blocks to simplify discussion. Video frames are shown input to video scene analyzer 102, which performs scene analysis such as scene change detection (and optionally scene transition detection) as well as having frames buffered to enable use of reordered frames (e.g., as per a group-of-pictures organization scheme). Next, a pair of frames (e.g., a current frame and a reference frame) are input to local block based motion field estimator 104, which computes motion-vectors for all blocks of the frame. Next, this motion-field is filtered by local motion filed noise reduction filter 106 to remove noisy motion vector regions. The filtered motion-field is then input to multiple global motion estimator and modeler 108, which computes estimate of global motion by trying per frame different motion models and selecting the best one. Next, the selected motion field parameters are encoded by global motion model parameter and headers entropy coder 112, and the motion field is provided to adaptive global motion compensator 110, which generates global motion compensated frame.

[0046] In operation, global motion analyzer system 100 may be operated based on the basic principle that exploitation of global motion in video scenes is key to further compression gains by integration in current generation coders as well as development of new generation coders. Further, the implementations described herein, as compared to the current state-of-the-art, offers improvements on all fronts, e.g., global motion estimation, global motion compensation, and global parameters coding.

[0047] As regards the global motion estimation, significant care is needed not only in selecting a global motion model but also how that motion model is computed. For lower to medium order models (such as 4 or parameters) implementations herein may use least square estimation and/or random sampling method. For higher order models (such as 8 and 12 parameters) implementations herein may use the Levenberg-Marquardt Algorithm (LMA) method. For an 8 parameter model, implementations herein may identify many choices that are available, such as the bi-linear model, the perspective model, and the pseudo-perspective model; via thorough testing, the pseudo-perspective model may often be utilized to provide consistent and robust results. Further, the task of finding any global motion model parameters is complicated by noisiness of motion field so a good algorithm for filtering of motion field was developed to separate outlier vectors that otherwise contribute to distorting calculation of global motion field. Further, while the same global motion model can be presumably used for a group of frames that have similar motion characteristics, content based adaptively and digital sampling may require more-or-less an independent selection of motion model per frame from among a number of available motion models. Further, rate-distortion constraints can also be used in selection of motion model due to cost of motion parameter coding bits. Lastly, in some implementations herein, additional care may be taken during motion estimation to not include inactive areas of a frame.

[0048] As will be described in greater detail below, in operation, once the best global motion model is selected per frame, the model parameters require efficient coding for which the implementations herein may use a hybrid approach that uses a combination of small codebook and direct coding of residual coefficients that use prediction from past if closest match is not found in the codebook. Some rate-distortion tradeoffs may be employed to keep coding bit cost low. Further, since a current global motion model and a past global motion model that is used for prediction may be different in number and type of coefficient, a coefficient mapping strategy may be used by implementations herein to enable successful prediction that can reduce the residual coefficients that need to be coded. The codebook index or coefficient residuals may be entropy coded and transmitted to a decoder.

[0049] At the decoder, after entropy decoding of coefficient residuals to which prediction is added to generate reconstructed coefficients, or alternatively using coefficients indexed from codebook, global motion compensation may be performed, which may require sub-pel interpolation. Headers in the encoded stream for a frame may be used to indicate the interpolation precision and filtering from among choice of 4 interpolation filter combinations available, to generate correct global motion compensated prediction; at encoder various filtering options were evaluated and best selection made and signaled per frame via bitstream.

[0050] FIG. 2 is an illustrative diagram of an example global motion analysis process 200, arranged in accordance with at least some implementations of the present disclosure. In various implementations, FIG. 2 pictorially depicts the various steps in this process using a selected fast moving portion of “Stefan” sequence. A reference frame F_ref of the sequence and current frame F are shown that are used in block motion estimation, which generates motion field MVF. The motion field is then filtered to Filtered MVF and used by multiple global motion models that perform global motion estimation generating candidate models from which the best model is selected. This model is then used to compute global motion compensated frame, the generation of which requires a matching motion interpolation filter that is used to generate high precision sub-pel motion compensation. The original frame is differenced with global motion compensated frame and the residual frame is shown that contains low energy everywhere except for boundary block extension region, and the uncovered and uncompensated local moving region.

[0051] Accordingly, implementations of global motion analyzer system 100 may be implemented so as to provide the following improvements as compared to other solutions: utilizes moderate complexity only when absolutely necessary to reduce motion compensated residual; provides a high degree of adaptively to complex content; provides a high degree of adaptively to noisy content; provides a high robustness in consistently and accurately measuring global motion; ability to deal with static black bars/borders so computed global motion is not adversely impacted; ability to deal with static logos and text overlays so computed global motion is not adversely impacted; improvements in computed global motion estimate results in a good global motion compensated frame and thus lower global motion compensated prediction error; typically provide a good gain from global motion in scenes with small or slowly moving local motion areas; and/or typically provide a low bit cost of coding global motion parameters.

[0052] FIG. 3 is an illustrative block diagram of a more detailed example global motion analyzer system 100, arranged in accordance with at least some implementations of the present disclosure. In various implementations, example global motion analyzer system 100 may include video scene analyzer 102 (e.g., Input Video GOP processor 302 and Video Pre-processor 304), local block based motion field estimator 104 (e.g., Block-based Motion Estimator), local motion filed noise reduction filter 106 (e.g., Motion Vector Noise Reduction Filter), multiple global motion estimator and modeler 108 (e.g., Multiple Global Motion Estimator and Modeler), adaptive global motion compensator 110 (e.g., Adaptive Global Motion Compensator), global motion model parameter and headers entropy coder 112 (e.g., Global Motion Model and Headers Entropy Coder), the like, and/or combinations thereof. For example, some of the individual components of global motion analyzer system 100 may not be utilized in all embodiments. In one such example, video scene analyzer 102 may be utilized in some implementations or eliminated in other implementations. Additionally, global motion analyzer system 100 may include reference frames memory buffer 306, parameters initializes 308, and parameters memory buffer 310.

[0053] As illustrated, global motion analyzer system 100 may operate so that input video is first organized into group of pictures (GOP) form via input video GOP processor 302. Next, current frame F and reference frame F_ref may be analyzed in a pre-processing step to detect scene changes and re-set memory buffers/codebook used for entropy coding via video pre-processor 304. If the current frame is not the first frame in the scene then block-based motion estimation may be performed between current frame F and reference frame F_ref via local block based motion field estimator 104, where F_ref may be retrieved via reference frames memory buffer 306. The resulting motion vector field (MVF) is prone to noise so that motion vector noise reduction filtering may be applied to the motion vector field (MVF) in an attempt to minimize the amount of outlier, noise-related vectors via local motion filed noise reduction filter 106. The core of the proposed algorithm is the adaptive global motion estimation and modeling, which may use the filtered motion vectors as input via multiple global motion estimator and modeler 108. This step may use adaptive selection of motion vectors for global motion estimation that combines a statistics-based approach and a simple segmentation-based approach. In addition, three models of different complexity may be evaluated and the most suitable model may be selected for modeling of the global moving area of the current frame. The computed global motion model (GMM) may then be passed to the compensation step, which may use an adaptively selected (e.g., out of four available filters) sub-pixel interpolation filtering that best suits the texture type in the globally moving area via adaptive global motion compensator 110. GMM parameters may be encoded and to the reference points motion vectors (MVs) representation and reconstructed at quantized accuracy. The compensator outputs the reconstructed frame and final sum of absolute differences (SAD)/residuals. Finally, the GMM parameters in the reference point form may be encoded with a codebook-based entropy coder via global motion model parameter and headers entropy coder 112. The parameters may either be coded as an index of the existing GMM from the codebook, or as residuals to an existing codeword. The residuals may be coded with an adaptive modified exp-Golomb codes (e.g., three tables may be used for codes of the most frequent values, while the rest of the values (e.g., less frequent values) may be represented via exp-Golomb codes formula).

[0054] Video pre-processor 304 may perform scene change detection. Current and reference (e.g. previous) frames are analyzed in order to detect the beginning of new scene and reinitialize past frames' related information. For example, video pre-processor 304 may signal parameters initializer to initialize parameters memory buffer 310 in response to a determined scene change.

[0055] Local block based motion field estimator 104 may use block-based motion estimation to create a block-level motion vector field between the current frame and the reference frame(s). In one implementation, graphics hardware-accelerated video motion estimation (VME) routines may be used to generate block-based motion vectors.

[0056] Local motion filed noise reduction filter 106 may use motion vector filtering to create a smoother motion vector field from the existing raw field that was created by the local block based motion field estimator 104. This process may serve to eliminate outlier vectors from the motion vector field.

[0057] Multiple global motion estimator and modeler 108 may use global motion model generation, which may include several steps. In this part of the process, a near-optimal global motion model may be computed for the current frame.

[0058] Multiple global motion estimator and modeler 108 may determine an initial affine global motion model via random sampling. For example, random sampling may be used to compute a best candidate affine model by random sampling and histogram peak analysis. This method may be used to create an initial rough estimate of affine parameters for global moving area. Highest peaks in each of the affine parameters likely correspond to a global motion model estimate. This process may be performed twice: once with all blocks used as input, and once with only likely reliable blocks used as input (e.g., as may be defined by an unreliable motion vectors mask). The global motion model with smallest error estimate (e.g., sum of absolute differences (SAD)-based) may be selected.

[0059] Multiple global motion estimator and modeler 108 may select motion vectors for global motion model estimation. In this step, the initial affine global motion model from the previous step may be used to estimate a selection mask, which may define blocks to be used for the global motion model parameters estimation. In one example, a total of eight candidate selection masks may be computed and the one that yields the smallest estimated error measure is chosen as the final selection mask. Although a different number of candidate selection masks could be used.

[0060] Multiple global motion estimator and modeler 108 may select an adaptive sub-pixel filter. This operation may be adaptively performed depending on the sharpness of the video content. For example, there may be four (or another suitable number) of sub-pixel filtering methods selected for different types of video content, for example, there may be the following filter types: (1) a 1/16-th pixel accurate bilinear filter used mostly for content with blurry texture, (2) a 1/16-th pixel accurate bicubic filter used for content with slightly blurry and normal texture levels, (3) a ⅛-th pixel accurate AVC-based filter usually used for normal and slightly sharp content, and (4) a ⅛-th pixel accurate HEVC-based filter typically used for the sharpest types of content.

[0061] Multiple global motion estimator and modeler 108 may perform adaptive global motion model computation and selection. In such an operation, there may be several (e.g., two) modes of operation defined that may adapt between different motion models: (1) Mode 0 (default mode) which may adaptively switch on a frame basis between translational 4-parameter, affine 6-parameter and pseudo-perspective 8-parameter global motion model, and (2) Mode 1 which may adaptively switch on a frame basis between affine 6-parameter, pseudo-perspective 8-parameter and bi-quadratic 12-parameter global motion model.

[0062] Adaptive global motion compensator 110 may perform global motion model-based compensation. For example, such global motion model-based compensation may be done for each block at a pixel level within the block using final motion model with the selected sub-pel filtering method. For each pixel within a block, a global motion may be computed and the pixel may be moved at a sub-pel position according to the previously determined sub-pel filtering method. Thus, a pixel on one side of the block may have different motion vector than a pixel on the other side of the same block. Compensation may be done with quantized/reconstructed global motion model parameters. In addition, coefficients may be represented as a quotient with denominator scaled (e.g., to a power of two) in order to achieve fast performance (e.g., by using bitwise shifting instead of division).

[0063] Global motion model parameter and headers entropy coder 112 may perform codebook-based global motion model parameters coding. For example, such codebook-based global motion model parameters coding may be used to encode the global motion model parameters. Such codebook-based global motion model parameters coding maybe based on the concept of reference points. The motion vectors corresponding to reference points may be predicted and the residuals may be coded with modified exp-Golomb codes. Predictions may be generated from the codebook that contains several (e.g., up to eight last occurring global motion model parameters).

[0064] FIG. 4 is an illustrative block diagram of a more detailed example global motion analyzer system 100 that is integrated with a video encoder 400 in accordance with at least some implementations of the present disclosure. In various implementations, example global motion analyzer system 100 may include, or may be adapted to operate with video encoder 400.

[0065] As illustrated, video encoder 400 may receive a compensated frame and a corresponding error value (e.g., SAD) from adaptive global motion compensator 110. Additionally, video encoder 400 may receive encoded GMM parameters and headers corresponding to the compensated frame. Video encoder 400 may process this and other information when generating an encoded bitstream.

[0066] As used herein, the term “coder” may refer to an encoder and/or a decoder. Similarly, as used herein, the term “coding” may refer to encoding via an encoder and/or decoding via a decoder. For example video encoder 400 may include a video encoder with an internal video decoder, as illustrated in FIG. 4, while a companion coder may only include a video decoder (not illustrated independently here), and both are examples of a “coder” capable of coding.

[0067] Some implementations described herein generally relate to improvements in estimation, representation and compensation of motion that are key components of an inter-frame coding system, which can directly improve the overall coding efficiency of inter-frame coding. Specifically, some implementations described herein introduce systems and methods to enable significant improvements in global motion estimation, global motion compensation, and global motion parameters coding to improve inter-frame coding efficiency. The improvements include but are not limited to improved modeling of complex global motion, and compact representation of global motion parameters. By comparison, traditional inter-frame video coding typically uses block based motion estimation, compensation and motion vector coding which can mainly compensate for local translator motion and is thus not only is limited in many ways in ability to deal with complex global motion, but also does not allow efficient motion representation.

[0068] For reference, block based motion estimation forms the core motion compensation approach in recent video coding standards such as ITU-T H.264/ISO MPEG AVC and ITU-T H.265/ISO MPEG HEVC as well as upcoming standards in development such as ITU-T H.266 and the AOM AV1 standard. FIGS. 5-7 below will briefly review inter-frame video coding at a high level.

[0069] With reference to global motion analyzer system 100 of FIGS. 1, 3, and/or 4, there are a number of practical issues in making a system for global motion estimation and compensation work. [1] high complexity—calculation of global motion estimation (that typically starts after a calculation of block motion vectors) is a heavily compute intensive open-form process, typically requiring a least square minimization type of solution, that is iterative and whose quick convergence is not always guaranteed; [2] motion range limitations—if the starting block motion range is insufficient with respect to fast actual motion, the resulting global motion estimate will likely be quite inaccurate resulting in large prediction residual; [3] insufficient robustness—noisy motion vectors contribute to misdirection of global motion estimation process, not only making convergence hard but also can result in poor global motion estimates; [4] Local/Global motion interaction—often local motion of objects interferes with calculation of global motion causing global motion estimates to be either somewhat inaccurate or even downright erroneous; [5] mismatch of motion model to actual motion in the scene—for instance, if a fixed four parameter global motion model is used to represent changes in perspective in a video scene, the measured motion parameters may be erroneous; [6] limitations in extension of frame boundaries for cases of large motion—while this issue impacts both local block motion compensation as well as global motion compensation, local block motion vectors do not have to follow actual motion and sometimes may provide adequate results due to random matches; [7] limitations due to inactive static area in content—if such an area (e.g., this includes presence of black bars, black borders, letter-boxing, pillar-boxing etc.) is not rejected from global motion estimation, the resulting estimates can be erroneous leading to poor motion compensated prediction; [8] limitations due to static logos or overlaid text—if static logo region and globally moving background region are not separated for global motion estimation then it is difficult to find an accurate global motion estimate and thus global motion compensation quality is likely to suffer; [9] coding bit cost of global motion parameters—since both local and global motion tends to co-exist in a video scene, sending global motion parameters is not sufficient by itself, and needs to be sent in addition to local motion vectors; thus only a limited global motion bit cost can be afforded; and [10] global motion compensation accuracy—if limited precision sub-pel interpolation with simpler filters is performed to reduce motion compensation complexity (e.g., this may be important as this process is needed to be performed both at encoder and decoder), the resulting prediction is often blurry and does not generate small residual signal.

[0070] FIG. 5 is an illustrative block diagram of an example video encoder 500, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video encoder 500 may be configured to undertake video coding and/or implement video codecs according to one or more advanced video codec standards, such as, for example, the Advanced Video Coding (e.g., AVC/H.264) video compression standard or the High Efficiency Video Coding (e.g., HEVC/H.265) video compression standard, but is not limited in this regard. Further, in various embodiments, video encoder 500 may be implemented as part of an image processor, video processor, and/or media processor.

[0071] As used herein, the term “coder” may refer to an encoder and/or a decoder. Similarly, as used herein, the term “coding” may refer to encoding via an encoder and/or decoding via a decoder. For example video encoder 500 may include a video encoder with an internal video decoder, as illustrated in FIG. 5, while a companion coder may only include a video decoder (not illustrated independently here), and both are examples of a “coder” capable of coding.

[0072] In some examples, video encoder 500 may include additional items that have not been shown in FIG. 5 for the sake of clarity. For example, video encoder 500 may include a processor, a radio frequency-type (RF) transceiver a display, an antenna, and/or the like. Further, video encoder 500 may include additional items such as a speaker, a microphone, an accelerometer, memory, a router, network interface logic, and/or the like that have not been shown in FIG. 5 for the sake of clarity.

[0073] Video encoder 500 may operate via the general principle of inter-frame coding, or more specifically, motion-compensated (DCT) transform coding that modern standards are based on (although some details may be different for each standard).

[0074] Motion estimation is done using fixed or variable size blocks of a frame of video with respect to another frame resulting in displacement motion vectors that are then encoded and sent to the decoder which uses these motion vectors to generate motion compensated prediction blocks. While interframe coders support both intra and inter coding, it is the interframe coding (which involves efficiently coding of residual signal between original blocks and corresponding motion compensated prediction blocks) that provides the significant coding gain. One thing to note is that it is coding of large number of high precision motion vectors of blocks (due to variable block size partitioning, and motion compensation with at least ¼ pixel accuracy as needed to reduce the residual signal) poses a challenge to efficient video coding due to needed coding bits for motion vectors even though clever techniques for motion vector prediction and coding have already been developed. Another issue with block motion vectors is that at best they can represent translatory motion model and are not capable of faithfully representing complex motion.

[0075] The key idea in modern interframe coding is thus to combine temporally predictive (motion compensated) coding that adapts to motion of objects between frames of video and is used to compute motion compensated differential residual signal, and spatial transform coding that converts spatial blocks of pixels to blocks of frequency coefficients typically by DCT (of block size such as 8×8) followed by reduction in precision of these DCT coefficients by quantization to adapt video quality to available bit-rate. Since the resulting transform coefficients have energy redistributed in lower frequencies, some of the small valued coefficients after quantization turn to zero, as well as some high frequency coefficients can be coded with higher quantization errors, or even skipped altogether. These and other characteristics of transform coefficients such as frequency location, as well as that some quantized levels occur more frequently than others, allows for using frequency domain scanning of coefficients and entropy coding (in its most basic form, variable word length coding) to achieve additional compression gains.

[0076] Inter-frame coding includes coding using up to three types picture types (e.g., I-pictures, P-Pictures, and B-pictures) arranged in a fixed or adaptive picture structure that is repeated a few times and collectively referred to as a group-of-pictures (GOP). I-pictures are typically used to provide clean refresh for random access (or channel switching) at frequent intervals. P-pictures are typically used for basic inter-frame coding using motion compensation and may be used successively or intertwined with an arrangement of B-pictures; where, P-pictures may provide moderate compression. B-pictures that are bi-directionally motion compensated and coded inter-frame pictures may provide the highest level of compression.

[0077] Since motion compensation is difficult to perform in the transform domain, the first step in an interframe coder is to create a motion compensated prediction error in the pixel domain. For each block of current frame, a prediction block in the reference frame is found using motion vector computed during motion estimation, and differenced to generate prediction error signal. The resulting error signal is transformed using 2D DCT, quantized by an adaptive quantizer (e.g., “quant”) 508, and encoded using an entropy coder 509 (e.g., a Variable Length Coder (VLC) or an arithmetic entropy coder) and buffered for transmission over a channel.

[0078] As illustrated, the video content may be differenced at operation 504 with the output from the internal decoding loop to form residual video content.

[0079] The residual content may be subjected to video transform operations at transform module (e.g., “block DCT”) 506 and subjected to video quantization processes at quantizer (e.g., “quant”) 508.

[0080] The output of transform module (e.g., “block DCT”) 506 and quantizer (e.g., “quant”) 508 may be provided to an entropy encoder 509 and to an inverse transform module (e.g., “inv quant”) 512 and a de-quantization module (e.g., “block inv DCT”) 514. Entropy encoder 509 may output an entropy encoded bitstream 510 for communication to a corresponding decoder.

[0081] Within an internal decoding loop of video encoder 500, inverse transform module (e.g., “inv quant”) 512 and de-quantization module (e.g., “block inv DCT”) 514 may implement the inverse of the operations undertaken transform module (e.g., “block DCT”) 506 and quantizer (e.g., “quant”) 508 to provide reconstituted residual content. The reconstituted residual content may be added to the output from the internal decoding loop to form reconstructed decoded video content. Those skilled in the art may recognize that transform and quantization modules and de-quantization and inverse transform modules as described herein may employ scaling techniques. The decoded video content may be provided to a decoded picture store 120, a motion estimator 522, a motion compensated predictor 524 and an intra predictor 526. A selector 528 (e.g., “Sel”) may send out mode information (e.g., intra-mode, inter-mode, etc.) based on the intra-prediction output of intra predictor 526 and the inter-prediction output of motion compensated predictor 524. It will be understood that the same and/or similar operations as described above may be performed in decoder-exclusive implementations of Video encoder 500.

[0082] FIG. 6 is an illustrative block diagram of an example Advanced Video Coding (AVC) video encoder 600, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video encoder 600 may be configured to undertake video coding and/or implement video codecs according to one or more advanced video codec standards, such as, for example, the Advanced Video Coding (e.g., AVC/H.264) video compression standard or the High Efficiency Video Coding (e.g., HEVC/H.265) video compression standard, but is not limited in this regard. Further, in various embodiments, video encoder 600 may be implemented as part of an image processor, video processor, and/or media processor.

[0083] As illustrated, FIG. 6 shows block diagram of an AVC encoder that follows the principles of the generalized inter-frame video encoder 500 of FIG. 5 discussed earlier. Each frame is partitioned into macroblocks (MB's) that correspond to 16×16 luma (and two corresponding 8×8 chroma signals). Each MB can potentially be used as is or partitioned into either two 16×8s, or two 8×16s or four 8×8s for prediction. Each 8×8 can also be used as is or partitioned into two 8×4s, or two 4×8s or four 4×4s for prediction. The exact partitioning decision depends on coding bit-rate available vs. distortion optimization (by full or partial).

[0084] For each MB a coding mode can be assigned from among intra, inter or skip modes in unidirectionally predicted (P-) pictures. B- (bidirectionally) predicted pictures are also supported and include an additional MB or block based direct mode. Even P-pictures can refer to multiple (4 to 5) past references.

[0085] In the high profile, transform block size allowed are 4×4 and 8×8 that encode residual signal (generated by intra prediction or motion compensated inter prediction). The generated transform coefficients are quantized and entropy coded using a Context-Adaptive Binary Arithmetic Coding (CABAC) arithmetic encoder. A filter in the coding loop ensures that spurious blockiness noise is filtered, benefitting both objective and subjective quality.

[0086] In some examples, during the operation of video encoder 600, current video information may be provided to a picture reorder 642 in the form of a slice of video data. Picture reorder 642 may determine the picture type (e.g., I-, P-, or B-slices) of each video slice and reorder the video slices as needed.

[0087] The current video frame may be split so that each MB can potentially be used as is or partitioned into either two 16×8's, or two 8×16's or four 8×8's for prediction, and each 8×8 can also be used as is or partitioned into two 8×4's, or two 4×8's or four 4×4's for prediction at prediction partitioner 644 (e.g., “MB Partitioner”). A coding partitioner 646 (e.g., “Res 4×4/8×8 Partitioner”) may partition residual macroblocks.

[0088] The coding partitioner 646 may be subjected to known video transform and quantization processes, first by a transform 648 (e.g., 4×4 DCT/8×8 DCT), which may perform a discrete cosine transform (DCT) operation, for example. Next, a quantizer 650 (e.g., Quant) may quantize the resultant transform coefficients.

[0089] The output of transform and quantization operations may be provided to an entropy encoder 652 as well as to an inverse quantizer 656 (e.g., Inv Quant) and inverse transform 658 (e.g., Inv 4×4DCT/Inv 8×8 DCT). Encoder 652 (e.g., “CAVLC/CABAC Encoder”) may output an entropy encoded bitstream 654 for communication to a corresponding decoder.

[0090] Within the internal decoding loop of video encoder 600, inverse quantizer 656 and inverse transform 658 may implement the inverse of the operations undertaken by transform 648 and quantizer 650 to provide output to a residual assembler 660 (e.g., Res 4×4/8×8 Assembler).

[0091] The output of residual assembler 660 may be provided to a loop including a prediction assembler 662 (e.g., Block Assembler), a de-block filter 664, a decoded picture buffer 668, a motion estimator 670, a motion compensated predictor 672, a decoded macroblock line plus one buffer 674 (e.g., Decoded MB Line+1 Buffer), an intra prediction direction estimator 676, and an intra predictor 678. As shown in FIG. 6B, the output of either motion compensated predictor 672 or intra predictor 678 is selected via selector 680 (e.g., Sel) and may be combined with the output of residual assembler 660 as input to de-blocking filter 664, and is differenced with the output of prediction partitioner 644 to act as input to coding partitioner 646. An encode controller 682 (e.g., Encode Controller RD Optimizer & Rate Controller) may operate to perform Rate Distortion Optimization (RDO) operations and control the rate of video encoder 600.

[0092] FIG. 7 is an illustrative diagram of an example High Efficiency Video Coder (HEVC) video encoder 700, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video encoder 700 may be configured to undertake video coding and/or implement video codecs according to one or more advanced video codec standards, such as, for example, the Advanced Video Coding (e.g., AVC/H.264) video compression standard or the High Efficiency Video Coding (e.g., HEVC/H.265) video compression standard, but is not limited in this regard. Further, in various embodiments, video encoder 700 may be implemented as part of an image processor, video processor, and/or media processor.

[0093] As illustrated in FIG. 7, the high level operation of video encoder 700 follows the principles of general inter-frame encoder discussed earlier via FIG. 5. For instance, video encoder 700 of FIG. 7 is also an inter-frame motion compensated transform encoder that typically either uses a combination of either I- and P-pictures only or I-, P- and B-pictures (note that in HEVC a generalized B-picture (GBP) can be used in place of P-picture) in a non-pyramid, or pyramid GOP arrangement. Further like H.264/AVC coding, not only B-pictures (that can use bi-directional references), but also P-picture can also use multiple references (these references are unidirectional for P-pictures). As in previous standards B-pictures implies forward and backward references, and hence picture reordering is necessary.

[0094] In some examples, during the operation of video encoder 700, current video information may be provided to a picture reorder 742 in the form of a frame of video data. Picture reorder 742 may determine the picture type (e.g., I-, P-, or B-frame) of each video frame and reorder the video frames as needed.

[0095] The current video frame may be split from Largest Coding Units (LCUs) to coding units (CUs), and a coding unit (CU) may be recursively partitioned into smaller coding units (CUs); additionally, the coding units (CUs) may be partitioned for prediction into prediction units (PUs) at prediction partitioner 744 (e.g., “LC_CU & PU Partitioner). A coding partitioner 746 (e.g., “Res CU_TU Partitioner) may partition residual coding units (CUs) into transform units (TUs).

[0096] The coding partitioner 746 may be subjected to known video transform and quantization processes, first by a transform 748 (e.g., 4×4DCT/VBS DCT), which may perform a discrete cosine transform (DCT) operation, for example. Next, a quantizer 750 (e.g., Quant) may quantize the resultant transform coefficients.

[0097] The output of transform and quantization operations may be provided to an entropy encoder 752 as well as to an inverse quantizer 756 (e.g., Inv Quant) and inverse transform 758 (e.g., Inv 4×4DCT/VBS DCT). Entropy encoder 752 may output an entropy encoded bitstream 754 for communication to a corresponding decoder.

[0098] Within the internal decoding loop of video encoder 700, inverse quantizer 756 and inverse transform 758 may implement the inverse of the operations undertaken by transform 748 and quantizer 750 to provide output to a residual assembler 760 (e.g., Res TU_CU Assembler).

[0099] The output of residual assembler 760 may be provided to a loop including a prediction assembler 762 (e.g., PU_CU & CU_LCU Assembler), a de-block filter 764, a sample adaptive offset filter 766 (e.g., Sample Adaptive Offset (SAO)), a decoded picture buffer 768, a motion estimator 770, a motion compensated predictor 772, a decoded largest coding unit line plus one buffer 774 (e.g., Decoded LCU Line+1 Buffer), an intra prediction direction estimator 776, and an intra predictor 778. As shown in FIG. 7B, the output of either motion compensated predictor 772 or intra predictor 778 is selected via selector 780 (e.g., Sel) and may be combined with the output of residual assembler 760 as input to de-blocking filter 764, and is differenced with the output of prediction partitioner 744 to act as input to coding partitioner 746. An encode controller 782 (e.g., Encode Controller RD Optimizer & Rate Controller) may operate to perform Rate Distortion Optimization (RDO) operations and control the rate of video encoder 700.

[0100] In operation, the Largest Coding Unit (LCU) to coding units (CU) partitioner partitions LCU's to CUs, and a CU can be recursively partitioned into smaller CU's. The CU to prediction unit (PU) partitioner partitions CUs for prediction into PUs, and the TU partitioner partitions residual CUs into Transforms Units (TUs). TUs correspond to the size of transform blocks used in transform coding. The transform coefficients are quantized according to Qp in the bitstream. Different Qps can be specified for each CU depending on maxCuDQpDepth with LCU based adaptation being of the least granularity. The encode decisions, quantized transformed difference and motion vectors and modes are encoded in the bitstream using Context Adaptive Binary Arithmetic Coder (CABAC).

[0101] An Encode Controller controls the degree of partitioning performed, which depends on quantizer used in transform coding. The CU/PU Assembler and TU Assembler perform the reverse function of partitioner. The decoded (every DPCM encoder incorporates a decoder loop) intra/motion compensated difference partitions are assembled following inverse DST/DCT to which prediction PUs are added and reconstructed signal then Deblock, and SAO Filtered that correspondingly reduce appearance of artifacts and restore edges impacted by coding. HEVC uses Intra and Inter prediction modes to predict portions of frames and encodes the difference signal by transforming it. HEVC uses various transform sizes called Transforms Units (TU). The transform coefficients are quantized according to Qp in the bitstream. Different Qps can be specified for each CU depending on maxCuDQpDepth.

[0102] AVC or HEVC encoding classifies pictures or frames into one of 3 basic picture types (pictype), I-Picture, P-Pictures, and B-Pictures. Both AVC and HEVC also allow out of order coding of B pictures, where the typical method is to encode a Group of Pictures (GOP) in out of order pyramid configuration. The typical Pyramid GOP configuration uses 8 pictures Group of Pictures (GOP) size (gopsz). The out of order delay of B Pictures in the Pyramid configuration is called the picture level in pyramid (piclvl).

[0103] FIG. 8 shows an example Group of Pictures 800 structure. Group of Pictures 800 shows a first 17 frames (frames 0 to 16) including a first frame (frame 0) an intra frame followed by two GOPs, each with eight pictures each. In the first GOP, frame 8 is a P frame (or can also be a Generalized B (GPB) frame) and is a level 0 frame in the pyramid. Whereas frame 1 is a first level B-frame, frame 2 and 6 are second level B-frames, and frames 1,3, 5 and 7 are all third level B-frames. For instance, frame 1 is called the first level B-frame, as it only needs the I-frame (or the last P-frame of previous GOP) as the previous reference and actual P-frame of current GOP as the next reference to create predictions necessary for encoding frame 1. In fact, frame 1 can use more than 2 references, although 2 references may be used to illustrate the principle. Further, frames 2 and 6 are called second level B-frames as they use first level B-frame (frame 1) as a reference, along with a neighboring I and P-frame. Similarly level 3 B-frames use at least one level 2 B-frame as a reference. A second GOP (frame 9 through 16) of the same size is shown, that uses decoded P-frame of previous GOP (instead of I-frame as in case of previous GOP), e.g., frame 8 as one reference; where the rest of the second GOP works identically to the first GOP. In terms of encoding order, the encoded bitstream encodes frame 0, followed by frame 8, frame 4, frame 2, frame 1, frame 3, frame 6, frame 5, frame 7, etc. as shown in the figure.

[0104] Global Motion Models:

[0105] FIG. 9 is an illustrative diagram of various example global motion models 900 with respect to chirping, arranged in accordance with at least some implementations of the present disclosure. In various implementations, example global motion models 900 may include a translational non-chirping model, an affine non-chirping model, a bi-liner non-chirping model, a perspective (e.g., projective) chirping model, a pseudo-perspective chirping model, a bi-biquadratic chirping model, the like, and/or combinations thereof.

[0106] A number of global motion models have been proposed in published literature. Generally speaking, a particular motion model establishes a tradeoff between the complexity of the model and the ability to handle different types of camera related motions, scene depth/perspective projections, etc. Models are often classified into linear (e.g., simple) models, and nonlinear (e.g., complex models). Linear models are capable of handling normal camera operations such as translational motion, rotation and even zoom. More complex models, which are typically non-linear and contain at least one quadratic (or higher order) term, are often used in cases when there is complex scene depth, strong perspective projection effects in the scene, or simply if more precision is needed for a given application. One disadvantage of non-linear models is that they have higher computational complexity. On the other hand, Translational and affine models are more prone to errors when noisy motion vector field is used for GME. The most commonly used models for global motion estimation in video coding applications are simpler, linear models.

[0107] Suppose we are given a motion vector field, (MX_i, MY_i), i=0, . . . N−1, where N is the number of motion vectors in the frame. Then, each position (x_i, y_i) corresponding to the center of the block i of the frame is moved to (x′_i, y′_i) as per motion vector (MX_i, MY_i) as follows:
x′_i=x_i+MX_i
y′_i=y_i+MY_i

[0108] A simple 4-parameter motion model aims to approximate these global motion moves of frame positions by a single linear equation with a total of 4 parameters {a₀, a₁, a₂, a₃}:
x′_i=a₀x_i+a₁
y′_i=a₂y_i+a₃

[0109] This equation defines translational 4-parameter motion model. Another 4-parameter model, is referred to as a pseudo-affine 4-parameter motion model. Pseudo-affine motion model is defined as:
x′_i=a₀x_i+a_iy_i+a₂
y′_i=a₀y_i−a_ix_i+a₃

[0110] The advantage of pseudo-affine model is that it often can estimate additional types of global motion while having the same number of parameters as a simple translational model. One of the most commonly used motion models in practice is the 6-parameter affine global motion model. It can more precisely estimate most of the typical global motion caused by camera operations. The affine model is defined as follows:
x′_i=a₀x_i+a_iy_i+a₂
y′_i=a₃x_i+a₄y_i+a₅

[0111] Unfortunately, linear models cannot handle camera pan and tilt properly. Thus, non-linear models are required for video scenes with these effects. More complex models are typically represented with quadratic terms. They are widely used for video applications such as medical imaging, remote sensing or computer graphics. The simplest non-linear model is bi-linear 8-parameter global motion model which is defined as:
x′_i=a₀x_iy_i+a₁x_i+a₂y_i+a₃
y′_i=a₄x_iy_i+a₅x_i+a₆y_i+a₇

[0112] Another popular 8-parameter model is perspective (or projective) 8-parameter global motion model. This model is designed to handle video scenes with strong perspective, which creates global motion field that follows more complex non-linear distribution. The Projective model is defined as follows:

[0113] $x_i^{\prime }=\frac{a_0{x}_i+a_1{y}_i+a_2}{a_6{x}_i+a_7{y}_i+1}$ $y_i^{\prime }=\frac{a_3{x}_i+a_4{y}_i+a_5}{a_6{x}_i+a_7{y}_i+1}$

[0114] A variant of the perspective model, called pseudo perspective model, has been is shown to have a good overall performance as it can handle perspective projections and related effects such as “chirping” (the effect of increasing or decreasing spatial frequency with respect to spatial location).

[0115] One 8-parameter pseudo-perspective model, is defined as follows:
x′_i=a₀x_i²+a₁x_iy_i+a₂x_i+a₃y_i+a₄
y′_i=a₁y_i²+a₀x_iy_i+a₅x_i+a₆y_i+a₇

[0116] Pseudo-projective model has an advantage over the perspective model because it typically has smaller computational complexity during the estimation process while at the same time is being able to handle all perspective-related effects on 2-D global motion field. Perspective model has been known to be notoriously difficult to estimate and often requires many more iterations in the estimation process.

[0117] FIG. 9 shows pictorial effects of different modeling functions. As illustrated, the pseudo-perspective model can produce both chirping and converging effects, and it is the best approximation of perspective mapping using low order polynomials. It also shows that bilinear function, although also has 8-parameters like perspective and pseudo-perspective models, fails to capture the chirping effect.

[0118] Finally, for video applications where very high precision in modeling is required, capable of handling all degrees of freedom in camera operations and perspective mapping effects, Bi-quadratic model can be used. It is a 12-parameter model, and thus most expensive in terms of coding cost. Bi-quadratic 12-parameter model is defines as follows:
x′_i=a₀x_i²+a₁y_i²+a₂x_iy_i+a₃x_i+a₄y_i+a₅
y′_i=a₆x_i²+a₇y_i²+a₈x_iy_i+a₉x_i+a₁₀y_i+a₁₁

[0119] Table 1 shows summary of the aforementioned global motion models. For example, other, even higher order polynomial models are possible to define (e.g., 20-parameter bi-cubic model) but are rarely used in practice because of extremely high coding cost.

[0120] Table 1, below, illustrates a summary of global motion models and their properties.

[0121]

TABLE 1
Motion		Number of
Model	Model Equation	Parameters
Translational	( x ′ y ′ ) = ( a 0 ⁢ x + a 1 a 2 ⁢ x + a 3 )	4
Pseudo- Affine	( x ′ y ′ ) = ( a 0 ⁢ x + a 1 ⁢ y + a 2 a 0 ⁢ y - a 1 ⁢ x + a 3 )	4
Affine	( x ′ y ′ ) = ( a 0 ⁢ x + a 1 ⁢ y + a 2 a 3 ⁢ x + a 4 ⁢ y + a 5 )	6
Bi-linear	( x ′ y ′ ) = ( a 0 ⁢ x ⁢ ⁢ y + a 1 ⁢ x + a 2 ⁢ y + a 3 a 4 ⁢ x ⁢ ⁢ y + a 5 ⁢ x + a 6 ⁢ y + a 7 )	8
Perspective	( x ′ y ′ ) = ( ( a 0 ⁢ x + a 1 ⁢ y + a 2 ) / ( a 6 ⁢ x + a 7 ⁢ y + 1 ) ( a 3 ⁢ x + a 4 ⁢ y + a 5 ) / ( a 6 ⁢ x + a 7 ⁢ y + 1 ) )	8
Pseudo- Perspective	( x ′ y ′ ) = ( a 0 ⁢ x i 2 + a 1 ⁢ x i ⁢ y i + a 2 ⁢ x i + a 3 ⁢ y i + a 4 a 1 ⁢ y i 2 + a 0 ⁢ x i ⁢ y i + a 5 ⁢ x i + a 6 ⁢ y i + a 7 )	8
Bi-quadratic	( x ′ y ′ ) = ( a 0 ⁢ x 2 + a 1 ⁢ y 2 + a 2 ⁢ xy + a 3 ⁢ x + a 4 ⁢ y + a 5 a 6 ⁢ x 2 + a 7 ⁢ y 2 + a 8 ⁢ xy + a 9 ⁢ x + a 10 ⁢ y + a 11 )	12

[0122] Global Motion Model Estimation Approaches:

[0123] Most common techniques used to estimate the desired model's parameters are based on the least squares fitting. Next describe several least squares based methods are described that are used to compute the parameters of a global motion model.

[0124] Global Motion Model—Least Square Estimation:

[0125] Least squares error fitting method is often used to estimate optimal motion model parameter values. It is a standard approach used to find solutions to over-determined systems (e.g., sets of equations with more equations than unknowns).

[0126] In global motion estimation a motion vector field is given, (MX₁, MY_i), i=0, . . . , N−1, where N is the number of motion vectors in the frame. According to the motion field, each position (x_i, y_i) corresponding to the center of the block i of the frame is moved to (x′_i, y′_i) as per motion vector (mx_i, my_i) as follows:
x′_i=x_i+MX_i
y′_i=y_i+MY_i

[0127] In a 4-parameter Translational motion model the goal is to approximate 4 parameters {a₀, a₁, a₂, a₃} so that the difference between observed data (x′_i, y′_i) and modeled data (a₀x_i+a₁, a₂y_i+a₃) is minimized. Least squares approach minimizes the following two squared errors with respect to parameters {a₀, a₁} and {a₂, a₃}:
SE_a0,a1=Σ_i=0^N-1(x′_i−(a₀x_i+a₁))²
SE_a2,a3=Σ_i=0^N-1(y′_i−(a₂y_i+a₃))²

[0128] Typically the number of parameters (4 in this example) is much smaller than the total number of vectors used for estimation, making it an over-determined system.

[0129] For linear global motion models (such as Translational, Pseudo-Affine and Affine, for example), the minimum of the sum of squares is found by taking the partial derivatives with respect to each parameter and setting it to zero. This results in the set of linear equations whose solution represents the global minimum in the squared error sense, e.g., the least squares error. The above equation for a 4-parameter affine motion model with respect to {a₀, a₁} is expanded as follows:

[0130] ${\mathrm{SE}}_{a_0{a}_1}={{\Sigma }_{i=0}^{N-1}\left(x_i^{\mathrm{\prime 2}}+a_0^2{x}_i^2+a_1^2-2a_0{x}_i{x}_i^{\prime }-2a_1{x}_i^{\prime }+2a_0{a}_1{x}_i\right)}^2=\sum _{i=0}^{N-1}{x}_i^{\mathrm{\prime 2}}+a_0^2\sum _{i=0}^{N-1}{x}_i^2+a_1^{2}N-2a_0\sum _{i=0}^{N-1}{x}_i{x}_i^{\prime }-2a_1\sum _{i=0}^{N-1}{x}_i^{\prime }+2a_0{a}_1\sum _{i=0}^{N-1}{x}_i$

[0131] Taking partial derivatives of the above equation yields the following system:

[0132] $\frac{\partial {\mathrm{SE}}_{a_0{a}_1}}{\partial a_0}=2a_0{\Sigma }_{i=0}^{N-1}{x}_i^2+2a_1{\Sigma }_{i=1}^{N-1}{x}_i-2{\Sigma }_{i=0}^{N-1}{x}_i{x}_i^{\prime }=0$ $\frac{\partial {\mathrm{SE}}_{a_0{a}_1}}{\partial a_1}=2a_0{\Sigma }_{i=0}^{N-1}{x}_i+2a_{1}N-2{\Sigma }_{i=0}^{N-1}{x}_i^{\prime }=0$

[0133] The system from above can be expressed as the following matrix equation which solution determines the two unknown parameters {a₀, a₁}:

[0134] $\left(\begin{array}{c}{a}_0\\ a_1\end{array}\right)={\left(\begin{array}{cc}{\Sigma }_{i=0}^{N-1}{x}_i^2& {\Sigma }_{i=0}^{N-1}{x}_i\\ {\Sigma }_{i=0}^{N-1}{x}_i& N\end{array}\right)}^{-1}\left(\begin{array}{c}{\Sigma }_{i=0}^{N-1}{x}_i{x}_i^{\prime }\\ {\Sigma }_{i=0}^{N-1}{x}_i^{\prime }\end{array}\right)$

[0135] Similarly, one is able to express the second set of parameters {a₂, a₃} as the solution to the following matrix equation:

[0136] $\left(\begin{array}{c}{a}_2\\ a_3\end{array}\right)={\left(\begin{array}{cc}{\Sigma }_{i=0}^{N-1}{y}_i^2& {\Sigma }_{i=0}^{N-1}{y}_i\\ {\Sigma }_{i=0}^{N-1}{y}_i& N\end{array}\right)}^{-1}\left(\begin{array}{c}{\Sigma }_{i=0}^{N-1}{y}_i{y}_i^{\prime }\\ {\Sigma }_{i=0}^{N-1}{y}_i^{\prime }\end{array}\right)$

[0137] If a determinant based solution to matrix inverse is used, the two matrix equations from above can be further expressed as:

[0138] $\left(\begin{array}{c}{a}_0\\ a_1\end{array}\right)=\frac{1}{N{\Sigma }_{i=0}^{N-1}{x}_i^2-{\left({\Sigma }_{i=0}^{N-1}{x}_i\right)}^2}\left(\begin{array}{cc}N& -{\Sigma }_{i=0}^{N-1}{x}_i\\ -{\Sigma }_{i=0}^{N-1}{x}_i& {\Sigma }_{i=0}^{N-1}{x}_i^2\end{array}\right)\left(\begin{array}{c}{\Sigma }_{i=0}^{N-1}{x}_i{x}_i^{\prime }\\ {\Sigma }_{i=0}^{N-1}{x}_i^{\prime }\end{array}\right);\mathrm{and}$ $\left(\begin{array}{c}{a}_2\\ a_3\end{array}\right)=\frac{1}{N{\Sigma }_{i=0}^{N-1}{y}_i^2-{\left({\Sigma }_{i=0}^{N-1}{y}_i\right)}^2}\left(\begin{array}{cc}N& -{\Sigma }_{i=0}^{N-1}{y}_i\\ -{\Sigma }_{i=0}^{N-1}{y}_i& {\Sigma }_{i=0}^{N-1}{y}_i^2\end{array}\right)\left(\begin{array}{c}{\Sigma }_{i=0}^{N-1}{y}_i{y}_i^{\prime }\\ {\Sigma }_{i=0}^{N-1}{y}_i^{\prime }\end{array}\right)$

[0139] Finally, the matrix equations yield the following least squares expressions for directly solving the unknown parameters of an affine 4-parameter global motion model:

[0140] $a_0=\frac{N{\Sigma }_{i=0}^{N-1}{x}_i{x}_i^{\prime }-{\Sigma }_{i=0}^{N-1}{x}_i{\Sigma }_{i=0}^{N-1}{x}_i^{\prime }}{N{\Sigma }_{i=0}^{N-1}{x}_i^2-{\left({\Sigma }_{i=0}^{N-1}{x}_i\right)}^2}$ $a_1=\frac{{\Sigma }_{i=0}^{N-1}{x}_i^2{\Sigma }_{i=0}^{N-1}{x}_i^{\prime }-{\Sigma }_{i=0}^{N-1}{x}_i{\Sigma }_{i=0}^{N-1}{x}_i{x}_i^{\prime }}{N{\Sigma }_{i=0}^{N-1}{x}_i^2-{\left({\Sigma }_{i=0}^{N-1}{x}_i\right)}^2}$ $a_2=\frac{N{\Sigma }_{i=0}^{N-1}{y}_i{y}_i^{\prime }-{\Sigma }_{i=0}^{N-1}{y}_i{\Sigma }_{i=0}^{N-1}{y}_i^{\prime }}{N{\Sigma }_{i=0}^{N-1}{y}_i^2-{\left({\Sigma }_{i=0}^{N-1}{y}_i\right)}^2}$ $a_3=\frac{{\Sigma }_{i=0}^{N-1}{y}_i^2{\Sigma }_{i=0}^{N-1}{y}_i^{\prime }-{\Sigma }_{i=0}^{N-1}{y}_i{\Sigma }_{i=0}^{N-1}{y}_i{y}_i^{\prime }}{N{\Sigma }_{i=0}^{N-1}{y}_i^2-{\left({\Sigma }_{i=0}^{N-1}{y}_i\right)}^2}$

[0141] Using the same procedure, least squares fitting equations for Pseudo-Affine 4-parameter and Affine 6-parameter global motion models can be determined. For non-linear global motion models, a non-linear least squares fitting method such as Levenberg-Marquardt algorithm (LMA for short) can be used. An overview of LMA is presented next.

[0142] Global Motion Model—Levenberg-Marquardt Least Squares Solution:

[0143] Levenberg-Marquardt algorithm is a well-established method for solving non-linear least squares problems. It was first published by Levenberg in 1944 and rediscovered by Marquardt in 1963. The LMA is an iterative procedure. To start a minimization, the user has to provide an initial guess for the parameters. Like many fitting algorithms, the LMA finds only a local minimum, which is not necessarily the global minimum. In case of multiple minima, the algorithm converges to the global minimum only if the initial guess is already somewhat close to the final solution. In the context of estimating global motion model parameters, setting the parameters to past values (e.g. previous frame(s)′ parameters) generally improves the performance.

[0144] The LMA interpolates between two different non-linear least squares solving methods: (1) the Gauss-Newton algorithm (GNA), and (2) gradient descent the method. The LMA is more robust than the GNA, in the sense that in many cases it finds a solution even if it starts very far off the final minimum. An analysis has shown that LMA is in fact GNA with a trust region, where the algorithm restricts the converging step size to the trust region size in each iteration in order to prevent stepping too far from the optimum.

[0145] Again, let (x′_i, y′_i), i=0, . . . , N−1, represent the observed data, e.g., the new positions of the center (x_i, y_i) of i-th block of a frame moved according to the block-based motion vector field. A model is referred to as separable if x′_i and y′_i model functions have exactly the same independent variables structure and parameter a_k is only used in computing either x′_i or y′_i but not both. Otherwise model is referred to as non-separable. Therefore, Affine, Bi-linear, and Bi-quadratic models are separable, while Translational, Pseudo-Affine, Perspective, and Pseudo-Perspective are non-separable.

[0146] Let β=(a₀, a₁, . . . , a_n−1) be the vector of parameters of an n-parameter model that is to be used to model the global motion. For a separable global motion model we first compute parameters β_x′=(a₀, . . . , a_(n/2)−1) and then we compute the remaining parameters β_y′=(a_n/2, . . . , a_n−1). On the other hand, for non-separable models we create 2N data points, and if i<N we use x′ model equation, while if N≤i<2N we use y′ model's equation. For simplicity of argument, we describe the LMA algorithm for global motion modeling by the 1^st part of separable parameters computation, e.g., computing the parameters associated with x′ model equation.

[0147] In each LMA iteration step, the parameter vector β is replaced by a new estimate β+δ. To determine the step vector δ, the functions ƒ(x_i, β+δ) are approximated by their linearizations as follows:

[0148] $f\left(x_i,\beta +\delta \right)\approx f\left(x_i,\beta \right)+J_i\delta$ $\mathrm{Where}$ $J_i=\frac{\partial f\left(x_i,\beta \right)}{\partial \beta }$

[0149] Then, the sum of square errors S(β+δ) is approximated as
S(β+δ)≈Σ_i=0^N-1(x′_i−ƒ(x_i,β)−J_iδ)²

[0150] The sum of squared errors function S is at its minimum at zero gradient with respect to β. Taking the derivative of S(β+δ) with respect to δ and setting the result to zero gives the following equality:
(J^TJ)δ=J^T(x′−ƒ(β))

[0151] Where J is the Jacobian matrix whose i-th row is J_i and ƒ and x′ are vectors whose i-th component is ƒ(x_i, β) and x′_i respectively. This defines a set of linear equations, whose solution is the unknown vector δ.

[0152] FIGS. 10A-10D are illustrative charts 1000, 1002, 1004, and 1006 of an example Levenberg-Marquardt Algorithm (LMA) curve fitting model for approximating global motion, arranged in accordance with at least some implementations of the present disclosure. In various implementations, LMA curve fitting model for approximating global motion: charts 1000 and 1002 show plots of motion vector field (x dimension) of global moving area of “Stefan” sequence (dots) and the Affine 6-parameter model fit (lines) computed using the LMA. On the other hand, charts 1004 and 1006 show Bi-quadratic 12-parameter model for “Stefan” computed via LMA. As it can be observed, the perspective and zoom effects in this scene require a higher order model than the 6-parameter linear Affine model.

[0153] Levenberg contributed to replace this equation by a “damped” variant which uses a non-negative parameter), to control the rate of reduction of error function S:
(J^TJ+λI)δ=x′−ƒ(β)

[0154] Smaller λ value brings the LMA closer to GNA, while larger value of λ brings it closer to gradient descent method. If either the length of the calculated step δ or the reduction of S from the latest parameter vector β+δ fall below predefined limits, the LMA iteration stops, and the last β is output as the solution.

[0155] Marquardt improved the final LMA equation in order to avoid slow convergence in the direction of small gradient. He replaced the identity matrix I with the diagonal matrix consisting of the diagonal elements of the matrix J^TJ, resulting in the final Levenberg-Marquardt algorithm equation:
(J^TJ+λdiag(J^TJ))δ=x′−ƒ(β)

[0156] Marquardt recommended an initial value of λ in a general case. However, for global motion modeling LMA, in some implementations herein, a method may instead be used where the initial parameter λ is set to the square root of the sum of the squared errors of the initial model parameters.

[0157] The LMA can be used to compute linear parameters as well. However, the empirical data shows that direct least square fitting estimate yields practically same SAD error when compared to the LMA, but with several key benefits: (1) computation of 4- and 6-parameter linear models can be done in one pass, and (2) while LMA gives more tuned coefficients, direct least square computation for linear models offers higher correlation of parameters from frame to frame, thus making the coding cost less expensive. Computing of non-linear models however is often best done with the LMA method. FIGS. 10A-10D show an example of the LMA estimation of 6- and 12-parameter global motion models.

[0158] Global Motion Model Parameters Coding Overview

[0159] Global motion parameters are typically computed as floating point numbers, and as such are not easily transmittable to the decoder. In MPEG-4 standard, coding of global motion parameters is proposed which uses so called “reference points” or “control grid points”. Motion vectors of reference points are transmitted as the global motion parameters. Motion vectors of the reference points are easier to encode, and at the decoder, the parameters are reconstructed from the decoded vectors. Since the vectors are quantized (e.g. to half-pel precision in MPEG-4), the method is lossy. However, reconstructed coefficients typically produce very similar global motion field and loss in quality is tolerable.

[0160] In MPEG-4, up to 4 reference points are used, which can support translational, affine and perspective models. The number of reference points that are needed to be sent to the decoder depends on the complexity of the motion model. When an 8-parameter model is used in MPEG-4 (e.g., as in a perspective model), then 4 points are needed to determine the unknown parameters by solving the linear system. For a 4-parameter model and 6-parameter models the number of needed reference points is reduced to 2 and 3 respectively.

[0161] The reference points are located at the corners of the bounding box. The bounding box can be the entire frame area or a smaller rectangular area inside the frame. The locations of these parameters are defined as follows:
z₀=(x₀,y₀)
z₁=(x₁,y₁)=(x₀+W,y₀)
z₂=(x₂,y₂)=(x₀,y₀+H)
z₃=(x₃,y₃)=(x₀+W,y₀+H)

[0162] Where (x₀, y₀) is the coordinate of the top left corner, W is the width and H is the height of the frame or the bounding box.

[0163] The estimated global motion model may be applied on the reference points resulting in the following motion vectors:
MX_i=x′_i−x_i
MY_i=y′_i−y_i

[0164] Where i=0, . . . , 3 and (x′_i, y′_i) may be computed using the global motion model equation. When the decoder receives the vectors (MX_i, MY_i) it may reconstruct the global motion parameters. If a 4-parameter model is used, the decoder receives two vectors (MX₀, MY₀) and (MX₃, MY₃) which correspond to reference points z₀ and z₃ respectively. For the case when global motion is defined over the entire frame, reference points are z₀=(0, 0) and z₃=(W, H) where W and H are the frame width and height. To reconstruct parameters a₀, . . . , a₃ of a translational global motion model, the following two systems are solved:

[0165] $\left(\begin{array}{c}{a}_0\\ a_1\end{array}\right)={\left(\begin{array}{cc}{x}_0& 1\\ x_3& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{x}_0+{\mathrm{MX}}_0\\ x_3+{\mathrm{MX}}_3\end{array}\right)={\left(\begin{array}{cc}0& 1\\ W& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{x}_0^{\prime }\\ x_3^{\prime }\end{array}\right)=\left(\begin{array}{cc}-\frac{1}{W}& \frac{1}{W}\\ 1& 0\end{array}\right)\left(\begin{array}{c}{x}_0^{\prime }\\ x_3^{\prime }\end{array}\right)$ $\left(\begin{array}{c}{a}_2\\ a_3\end{array}\right)={\left(\begin{array}{cc}{y}_0& 1\\ y_3& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{y}_0+{\mathrm{MY}}_0\\ y_3+{\mathrm{MY}}_3\end{array}\right)={\left(\begin{array}{cc}0& 1\\ H& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{y}_0^{\prime }\\ y_3^{\prime }\end{array}\right)=\left(\begin{array}{cc}-\frac{1}{H}& \frac{1}{H}\\ 1& 0\end{array}\right)\left(\begin{array}{c}{y}_0^{\prime }\\ y_3^{\prime }\end{array}\right)$

[0166] When a 6-parameter model is used, the decoder may receive three vectors (MX₀, MY₀), (MX₁, MY₁), and (MX₂, MY₂), which correspond to reference points z₀, and z₂ respectively. The reference points are z₀=(0, 0), z₁=(W, 0) and z₂=(0, H). Reconstructing parameters a₀, . . . , a₅ of an affine global motion model may be done by solving the following two systems:

[0167] $\left(\begin{array}{c}{a}_0\\ a_1\\ a_2\end{array}\right)={\left(\begin{array}{ccc}0& 0& 1\\ W& 0& 1\\ 0& H& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{x}_0+{\mathrm{MX}}_0\\ x_1+{\mathrm{MX}}_1\\ x_2+{\mathrm{MX}}_2\end{array}\right)=\left(\begin{array}{ccc}-\frac{1}{W}& \frac{1}{W}& 0\\ -\frac{1}{H}& 0& \frac{1}{H}\\ 1& 0& 0\end{array}\right)\left(\begin{array}{c}{x}_0^{\prime }\\ x_1^{\prime }\\ x_2^{\prime }\end{array}\right)$ $\left(\begin{array}{c}{a}_3\\ a_4\\ a_5\end{array}\right)={\left(\begin{array}{ccc}0& 0& 1\\ W& 0& 1\\ 0& H& 1\end{array}\right)}^{-1}\left(\begin{array}{c}{y}_0+{\mathrm{MY}}_0\\ y_1+{\mathrm{MY}}_1\\ y_2+{\mathrm{MY}}_2\end{array}\right)=\left(\begin{array}{ccc}-\frac{1}{W}& \frac{1}{W}& 0\\ -\frac{1}{H}& 0& \frac{1}{H}\\ 1& 0& 0\end{array}\right)\left(\begin{array}{c}{y}_0^{\prime }\\ y_1^{\prime }\\ y_2^{\prime }\end{array}\right)$

[0168] Similarly, other parameter models can be reconstructed by solving the linear system determined by the motion vectors of reference points.

[0169] For efficient representation, in MPEG-4 the motion vectors may be transmitted differentially. Suppose a 4-parameter model is used. Then, the motion vector (MX₀, MY₀) for grid point z₀ will be coded as is, while the motion vector for grid point z₃ will be coded differentially by using (MX₃−MX₀, MY₃−MY₀) [21]. The differentials are encoded using the exponential-Golomb code.

[0170] An exponential-Golomb code, or exp-Golomb code for short, is a type of universal code used to encode any non-negative integer. The following rule can be used to encode a non-negative integer n with exp-Golomb code: 1) represent n+1 in and write that number of zero bits preceding the previous bit string; 2) since motion vector differentials are not strictly non-negative integers, in MPEG-4 standard they are converted to non-negative binary digits; and 3) count the number of digits in binary representation of n+1, subtract one representation. The motion vector differential value m is represented as v_m as follows:

[0171] $v_m=\{\begin{array}{cc}2m-1& \mathrm{when}m>0,\\ -2m& \mathrm{when}m\le 0.\end{array}$

[0172] In Table 2 below, the first 11 exp-Golomb codes for integers (m) and non-negative integers (v_m) are illustrated.

[0173]

	TABLE 2
	m	vm	Exp-Golomb Code	Bit Length
	0	0	1	1
	1	1	010	3
	−1	2	011	3
	2	3	00100	5
	−2	4	00101	5
	3	5	00110	5
	−3	6	00111	5
	4	7	0001000	7
	−4	8	0001001	7
	5	9	0001010	7
	−5	10	0001011	7
	. . .	. . .	. . .	. . .

[0174] Table 2, above, shows the first few exp-Golomb codes. For example, if a motion vector (differential) in MPEG-4 to be coded is −1, the encoder may represent it with a 3-bit codeword “011”. This representation may be efficient since the probability of differentials is similar to the probability distribution represented by exp-Golomb coding.

[0175] Preprocessing

[0176] Detecting a scene change may be necessary in order to properly reset the algorithm parameters in some implementations. Generally speaking, any generic scene change detector can be used in this step; however, we use an advanced scene change detector (SCD), which reliably and efficiently performs scene change detection as the pre-processing stage. In scene change detection, each input frame at original pixel resolution is passed into the SCD algorithm, which computes a scene change flag scf. If the flag is on, the current frame is a part of the new scene and the buffer of past GMM parameters is initialized.

[0177] Motion Estimation

[0178] The proposed global motion modeling approach uses block-based motion vector field as a basis from which the model is computed. Although in general, any block-based motion estimator could be used to compute a motion vector field, one such estimator may be based on GPU graphics hardware-accelerated VME routines. Hardware-accelerated motion estimation approach allows for a significantly faster processing.

[0179] VME is a motion estimation routine which, relying on a graphics GPU, estimates motion vector field at one or more block accuracies. In some implementation described herein, VME may be used to obtain block-based motion vector fields at 16×16 and 8×8 levels. VME routine may use full search motion estimation method with a given search range. Unfortunately, the maximum VME search range is often limited and cannot handle very fast moving areas and/or larger distances between current and reference frames. Therefore, a multistage VME-based method may be used for block-based motion estimation in order to support larger search ranges. In particular, a 3-stage VME method may be used, which is described next.

[0180] A multistage VME may use subsampled frames in the previous stage in order to estimate the initial motion vectors for the current frame, e.g., the starting position of the VME motion search for each block. The subsampling factor may depend on the stage number as well as the frame resolution. In the first stage, the current and reference frames of low definition sequences are subsampled in each direction by 8. If a frame width is smaller than 600, frame height is smaller than 300, and the product of frame width and height is smaller than 180,000, then sequence is classified as the low definition sequence. On the other hand, the first stage for other (larger) resolutions may uses subsampling factor of 16 in each direction. Subsampling in 2^nd stage is by 4 in each direction for all resolutions. Finally, a 3^rd (final) stage VME may use full resolution frames and produces motion vector fields at 16×16 and 8×8 block accuracies. One such example of such a 3-stage VME algorithm may include the following steps:

• • [0181] 1. If H<300 and W<600 and W×H<180,000 then set ld=1; otherwise set ld=0.
  • [0182] 2. Given the current frame F and the reference frame F_ref, create subsampled luma frames SF′ and SF′_ref as the input to the 1^st stage VME. The subsampling is performed in each direction by 8 if ld=1 and by 16 if ld=0.
  • [0183] 3. Perform 1^st stage VME routine using SF′ and SF′_ref with search range set to 64×32.
  • [0184] 4. Filter and resize output of 1^st stage motion vector field to create input to 2^nd stage as follows:
    • [0185] a. Remove isolated noise-like motion vectors from the 16×16 and 8×8 output motion vector fields. For a given vector (mx_(j,i), my_(j,i)) at subsampled position (j, i) where w and h are subsampled motion vector field width and height (respectively), do:
      • [0186] i. If j>0 set d_L=abs(mx_(j,i)−mx_(j−1,i)+abs(my_(j,i)−my_(j−1,i); otherwise set d_L=∞.
      • [0187] ii. If i>0 set d_T=abs(mx_(j,i))−mx_(j,i−1))+abs(my_(j,i)−my_(j,i−1)); otherwise set d_T=∞.
      • [0188] iii. If j<w−1 set d_R=abs(mx_(j,i)−mx_(j+1,i))+abs(my_(j,i)−my_(j+1,i)); otherwise set d_R=∞.
      • [0189] iv. If i<h−1 set d_B=abs(mx_(j,i)−mx_(j,i+1))+abs(my_(j,i)−my_(j,i+1)); otherwise set d_B=∞.
      • [0190] v. Set d=min(d_L, d_T, d_R, d_B)
      • [0191] vi. If d>T (in our implementation T=16) then do the following:
        • [0192] 1. If d=d_L then replace (mx_(j,i), my_(j,i)) with (mx_(j−1,i), my_(j−1,i))
        • [0193] 2. Else If d=d_T replace (mx_(j,i), my_(j,i)) with (mx_(j,i−1), my_(j,i−1))
        • [0194] 3. Else If d=d_R replace (mx_(j,i), my_(j,i)) with (mx_(j,i+1), my_(j,i+1))
        • [0195] 4. Else If d=d_B replace (mx_(j,i), my_(j,i)) with (mx_(j,i+1), my_(j,i+1))
    • [0196] b. Merge 16×16 and 8×8 output motion vectors into merged 8×8 motion vector field: if SAD of a 16×16 block is up to 2% higher than sum of 4 collocated 8×8 blocks, then use repeat motion vector of a 16×16 block into the merged field; otherwise, otherwise copy 4 collocated motion vectors from 8×8 motion vector field. Note that here, for low definition sequences the resulting 8×8 block size in the subsampled resolution corresponds to 64×64 block size in the original full resolution, while in the other (higher) resolutions it corresponds to a 128×128 blocks in the original resolution.
    • [0197] c. Up-sample (resize) the merged motion vector field in each dimension by 2 for low definition and by 4 for other resolutions. Also for other resolutions, rescale motion vectors in the merged motion vector field by 2 (i.e., multiply each coordinate by 2).
  • [0198] 5. Use the resulting merged motion vector field as the input motion vectors for 2^nd stage VME
  • [0199] 6. Given the current frame F and the reference frame F_ref, create subsampled luma frames SF and SF_ref as the input to the 2^nd stage VME. The subsampling is performed in each direction by 4.
  • [0200] 7. Perform 2^nd stage VME routine using SF and SF_ref with search range set to 64×32.
  • [0201] 8. Filter and resize output of 2^nd stage motion vector field to create input to 3^rd stage as follows:
    • [0202] a. Remove isolated noise-like motion vectors from the 16×16 and 8×8 output motion vector fields. For a given vector (mx_(j,i), my_(j,i)) at subsampled position (j, i) where w and h are subsampled motion vector field width and height (respectively), using same algorithm as in 4.a.
    • [0203] b. Merge 16×16 and 8×8 output motion vectors into merged 8×8 motion vector field as in 4.b
    • [0204] c. Compute median merged motion vector field by applying 5×5 median filter to merged motion vector field
    • [0205] d. Compute block based SAD for both merged MVF and median merged MMF using the current luma frame SF and the reference luma frame SF_ref
    • [0206] e. Create final merged motion vector field by choosing either vector from merged MVF of from median merged MMF, depending on which one of the two has a smaller block SAD.
    • [0207] f. Up-sample (resize) the final merged motion vector field in each dimension by 4, and rescale motion vectors in the merged motion vector field by 2 (i.e., multiply each coordinate by 2).
  • [0208] 9. Use the resulting merged motion vector field as the input motion vectors for 3^rd stage VME
  • [0209] 10. Perform 3^rd stage VME routine using SF and SF_ref with search range set to 64×32.

[0210] The output of the 3-stage VME algorithm includes 16×16 and 8×8 block-based motion vector fields (e.g., where block size is relative to full frame resolution). Next how these vectors are filtered is described so that noisy matches during motion estimation stage are removed and replaced with more correct motion vectors in respect to the actual motion of the underlying visual objects in the scene.

[0211] Motion Vector Filtering

[0212] The motion estimation search often creates incorrect motion vector matches, referred to as outlier motion vectors. The outlier motion vectors are created because of the random matches during motion estimation phase and they do not correspond to the actual motion. Outliers occur either in flat areas or in blocks that contain edges/texture patterns that are prone to the aperture problem. The aperture problem refers to the fact that the motion of a visual object, which resembles a repeated 1-dimensional pattern (e.g. a bar or an edge) cannot be determined unambiguously when viewed through a small aperture (e.g. a block size window in block-based motion estimation). This is exactly what is happening during block-based motion estimation phase.

[0213] Incorrect motion vectors, even though they have small prediction error, can quite negatively affect global motion estimation phase. If several incorrect vectors are used to compute global motion the equation would be incorrect and thus global motion error would be large.

[0214] In order to cope with this problem, some implementations described herein are designed and implemented with a motion filtering method that reduces motion vector outliers and improves the motion vector field used for global motion estimation, as will be described in greater detail below.

[0215] FIG. 11 is an illustrative block diagram of an example local motion field noise reduction filter, arranged in accordance with at least some implementations of the present disclosure. In various implementations of local motion field noise reduction filter 106, an ld signal may be used to switch between filtering 8×8 block-based motion vectors at isolated motion vector refiner 1102 and filtering 16×16 block-based motion vectors at isolated motion vector refiner 1104. The signal value may be previously set to ld=1 if the sequence is a low-definition sequence, or to ld=0 otherwise. For low definition sequences, the input may be an 8×8 block-based motion vector field, which is then filtered in 2 steps: (1) by removing isolated motion vectors (e.g., motion vectors that are very different than its 4 direct neighbors) at isolated motion vector refiner 1102, and (2) by merging some 4 8×8 vectors into a single collocated 16×16 vector at 16×16 and 8×8 motion vectors merger 1106. For other resolutions the filtering is in performed in one step, simply by removing of the isolated motion vectors. The isolated motion vectors removal may be performed by comparing the sum of absolute differences (SAD) coordinate-wise between a motion vector and its top, left, right and bottom direct neighbors. If all 4 differences are larger than the similarity threshold (e.g., which in some implementations may be set to 16, for example) then the vector is replaced with the smallest sum of absolute differences (SAD) of a corresponding direct neighbor.

[0216] In case of low definition sequences, the merging step may be performed by computing the sum of SADs of the 4 8×8 vectors in the 8×8 field and comparing it to the SAD of the collocated 16×16 motion vector. If the SAD of the 16×16 vector is within a small percentage (e.g., 1%) of error from the sum of 4 collocated 8×8s, then the 4 8×8 vectors may be merged and replaced with the single 16×6 collocated vector. One example of such an algorithm may include the following steps:

• • [0217] 1. If H<300 and W<600 and W×H<180,000 then set ld=1; otherwise set ld=0.
  • [0218] 2. If ld=1 then do the following:
    • [0219] a. Remove isolated noise-like motion vectors from the 16×16 and 8×8 output motion vector fields. For a given vector (mx_(j,i), my_(j,i)) at subsampled position (j, i) where w and h are subsampled motion vector field width and height (respectively), do:
      • [0220] i. If j>0 set d_L=abs(mx_(j,i)−mx_(j−1,i))+abs(my_(j,i)−my_(j−1,i)); otherwise set d_L=∞.
      • [0221] ii. If i>0 set d_T=abs(mx_(j,i)−mx_(j,i−1))+abs(my_(j,i)−my_(j,i−1)); otherwise set d_T=∞.
      • [0222] iii. If j<w−1 set d_R=abs(mx_(j,i)−mx_(j+1,i))+abs(my_(j,i)−my_(j,i+1)); otherwise set d_R=∞.
      • [0223] iv. If i<h−1 set d_B=abs(mx_(j,i)−mx_(j,i+1))+abs(my_(j,i)−my_(j,i+1)); otherwise set d_B=∞.
      • [0224] v. Set d=min(d_L, d_T, d_B, d_B)
      • [0225] vi. If d>T (in our implementation T=16) then do the following:
        • [0226] 1. If d=d_L then replace (mx_(j,i), my_(j,i)) with (mx_(j−1,i), my_(j−1,i))
        • [0227] 2. Else If d=d_T replace (mx_(j,i), my_(j,i)) with (mx_(j,i−1), my_(j,i−1))
        • [0228] 3. Else If d=d_R replace (mx_(j,i), my_(j,i)) with (mx_(j+1,i), my_(j+1,i))
        • [0229] 4. Else If d=d_B replace (mx_(j,i), my_(j,i)) with (mx_(j+1,i), my_(j+1,i))
    • [0230] b. Merge 16×16 and 8×8 output motion vectors into merged 8×8 motion vector field: if SAD of a 16×16 block is up to 2% higher than sum of 4 collocated 8×8 blocks, then use repeat motion vector of a 16×16 block into the merged field; otherwise, otherwise copy 4 collocated motion vectors from 8×8 motion vector field. Note that here, for low definition sequences the resulting 8×8 block size in the subsampled resolution corresponds to 64×64 block size in the original full resolution, while in the other (higher) resolutions it corresponds to a 128×128 blocks in the original resolution.
    • [0231] c. Output merged 8×8 motion vector field to be used for computing the global motion model parameters
  • [0232] 3. Otherwise if ld=0 then do the following:
    • [0233] a. Remove isolated noise-like motion vectors from the 16×16 motion vector field. For a given vector (mx_(j,i), my_(j,i)) at subsampled position (j, i) where w and h are subsampled motion vector field width and height (respectively), do:
      • [0234] i. If j>0 set d_L=abs(mx_(j,i)−mx_(j−1,i))+abs(my_(j,i)−my_(j−1,i)); otherwise set d_L=∞.
      • [0235] ii. If i>0 set d_T=abs(mx_(j,i)−mx_(j,i−1))+abs(my_(j,i)−my_(j,i−1)); otherwise set d_T=∞.
      • [0236] iii. If j<w−1 set d_R=abs(mx_(j,i)−mx_(j+1,i))+abs(my_(j,i)−my_(j+1,i)); otherwise set d_R=∞.
      • [0237] iv. If i<h−1 set d_B=abs(mx_(j,i)−mx_(j,i+1))+abs(my_(j,i)−my_(j,i+1)); otherwise set d_B=∞.
      • [0238] v. Set d=min(d_L, d_T, d_B, d_B)
      • [0239] vi. If d>T (in our implementation T=16) then do the following:
        • [0240] 1. If d=d_L then replace (mx_(j,i), my_(j,i)) with (mx_(j−1,i), my_(j−1,i))
        • [0241] 2. Else If d=d_T replace (mx_(j,i), my_(j,i)) with (mx_(j−1,i), my_(j−1,i))
        • [0242] 3. Else If d=d_R replace (mx_(j,i), my_(j,i)) with (mx_(j+1,i), my_(j+1,i))
        • [0243] 4. Else If d=d_B replace (mx_(j,i), my_(j,i)) with (mx_(j+1,i), my_(j+1,i))
    • [0244] b. Output the filtered 16×16 motion vector field to be used for computing the global motion model parameters

[0245] Global Motion Model Generation

[0246] Several factors impact the quality of estimated global motion from the given motion vector field. For example, the number of parameters and the model type, the GMM computation method (least squares, LMA), or a sub-pixel filtering method, all affect the quality of GMM estimation. However, the most important factor may be the selection of motion vectors from which global motion model parameters are computed. In a typical video scene there are many blocks whose motion does not correspond to the globally moving area. Blocks whose motion corresponds to locally moving objects, blocks that contain incorrect motion estimate (e.g., due to aperture effect or insufficient search range), or blocks that belong to uncovered area (e.g., a new area which enters the scene and it is not present in the reference frames), are all examples of blocks that are not part of the global motion in the scene. If a significant number of such non-globally moving blocks are used in the GMM estimation process, the computed model is inaccurate and it causes a large SAD error. Unfortunately, determining which blocks are truly part of globally moving area and which blocks are not, is not an easy task.

[0247] Generally, past research proposals tackle this problem in two different ways. One group of approaches uses statistical methods to eliminate the outlier motion blocks. Methods that rely on Helmholtz principle are examples of this group. The second group of approaches uses some form of segmentation as a pre-processing operation in order to directly estimate foreground/background regions. Here, background region is assumed to be pertinent to globally moving area and corresponding blocks within the frame are selected and used for global motion estimation. All other blocks (i.e., foreground corresponding blocks) are eliminated from the computation. In one such example, a coarse k-means segmentation may be used to estimate background moving region from which a global motion is computed.

[0248] FIG. 12 is an illustrative block diagram of an example multiple global motion estimator and modeler 108, arranged in accordance with at least some implementations of the present disclosure. In various implementations, multiple global motion estimator and modeler 108 may include an initial affine global motion model computer 1202, a parameters buffer 1204, a motion vectors for GMM estimation selector 1206, an adaptive sub-pel interpolation filter selector 1208, and an adaptive global motion model computer and selector 1210.

[0249] FIG. 12 illustrates an example where the portion of the algorithm in which the final global motion model parameters for the frame are estimated. In the first step, the input motion vectors may be used to compute the initial affine 6-parameter model by random sampling via initial affine global motion model computer 1202. This step also uses parameters buffer 1204 of previous affine parameters to select the best affine model based on estimated error (e.g., subsampled frame SAD, which uses the current frame and the reference frame as input).

[0250] Once the initial affine model is computed, the next step is to select motion vectors to be used for final GMM parameters estimation via motion vectors for GMM estimation selector 1206. This step aims to remove the vectors belonging to the locally moving blocks as well as the remaining noisy vectors from the motion estimation phase. The pool of candidate masks may be computed and the best selection mask may be selected (e.g., based on the smallest subsampled SAD).

[0251] In the following step, the sub-pixel filtering method is selected from the 4 different filters via adaptive sub-pel interpolation filter selector 1208. For example, there may be several (e.g., 4) predefined filters in the systems described herein. In a 4 filter example the filters may include: (1) 1/16^th-pel smooth texture filter (bilinear), (2) 1/16^th-pel medium texture filter (bicubic), (3) ⅛^th-pel medium sharp texture filter (modified AVC filter), and (4) ⅛^th-pel sharp texture filter (modified HEVC filter). The best filter may be selected based on measured subsampled frame SAD.

[0252] Finally, given the previously computed selection mask, interpolation filter and the current and reference frames the last step is to adaptively choose the motion model to represent global motion in the current frame via adaptive global motion model computer and selector 1210. Depending on the value of the control signal mode, either standard or high-complexity models are used as candidates. If the value of the signal mode=0, the system may adaptively select one of the following models: (1) translational 4-parameter model, (2) affine 6-parameter model, and (3) pseudo-perspective 8-parameter model. On the other hand, if mode=1 the system may select between: (1) affine 6-parameter model, (2) pseudo-perspective 8-parameter model, and (3) bi-quadratic 12-parameter model.

[0253] In one such proposed GMM method, a hybrid type of approach may be used to select globally moving blocks. Such a scheme typically outperforms a method that solely relies on one type of approach. This is due to the fact that both types (groups) of approaches are highly stochastic in nature, and often one of them yields a more accurate estimate. A hybrid method helps ensure that the best type is selected for the given content. In the next two subsections some approaches are described for selecting globally moving blocks in detail.

[0254] Initial Global Motion Model Generation

[0255] In some implementations described herein, the first step in estimating global motion parameters may be to compute an initial affine 6-parameter global motion model by random sampling. An advantage of random sampling based global motion estimation is that it provides statistics from which a stable model can be deduced.

[0256] An affine global motion model may include 6 unknown parameters that are to be estimated, and therefore any 3 chosen motion vectors (MX₀, MY₀), (MX₁, MY₁) and (MX₂, MY₂) at positions (x₀, y₀), (x₁, y₁) and (x₂, y₂) from the motion vector field can be used to solve the system of equations for the parameters (provided they form the independent system) as follows:

[0257] $a_0=\frac{x_0^{\prime }\left(y_1-y_2\right)-x_1^{\prime }\left(y_0-y_2\right)+x_2^{\prime }\left(y_0-y_1\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$ $a_1=\frac{-x_0^{\prime }\left(x_1-x_2\right)+x_1^{\prime }\left(x_0-x_2\right)-x_2^{\prime }\left(x_0-x_1\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$ $a_2=\frac{x_0^{\prime }\left(x_1{y}_2-x_2{y}_1\right)-x_1^{\prime }\left(x_0{y}_2-x_2{y}_0\right)+x_2^{\prime }\left(x_0{y}_1-x_1{y}_0\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$ $a_3=\frac{y_0^{\prime }\left(y_1-y_2\right)-y_1^{\prime }\left(y_0-y_2\right)+y_2^{\prime }\left(y_0-y_1\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$ $a_4=\frac{-y_0^{\prime }\left(x_1-x_2\right)+y_1^{\prime }\left(x_0-x_2\right)-y_2^{\prime }\left(x_0-x_1\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$ $a_5=\frac{y_0^{\prime }\left(x_1{y}_2-x_2{y}_1\right)-y_1^{\prime }\left(x_0{y}_2-x_2{y}_0\right)+y_2^{\prime }\left(x_0{y}_1-x_1{y}_0\right)}{x_0{y}_1-x_0{y}_2-x_1{y}_0+x_1{y}_2+x_2{y}_0-x_2{y}_1}$

[0258] Where x′₁=x_i+MX_i and y′_i=y_i+MY_i for i={0,1,2}.

[0259] FIG. 13 is an illustrative block diagram of an example initial affine global motion model computer 1202, arranged in accordance with at least some implementations of the present disclosure. In various implementations, initial affine global motion model computer 1202 may include a range of parameters histogram initializer 1302, a randomly sampled MV (e.g., motion vector) based affine parameters histogram generator 1304, a histogram peak selector and peak to parameter converter 1306, an SAD based affine GMM Selector 1308, and a parameters buffer 1310.

[0260] In the illustrated example, FIG. 13 shows details of the initial affine global motion model computer 1202 of FIG. 12. As illustrated, initial affine global motion model computer 1202 may compute the initial affine 6-parameter model. In the illustrated example, first, the range histograms are initialized to all 0 counts via range of parameters histogram initializer 1302. Ranges of the histogram may be determined empirically as described previously.

[0261] Next, in one example implementation, for the given block-based motion vector field, three MVs (or another suitable number) may be chosen at random frm_sz times via randomly sampled MV (e.g., motion vector) based affine parameters histogram generator 1304. For each triple of randomly selected MVs, a 6-parameter motion model may be computed using least squares approach. Then, each of the 6 parameters may be mapped to a range in the corresponding histogram and histogram count in that range is increased.

[0262] After the histograms are collected, in one example implementation, the next step may be to analyze and select the highest histogram peaks via histogram peak selector and peak to parameter converter 1306. For each selected peak, a parameter value may be computed as the mid-point of the given range. This results in an estimated 6-parameter affine global motion model for the frame.

[0263] In the final step, in one example implementation, previous models (e.g., up to 2) stored via a parameters buffer 1310 may be tested along with the computed model in order to select the model which yields the smallest subsampled SAD via SAD based affine GMM Selector 1308.

[0264] The number of motion vectors from which random samples are taken depends on the video resolution. For example, for standard and high definition, the block size may be set to 8; while for low definition sequences, the block size may be set to 16. If a frame width is smaller than 600, frame height is smaller than 300, and the product of frame width and height is smaller than 180,000, then sequence may be classified as the low definition sequence and the motion vector field from which the samples are taken is an 8×8 motion vector field, for example. Otherwise, 16×16 based motion vector field may be used as a pool from which random motion vector samples are drawn.

[0265] The random sampling approach may use the equations above to solve for parameters a₀, . . . , a₅ by selecting three motion vectors at random. The parameters computed from selected vectors that form an independent system are referred to as local parameters. After a large sample of local parameters are collected, statistical properties of collected data may be used to estimate a stable set of global motion parameters. The final random sampling based estimated parameters may be referred to as the initial affine global motion model. An example algorithm for the initial affine global motion model computation is described below:

• • [0266] 1. Set N to a total number of motion vectors in the input motion vector field
  • [0267] 2. Initialize 6 histograms H₀, . . . , H₅ of a chosen size to 0. The histogram size, denoted here by S_H, determines how many bins are supported by each of the 6 histograms. More bins means more precision of estimating a parameter within the parameter range. However, too many bins would create a flat-looking histogram and determining the correct peak would be harder. In our implementation we set S_H=128.
  • [0268] 3. Select range of values for each parameter. We use the following ranges: a_0,4∈[0.95, 1.05), a_1,3∈[−0.1, 0,1), a₂∈[−64, 64), a₅∈[−48,48).
  • [0269] 4. For each parameter assign (in our case 128) equidistant sub-ranges within the selected range to a bin in the histogram. For example, for parameter a₀, a range [0.95,1.05) is subdivided to 128 bins (sub-ranges): [0.95,0.95078125), [0.95078125,0.9515625), . . . , [1.04921875,1.05).
  • [0270] 5. For i=0 to N do the following:
    • [0271] a. Pick 3 random positions and corresponding vectors in the motion vector field
    • [0272] b. Compute local affine 6-parameter model from 3 points/vectors
    • [0273] c. For each parameter determine the histogram bin whose sub-range the parameter value falls into
    • [0274] d. If a parameter value falls in a valid sub-range, increment histogram count at the index of that sub-range
  • [0275] 6. Detect 6 highest peaks in each of the 6 histograms and select corresponding sub-ranges.
  • [0276] 7. Set the initial affine global motion model candidate to the parameters corresponding to the mid-value of their peak sub-range. For example, if a peak in H₀ is at 2^nd position, then the peak sub-range for parameter a₀ is [0.95078125,0.9515625) and the parameter a₀=(0.95078125+0.9515625)/2=0.951171875.
  • [0277] 8. Add the previous two initial affine motion models to the candidate set (clearly, at the beginning of the scene nothing is added and after the first frame one model is added)
  • [0278] 9. If there is only 1 candidate, select it as the initial affine motion model for the current frame. Otherwise, if the number of candidates is more than 1 then:
    • [0279] a. Compute SAD measure of all candidates as follows. For each candidate:
      • [0280] i. Create reconstructed frame at pixel accuracy using global motion model candidate parameters
      • [0281] ii. Compute SAD between reconstructed frame pixels and current frame pixels
    • [0282] b. Select candidate with smallest SAD as the initial affine motion model for the current frame

[0283] FIG. 14 is an illustrative chart of an example histogram distribution 1400 of locally computed affine global motion model parameters, arranged in accordance with at least some implementations of the present disclosure. In various implementations, histogram distribution 1400 illustrates locally computed affine global motion model parameters using random sampling for the “City” sequence where current frame is frame #1 and reference frame is frame #0. In the illustrated example, chart (a) shows an H₀ histogram where peak is in position 64 which corresponds to sub-range [1.0,1.00078125) so that parameter a₀ is set to the mid-point 1.000390625, chart (b) shows an H₁ histogram where peak is in position 64 which corresponds to sub-range [0.0,0.0015625) so that parameter a₁ is set to the mid-point 0.00078125, chart (c) shows an H₂ histogram where peak is in position 66 which corresponds to sub-range [2.0,3.0) so that parameter a₂ is set to the mid-point 2.5, chart (d) shows an H₃ histogram where peak is in position 64 which corresponds to sub-range [0.0,0.0015625) so that parameter a₃ is set to the mid-point 0.00078125, chart (e) shows an H₄ histogram where peak is in position 64 which corresponds to sub-range [1.0,1.00078125) so that parameter a₄ is set to the mid-point 1.000390625, and chart (f) shows an H₅ histogram where peak is in position 64 which corresponds to sub-range [0.0,0.75) so that parameter a₅ is set to the mid-point 0.375.

[0284] FIG. 15 is an illustrative video sequence 1500 of an example of the difference between global and local block based vectors, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video sequence 1500 shows an example of the “City” sequence showing an initial affine global motion model from the previous figure, FIG. 14, where: frame (a) illustrates the current frame with an 8×8 block-based motion vector field shown with arrows, frame (b) illustrates the current frame with an 8×8 global motion vector field (also shown with arrows) derived from the computed initial affine global motion model, and frame (c) illustrates the difference heat map (e.g., darker shade indicate smaller differences between global and local block-based vectors, while lighter shade indicate larger differences).

[0285] FIG. 16 is an illustrative chart of an example histogram distribution 1600 of locally computed affine global motion model parameters using a random sampling approach, arranged in accordance with at least some implementations of the present disclosure. In various implementations, histogram distribution 1600 illustrates an example of histograms of locally computed affine global motion model parameters using random sampling approach for the “Stefan” sequence with current and reference frames being one frame apart. In the illustrated example, chart (a) shows an H₀ histogram where peak is in position 84 which corresponds to sub-range [1.015625,1.01640625) so that parameter a₀ is set to the mid-point 1.016015625, chart (b) shows an H₁ histogram where peak is in position 64 which corresponds to sub-range [0.0,0.0015625) so that parameter a₁ is set to the mid-point 0.00078125, chart (c) shows an H₂ histogram where peak is in position 35 which corresponds to sub-range [−29.0, −28.0) so that parameter a₂ is set to the mid-point −28.5, chart (d) shows an H₃ histogram where peak is in position 64 which corresponds to sub-range [0.0,0.0015625) so that parameter a₃ is set to the mid-point 0.00078125, chart (e) shows an H₄ histogram where peak is in position 79 which corresponds to sub-range [1.01171875,1.0125) so that parameter a₄ is set to the mid-point 1.012109375, and chart (f) an shows H₅ histogram where peak is in position 58 which corresponds to sub-range [−4.5, −3.75) so that parameter a₅ is set to the mid-point −4.125.

[0286] FIG. 17 is an illustrative video sequence 1700 of an example of the difference between global and local block based vectors, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video sequence 1700 illustrates an example of the “Stefan” sequence showing an initial affine global motion model from the previous figure, FIG. 16. In the illustrated example, frame (a) illustrates the current frame with an 8×8 block-based motion vector field (shown with arrows), frame (b) illustrates the current frame with an 8×8 global motion vector field (also shown with arrows) derived from the computed initial affine global motion model, and frame (c) the difference heat map (darker shade indicate smaller differences between global and local block-based vectors, while lighter shade indicate larger differences).

[0287] In some examples, the initial affine global motion model may be used to select motion vectors that may be used for global motion model estimation. The selection process may include generation of a number of candidate selection masks and choosing the selection mask that yields smallest error. The proposed selection method is described next.

[0288] Selection of Motion Vectors for Global Motion Model Estimation

[0289] In order to correctly estimate global motion from the given motion vector field, it may be vital to first select which motion vectors should be included as well as which ones should be excluded. This task is not easy due to imperfect motion vector fields and the difficulty of perfectly separating blocks into moving visual objects. To solve this problem, some implementations described herein may use a candidate set (e.g., a set of 8, although a different number could be used) possible block selection masks from which the final selection mask is chosen.

[0290] The initial affine global motion model may first used to generate several candidate selection masks (e.g., 5, although a different number could be used). The selection masks obtained from initial affine model are in essence binary masks, which classify all frame blocks into two classes: 1) globally moving blocks, and 2) locally moving blocks. Blocks whose global motion vector computed from the initial model is not similar to corresponding block-based motion vector are marked as local while the other blocks are marked as global. A binary mask may be used to indicate the motion vectors that are pertinent to global motion. An additional mask may be obtained by eroding the mask from the first level of hierarchy. Examples of the computed masks are shown in FIGS. 19 and 20. For each of the 5 masks, an affine global motion model may be computed using the described least squares fitting algorithm such that only the motion vectors indicated by the mask are used in least squares computation process. Finally, the mask that yield the smallest estimated error measure may be selected as current selection mask. If none of the hierarchical refinement models beats the initial model (e.g., in terms of smallest error), the selected model is set to the initial model.

[0291] Next, additional refinement steps (e.g., 2, although a different number could be used) may be performed on the current selected mask in attempt to create a more accurate selection mask. First, all blocks lying on a frame border may be removed as well as all blocks with very low texture activity. This alternate selection mask's error is compared to the error of the current selected mask and better mask is set as the current one. Finally, only the high texture blocks may be selected (e.g., blocks containing multiple edges, corners and complex patterns) from the current selection mask and final candidate mask is formed. Again, the final selection mask's error may be compared to the error of the current selected mask and better mask may be set as the final block selection mask, which defines blocks to be used for the global motion model computation. As a byproduct, this process produces an affine 6-parameter model for the frame.

[0292] FIG. 18 is an illustrative block diagram of an example motion vectors for GMM estimation selector 1206, arranged in accordance with at least some implementations of the present disclosure. In various implementations, motion vectors for GMM estimation selector 1206 may include an initial selection masks of MVs for GMM estimation generator 1802, a least squares affine GMM parameters computer 1804, a binary 2×2 kernel erosion operator 1806, a downsampled SAD residual computer 1808, a minimal SAD residual based candidate selector 1810, a selection mask medium to strong texture based refiner 1812, an affine GMM parameters computer 1814, a downsampled SAD residual computer 1816, a minimal SAD residual based candidate selector 1818, a selection mask blocks with strong corners based refiner 1822, an affine GMM parameters computer 1824, a downsampled SAD residual computer 1826, and a minimal SAD residual based candidate selector 1828.

[0293] As illustrated, shows a detailed block diagram of the second block of FIG. 12, motion vectors for GMM estimation selector 1206. FIG. 18 illustrates an example of the steps that may be used for computation of the selection mask, which may be used to identify which motion vectors are to be used in the global motion model estimation phase. In the first step of this process, the initial affine model is used to generate an estimated global motion field at the center of the block of the same size as the blocks of the block-based motion vector field via initial selection masks of MVs for GMM estimation generator 1802. Such global motion vector field is then differenced with the block-based field (e.g., by computing the sum of absolute differences for each vector coordinate). The differences are classified with 4 different adaptively chosen thresholds to obtain 4 candidate binary selection masks M_{1, . . . , 4}.

[0294] An additional mask M₀ may be computed by eroding mask M₁ with a 2×2 kernel via binary 2×2 kernel erosion operator 1806.

[0295] Next, 5 affine models are computed using the least squares fitting method according to the 5 binary selection masks (e.g., a vector is used in the fitting process if the mask value is 1; otherwise, it is skipped) via least squares affine GMM parameters computer 1804. This produces the initial 5 candidate models denoted by params_{0, . . . , 4}.

[0296] For each of them a subsampled SAD error may be computed using the current and the reference frames as input via downsampled SAD residual computer 1808, and the mask M′ is selected which corresponds to the minimal error via minimal SAD residual based candidate selector 1810.

[0297] After that, two more candidate masks may be generated. The first one, denoted M₅, may be obtained by refining M′ so that only medium and strong texture blocks are kept while flat texture blocks are removed via selection mask medium to strong texture based refiner 1812. In addition, frame borders may also be removed since most of the uncovered area appears there, which yields unreliable vectors. Similarly the corresponding affine model for M₅ and the corresponding subsampled SAD error may be computed via affine GMM parameters computer 1814. Then, either M₅ or M′ is chosen (and denoted by M″) via downsampled SAD residual computer 1816 and minimal SAD residual based candidate selector 1818.

[0298] The chosen M″ may be input to the 2^nd refinement step, which may produce the candidate selection mask M₆ by selecting only the high texture blocks (e.g., blocks with both Rs and Cs values high) from the input mask M″ via selection mask blocks with strong corners based refiner 1822. Using the same steps as before, the corresponding affine model may be computed for M₆ via affine GMM parameters computer 1824 and the corresponding subsampled SAD error, and, according to the smallest error, either M₆ or M″ may be chosen as the final selection mask via downsampled SAD residual computer 1826 and minimal SAD residual based candidate selector 1828.

[0299] In some implementations, the algorithm for selection of motion vectors for global motion model estimation may include the following steps:

• • [0300] 1. For i=1 to 4 do the following:
    • [0301] a. Set t=0
    • [0302] b. Set minimum local objects size m to a value that estimates how many global blocks should minimally be present in the mask. In our implementation m=0.1×N (10% of total number of blocks).
    • [0303] c. Compute global motion vector field {GMX_j, GMY_j}, j=0, . . . , N−1 using the initial affine global motion model
    • [0304] d. Set t=t+i
    • [0305] e. For each position j in the motion vector field compute e_j=abs(GMX_j−MX_j)+abs(GMY_j−MY_j). If e_j≤t then set mask M_i[j]=1; otherwise set M_i[j]=0
    • [0306] f. If sum of all values of M_i is less than m then repeat go back to step 1c
  • [0307] 2. Set mask M₀ to erosion of mask M₁
  • [0308] 3. For all 5 masks M₀, . . . , M₄ compute affine 6 parameter models using the described least squares fitting algorithm such that only the motion vectors indicated by the mask are used in least squares computation process
  • [0309] 4. Compute SAD measure for all 5 least square fit affine models and set l∈{0, . . . , 4} to the index of the model with the smallest SAD measure value. Set the current selection mask to mask M_l.
  • [0310] 5. Compare SAD measure of the selected l-th affine parameter model with the SAD measure of the initial affine global motion vector model and set the current best initial affine global motion model to the model that yields smaller SAD measure.
  • [0311] 6. If H<300 and W<600 and W×H<180,000 then set T=4; otherwise set T=6.
  • [0312] 7. Create additional candidate mask M₅ by refining the current selection mask as follows:
    • [0313] a. Remove all blocks that lie on the frame border
    • [0314] b. Remove all blocks whose minimum of Rs and Cs texture measures is smaller than the threshold T
  • [0315] 8. For mask M₅ compute affine 6 parameter model using the least squares fitting algorithm such that only the motion vectors indicated by the mask are used in least squares computation process
  • [0316] 9. Compute SAD measure the computed affine model for M₅
  • [0317] 10. Compare SAD measures of the current model and computed model for M₅ mask and set the current model and mask to the one that has the smallest SAD measure.
  • [0318] 11. Set thresholds T_RS to 1.5× average Rs value in the Rs/Cs 2-D array, and T_CS to 1.5× average Cs value in the Rs/Cs 2-D array
  • [0319] 12. Create final candidate selection mask M₆ by refining the current selection mask as follows:
    • [0320] a. Remove all blocks whose Rs texture measure is smaller than threshold T_RS and whose Cs texture measure is smaller than threshold T_CS
  • [0321] 13. For mask M₆ compute affine 6 parameter model using the least squares fitting algorithm such that only the motion vectors indicated by the mask are used in least squares computation process
  • [0322] 14. Compute SAD measure the computed affine model for M₆
  • [0323] 15. Compare SAD measures of the current model and computed model for M₆ mask and set the current model and mask to the one that has the smallest SAD measure. Output the current model and mask as the final selection mask to be used in the global motion model computation.

[0324] FIG. 19 is an illustrative video sequence of an example of different computed candidate selection masks 1900, arranged in accordance with at least some implementations of the present disclosure. In various implementations, this example of the computed candidate selection masks 1900 for the “Flower” sequence may include: frame (a) original YUV frame, candidate selection mask (b) M₀ eroded estimated mask in the 1^st level of hierarchy (M₀-based error measure=987505), candidate selection mask (c) M₁ estimated mask in the 1^st level of hierarchy (M₁-based error measure=970341), candidate selection mask (d) M₂ estimated mask in the 2^nd level of hierarchy (M₂-based error measure=1002673), candidate selection mask (e) M₃ estimated mask in the 3^rd level of hierarchy (M₃-based error measure=1373757), candidate selection mask (f) M₄ estimated mask in the 4^th level of hierarchy (M₄-based error measure=1417258), candidate selection mask (g) M₅ refined mask using best mask from the 5 hierarchical candidates (e.g., in this case the best candidate is M₁, e.g., the candidate with the smallest error measure) where flat blocks and frame border blocks are removed from the mask (M₅-based error measure=972156), and candidate selection mask (h) M₆ refined mask using the best mask from the previous 6 candidates (e.g., in this case it is still mask M₁) where only high texture blocks (e.g., such as blocks containing multiple edges, corners and complex patterns) are selected (M₆-based error measure=981807). In this example, the final candidate selection mask is set to M₁.

[0325] FIG. 20 is an illustrative video sequence of an example of different computed candidate selection masks 2000, arranged in accordance with at least some implementations of the present disclosure. In various implementations, this example of the computed candidate selection masks 2000 for the “Stefan” sequence may include: frame (a) original YUV frame, candidate selection mask (b) M₀ eroded estimated mask in the 1^st level of hierarchy (M₀-based error measure=1365848), candidate selection mask (c) M₁ estimated mask in the 1^st level of hierarchy (M₁-based error measure=1363467), candidate selection mask (d) M₂ estimated mask in the 2^nd level of hierarchy (M₂-based error measure=1318886), candidate selection mask (e) M₃ estimated mask in the 3^rd level of hierarchy (M₃-based error measure=1327907), candidate selection mask (f) M₄ estimated mask in the 4^th level of hierarchy (M₄-based error measure=1349339), candidate selection mask (g) M₅ refined mask using best mask from the 5 hierarchical candidates (in this case the best candidate is M₂, e.g., candidate with the smallest error measure) where flat blocks and frame border blocks are removed from the mask (M₅-based error measure=1313352), and candidate selection mask (h) M₆ refined mask using the best mask from the previous 6 candidates (in this case it is mask M₅) where only high texture blocks (e.g., such as blocks containing multiple edges, corners and complex patterns) are selected (M₆-based error measure=1348624). In this example, the final candidate selection mask is set to M₅.

[0326] Adaptive Sub-Pel Filter Selection

[0327] Once the initial affine global motion parameters are refined, the next stage may be to select optimal sub-pixel filtering used in global motion compensation phase. In some implementations described herein, one of several different sub-pixel filtering methods (e.g., 4, although a different number may be used) may be selected. Table 3 lists the 4 filters used in one such implementation.

[0328]

TABLE 3
Sub-pixel filters used in global motion compensation
	# of
Filter	Taps	Accuracy	Typically Suited For
Bilinear filter for all 1/16 pel	2	1/16	pel	Blurry texture
positions
Bicubic filter for all 1/16 pel	16	1/16	pel	Blurry and normal
positions				texture
AVC-based filter
[1 −5 20 20 −5 1] for ½ pel	6	⅛	pel	Normal and sharp
and ¼ pel positions				texture
Bilinear for ⅛ pel positions	2
HEVC-based filter
[−1 4 −11 40 40 −11 4 −1] for	8	⅛	pel	Sharp texture
½ pel
[−1 4 −10 58 17 −5 1 0] and	8
[0 1 −5 17 58 −10 4 −1] for	8
¼ pel positions
[0 −1 9 9 −1 0] for ⅛ pel	6
positions

[0329] The optimal filter for the given frame may be content dependent. Typically, sharper luma content may be better filtered via HEVC-based filters and AVC-based filters. For example, HEVC-based filter usually may work better on content with very sharp texture. On the other hand, more blurry textured luma frames may be better filtered with Bicubic and Bilinear filters, where Bicubic filters likely work better in interpolating medium textured scenes. Clearly, the best-suited filter yields the smallest SAD of the reconstructed frame in comparison to the current frame. In order to select the most optimal filter for the given frame, in the interest of speed, a simplified, sub-sampled SAD (SSAD) measure may be computed. The method for automatically selecting an optimal filter is described next.

[0330] FIG. 21 is an illustrative block diagram of an example adaptive sub-pel interpolation filter selector 1208, arranged in accordance with at least some implementations of the present disclosure. In various implementations, adaptive sub-pel interpolation filter selector 1208 may include a frame downsampler 2102, a GMM based prediction downsampled frame generator 2104, a soft (Bilinear) filter coefficient 2106, a GMM based prediction downsampled frame generator 2108, a medium (BiCubic) filter coefficient 2110, a GMM based prediction downsampled frame generator 2112, a medium (AVC based) filter coefficient 2114, a GMM based prediction downsampled frame generator 2116, a sharp (HEVC based) filter coefficient 2118, a frame downsampler 2120, an SAD residual computer 2122, an SAD residual computer 2124, an SAD residual computer 2126, an SAD residual computer 2128, and a minimal SAD based selector 2130.

[0331] The illustrated example shows a detailed view of the third block of FIG. 12, adaptive sub-pel interpolation filter selector 1208. In FIG. 21, adaptive sub-pel interpolation filter selector 1208 serves to adaptively select the adequate sub-pixel filter according to the video content. In the example adaptive sub-pel interpolation filter selector 1208 illustrated in FIG. 21, there are 4 predefined filters (although a different number could be used): (1) 1/16^th-pel smooth texture filter (bilinear), (2) 1/16^th-pel medium texture filter (bicubic), (3) ⅛^th-pel medium sharp texture filter (modified AVC filter), and (4) ⅛^th-pel sharp texture filter (modified HEVC filter). The initial affine global motion model computed previously is used to move all pixels in the reference frame according to the model and all four filter candidates.

[0332] The reference frame F_ref may be subsampled to generate a subsampled reference frame SF_ref via frame downsampler 2102. Similarly, the current frame F may be subsampled to generate a subsampled current frame SF via frame downsampler 2120.

[0333] For each pixel in the subsampled reference frame SF_ref the resulting motion vectors are rounded to either 1/16^th-pel or ⅛^th-pel accuracy (depending on the filter candidate) via GMM based prediction downsampled frame generators 2104, 2108, 2112, and 2116. This results in four prediction frames denoted by PSF_S (which is computed by using the smooth sub-pel filter candidate via soft (Bilinear) filter coefficient 2106), PSF_M (result of using the medium sub-pel filter candidate via medium (BiCubic) filter coefficient 2110), PSF_MSh (result of using the medium sharp sub-pel filter candidate via medium (AVC based) filter coefficient 2114) and PSF_Sh (result of using the sharp sub-pel filter candidate sharp (HEVC based) filter coefficient 2118). Next, subsampled SAD error is computed for all 4 candidates via SAD residual computers 2122, 2124, 2126, and 2128 and the minimal SAD criterion may be used to select the final candidate sub-pel filter filt via minimal SAD based selector 2130. In addition, two control signals ƒ_hi and h, are set as follows: ƒ_hi=0 and ƒ_lo=0 if the soft sub-pel filter was selected, ƒ_hi=0 and ƒ_lo=1 if medium sub-pel filter was selected, ƒ_hi=1 and ƒ_lo=0 if medium sharp sub-pel filer was selected, and ƒ_hi=1 and ƒ_lo=1 if sharp sub-pel filter was selected.

[0334] An example algorithm for automatically selecting optimal sub-pixel filtering may include the following steps:

• • [0335] 1. Set SSAD_i=0, i=0, . . . , 3.
  • [0336] 2. For each filter flt_i, i=0, . . . , 3, do the following:
    • [0337] a. For each N×N block in the reference frame:
      • [0338] i. Take the pixel in the center of the frame, compute motion vector according to the computed initial affine global motion model.
      • [0339] ii. Round the computed vector either to ⅛^th or 1/16^th pixel accuracy depending on the filter flt_i (corresponding filter accuracy shown in Table 3).
      • [0340] iii. Compute interpolated sub-pixel value corresponding to the computed motion vector using flt_i filter.
      • [0341] iv. Compute absolute difference between the current block's center pixel in the current frame and the computed interpolated sub-pixel value and increase SSAD_i by that amount.
  • [0342] 3. Select filter flt_i for which SSAD_i is the smallest.

[0343] FIG. 22 is an illustrative video sequence 2200 of an example of adaptive content dependent sub-pel filtering, arranged in accordance with at least some implementations of the present disclosure. In various implementations, video sequence 2200 illustrates an example of content dependent sub-pixel filtering where: frame (a) illustrates a blurry luma frame of “Football” sequence using a bilinear filter as an optimal sub-pel filter (e.g., SAD with bilinear filter is 984309, SAD with bicubic filter is 994009, SAD with AVC-based filter is 996384, and SAD with HEVC-based filter is 998296), and frame (b) illustrates a sharp texture luma frame of “City” sequence using an HEVC-based filter as an optimal sub-pel filter (e.g., SAD with bilinear filter is 444644, SAD with bicubic filter is 439190, SAD with AVC-based filter is 432654, and SAD with HEVC-based filter is 428042).

[0344] In some implementations described herein, an N×N block size may be set to 16×16, however smaller sizes could be used depending on the quality/speed tradeoff adequate for the given application.

[0345] Adaptive Global Motion Model Computation and Selection

[0346] Depending on the mode of operation, in this step the algorithm may select optimal complexity global motion model. There are may be several modes of operation (e.g., 2 modes, although the number could vary) defined in some implementations described herein. In one such example, the modes may include:

• • [0347] 1. Mode 0 (default mode)—is a mode that may be designed for sequences with normal motion complexity. Mode 0 may adaptively switch on a frame basis between translational 4-parameter, affine 6-parameter, and pseudo-perspective 8-parameter global motion models, for example.
  • [0348] 2. Mode 1—is a mode that may be designed for sequences with complex motion (such as sequences with high perspective depth, fast motion etc.). Mode 1 may adaptively switch on a frame basis between affine 6-parameter, pseudo-perspective 8-parameter, and bi-quadratic 12-parameter global motion models, for example.

[0349] For typical applications, the adaptive translational 4-parameter, affine 6-parameter, and pseudo-perspective 8-parameter mode (e.g., Mode 0) may be used. Therefore, it Mode 0 may be set as a default mode of operation in some implementations described herein.

[0350] FIG. 23 is an illustrative block diagram of an example adaptive GMM computer and selector 1210, arranged in accordance with at least some implementations of the present disclosure. In various implementations, adaptive GMM computer and selector 1210 may include a least squares translational 4 parameter GMM computer 2302, a GMM based prediction frame generator 2304, an SAD residual computer 2306, a least squares affine 6 parameter GMM computer 2312, a GMM based prediction frame generator 2314, an SAD residual computer 2316, an LMA (Levenberg-Marquardt algorithm) based pseudo perspective 8 parameter GMM computer 2322, a GMM based prediction frame generator 2324, an SAD residual computer 2326, an LMA (Levenberg-Marquardt algorithm) based BiQuadratic 12 parameter GMM computer 2332, a GMM based prediction frame generator 2334, an SAD residual computer 2336, and a minimal SAD parameter index (parindx) calculator and parameter index (parindx) based GMM selector.

[0351] In the illustrated example, FIG. 23 shows a detailed view of the fourth block of FIG. 12, adaptive GMM computer and selector 1210. In FIG. 23, the final global motion model is generated via adaptive GMM computer and selector 1210. A control signal mode may be used to select between standard and high-complexity models. While the illustrated example shows 4 total models with 3 models being used in a first mode and 3 models being used in a second mode, it will be appreciated that a different number of modes may be use, a different number of total models may be used, an/or a different number of models per mode may be used.

[0352] In the illustrated example, the control signal mode may be used to select between standard and high-complexity models as follows: if mode=0, adaptive GMM computer and selector 1210 may adaptively selects one of the following models: (1) translational 4-parameter model, (2) affine 6-parameter model, and (3) pseudo-perspective 8-parameter model. Otherwise, if mode=1 adaptive GMM computer and selector 1210 may select between: (1) affine 6-parameter model, (2) pseudo-perspective 8-parameter model, and (3) bi-quadratic 12-parameter model.

[0353] In either case, 3 of the 4 models may be computed using the motion vector selection mask M and the corresponding model computation method (e.g., least squares fitting for 4-parameter models and 6-parameter models, and Levenberg-Marquardt algorithm (LMA) for 8-parameter models and 12-parameter models). For example, 3 of the 4 models may be computed using the motion vector selection mask M and the corresponding model computation method via corresponding least squares translational 4 parameter GMM computer 2302, least squares affine 6 parameter GMM computer 2312, LMA (Levenberg-Marquardt algorithm) based pseudo perspective 8 parameter GMM computer 2322, and LMA (Levenberg-Marquardt algorithm) based BiQuadratic 12 parameter GMM computer 2332.

[0354] For the 3 computed models, using the previously selected sub-pixel filtering method filt and the reference frame F_ref the corresponding prediction frames may be generated via corresponding GMM based prediction frame generators 2304, 2314, 2324, and/or 2334.

[0355] Furthermore, the frame-based SAD error may be computed for the 3 prediction frames in respect to the current frame F via SAD residual computers 2306, 2316, 2326, and/or 2336.

[0356] Finally, SAD errors are weighted and compared so that the smallest weighted SAD is used to select the corresponding model via minimal SAD parameter index (parindx) calculator and parameter index (parindx) based GMM selector.

[0357] In Mode 0, the affine 6-parameter model may be set to the initial affine global motion model computed in the refinement step (e.g., the previous step). The transitional 4-parameter motion model may be computed using direct least squares fitting approach described above. It is important to note that the selected global/local binary mask computed in the refinement step may be used to filter only motion vectors pertinent to global motion. The least squares fitting may be done on motion vectors from the motion vector field whose corresponding value in the global/local binary mask is 1. Next, the pseudo-perspective 8-parameter model may be computed using Levenberg-Marquardt (LMA) algorithm for non-linear least squares fitting. Likewise, the new parameter set (8-parameter model) may be computed using only motion vectors from the motion vector field whose corresponding value in the global/local binary mask from the previous step is 1. Once the parameters for all models are available, SAD measure for 4-, 6-, and 8-parameter models may be computed, denoted by SAD_4p, SAD_6p and SAD_8p, respectively. The SAD measure may be the sum of absolute differences between the current luma frame, and reconstructed luma frame. The reconstructed frame may be obtained by applying global motion equations on all pixels in the reference frame. In this process, either a ⅛^th or a 1/16^th pixel precision may be used, depending on the sub-pel filter chosen.

[0358] The quality control parameter in Mode 0, denoted by δ₀, may be computed as follows:
δ₀=0.01×min(SAD_4p,SAD_6p,SAD_8p)

[0359] The selection of final parameter model may be done as follows:

[0360] If SAD_6p<SAD₈+δ₀ and SAD_4p<SAD_6p+δ₀ then select translational 4-parameter model to model global motion in the current frame;

[0361] If SAD_6p<SAD_8p+δ₀ and SAD_4p≥SAD_6p+δ₀ then select affine 6-parameter model to model global motion in the current frame;

[0362] If SAD_6p≥SAD_8p+δ₀ and SAD_4p<SAD_6p+δ₀ then select translational 4-parameter model to model global motion in the current frame; and

[0363] If SAD_6p≥SAD_8p+δ₀ and SAD_4p≥SAD_6p+δ₀ then select pseudo-perspective 8-parameter model to model global motion in the current frame.

[0364] In Mode 1, the affine 6-parameter model may also be set to the initial affine global motion model computed in the refinement step. The pseudo-perspective 8-parameter model and bi-quadratic 12-parameter model may be computed using Levenberg-Marquardt (LMA) algorithm for non-linear least squares fitting. These parameter sets may be computed using only motion vectors from the motion vector field whose corresponding value in the global/local binary mask from the previous step is 1. Once the parameters for all models are available, SAD measure for 6-, 8-, and 12-parameter models may be computed, denoted by SAD_6p, SAD_8p and SAD₁₂, respectively. The SAD measure may be the sum of absolute differences between the current luma frame, and reconstructed luma frame. The reconstructed frame may be obtained by applying global motion equations on all pixels in the reference frame. In this process, either a ⅛^th or a 1/16^th pixel precision is used, depending on the sub-pel filter chosen.

[0365] The quality control parameter in Mode 1, denoted by δ₁, may be computed as follows:
δ₁=0.01×min(SAD_6p,SAD_8p,SAD_12p)

[0366] The selection of final parameter model may be done as follows:

[0367] If SAD_8p<SAD_12p+δ₁ and SAD_6p<SAD_8p+δ₁ then select translational 4-parameter model to model global motion in the current frame;

[0368] If SAD_8p<SAD_12p+δ₁ and SAD_6p≥SAD_8p+δ₁ then select affine 6-parameter model to model global motion in the current frame;

[0369] If SAD_8p≥SAD_12p+δ₁ and SAD_6p<SAD_8p+δ₁ then select translational 4-parameter model to model global motion in the current frame; and

[0370] If SAD_8p≥SAD_12p+δ₁ and SAD_6p≥SAD_8p+δ₁ then select pseudo-perspective 8-parameter model to model global motion in the current frame.

[0371] Impact of Non-Active Area on Global Motion Estimation

[0372] Video can often contain a non-active content area, which can cause problems when computing or applying global motion. Such non-content areas may include: black bars and areas due to letterboxing, pillar-boxing, circular or cropped circular fisheye cameras capture, etc. Detecting and excluding such area may greatly improve the GMM results.

[0373] FIG. 24 is an illustrative video sequence 2400 of an example of compensation of detected non-content areas, arranged in accordance with at least some implementations of the present disclosure. In various implementations, FIG. 24 shows an example video sequence 2400 where black bars are detected and removed from GMM and the resulting impact on the quality. The algorithm for letterboxing and pillar-boxing area detection and removal from GMM is described next:

• • [0374] 1. For all pixels in F that are at the left edge of the frame do:
    • [0375] a. Scan current luma frame F_y from left towards right and break at break position when RsCs(F_y) is larger than threshold T_bar (which is in our implementation set to 240) or if the pixel value of F_y exceeds black bar threshold T_blk (we use T_blk=20);
  • [0376] 2. Determine the dominant break position of the left frame edge, denoted L_brp as the multiple of 4 pels that is closest to the majority of left edge break positions;
  • [0377] 3. If L_brp is larger than 4 pels, smaller than ⅓ of W (the frame width) and 90% or more left edge break positions are within 4 pixel distance of L_brp, then declare non-content area at left edge that spans to L_brp pixels wide; and
  • [0378] 4. Repeat steps 1-3 for right edge, top, edge, and bottom edge to detect non-content area at remaining sides of the frame.

[0379] In the example illustrated in FIG. 24, shows video sequence 2400, based on the “Stefan” sequence, there are 4 pixel thick bars detected on top and on right frame edge, while in another scene (“Football” sequence) there is one 8 pel bar detected on the right side. The non-content area is then excluded from GMM compensation and zero motion is applied. Remaining area is normally modeled with GMM, as FIG. 24 depicts.

[0380] For example, the “Stefan” video sequence 2400 shows compensation of detected non-content area (e.g., 2 bars, top and right, both 4 pixel thick are detected and coded, [0,0] motion is used at bar area) where: frame (a) is the current original luma frame, frame (b) is the reference luma frame (1 frame apart), frame (c) is the reconstructed frame without bar detection, frame (d) is the residuals frame without bar detection (SAD=1087071), frame (e) is the reconstructed frame with bar detection, and frame (f) is the residuals frame without bar detection (SAD=933913).

[0381] Global Motion Model Based Accurate Motion Compensation

[0382] At the beginning of the global motion compensation phase, a model was selected (e.g., depending on the mode of operation, either with 4, 6, 8, or 12 parameters), as well as a sub-pixel filtering method. Although the global motion compensation processes blocks of frame at a time, GMM may be applied on a pixel level within the given block. In other words, for each pixel within a block, a global motion may be computed and the pixel may be moved at a sub-pel position according to the previously determined sub-pel filtering method. Thus, a pixel on one side of the block may have different motion vector than a pixel on the other side of the same block, as illustrated by an example in FIG. 25 below.

[0383] FIG. 25 is an illustrative chart of an example of translational 4-parameter global motion model 2500, arranged in accordance with at least some implementations of the present disclosure. In various implementations, an example of a translational 4-parameter model 2500 may be applied on different pixel positions within an 8×8 block. Note that different global motion vectors could appear within a block.

[0384] In the illustrated example, the chosen block size depends on the resolution. In one example, for standard and high definition, the block size may be set to 8; while, for low definition sequences the block size may be set to 16. If a frame width is smaller than 600, frame height is smaller than 300, and the product of frame width and height is smaller than 180,000, then sequence may classified as a low definition sequence, although different numbers may be used.

[0385] FIG. 26 is an illustrative block diagram of an example adaptive global motion compensator 110, arranged in accordance with at least some implementations of the present disclosure. In various implementations, adaptive global motion compensator 110 may include a GMM parameters to reference points MVs converter 2602, a reference points MVs to GMM parameters reconstructor 2604, a global motion model based prediction frame generator 2606, a soft (Bilinear) filter coefficient 2608, a medium (BiCubic) filter coefficient 2610, a medium sharp (AVC based) filter coefficient 2612, a sharp (HEVC based) filter coefficient 2614, and an SAD residual computer 2616.

[0386] In the illustrated example, FIG. 26 shows the details of adaptive global motion compensator 110 (originally discussed in FIG. 1) that may produce the final predicted frame and the corresponding SAD. The input into the first block of this method may be the final global motion model parameters, which are applied to the frame-based reference points via GMM parameters to reference points MVs converter 2602. As previously described in detail, the number of reference points depends on the model. An n-parameter model uses n/2 reference points. Therefore, an n/2 motion vectors corresponding to the motion at the reference points may be computed in the first step. The computed motion vectors may be quantized to a ¼-pel accuracy.

[0387] Next, from the reference points, the reconstructed parameters may be generated via reference points MVs to GMM parameters reconstructor 2604. The reconstructed parameters may be obtained by solving the system of equations for the motion vectors at the reference points. Also, the reconstructed parameters may be represented as a quotient where the denominator is scaled to a power of 2. This means that the parameters can be applied with just multiplication and binary shifting operations in the interest of speed.

[0388] After that, the prediction frame P may generated by applying the reconstructed motion model parameters to the pixels of the reference frame F_ref where sub-pixel positions are interpolated via global motion model based prediction frame generator 2606 with the previously chosen filter filt via filters 2608, 2610, 2612, and/or 2614. In this diagram selected filter may be redirected to global motion model based prediction frame generator 2606 using the control signals ƒ_hi and ƒ_lo. Finally, the corresponding frame-based SAD may be computed from the predicted frame P and the current frame F via SAD residual computer 2616.

[0389] Since it is not feasible to encode the actual floating point representation of the global motion model parameters, an approximation of the parameters is performed. The method of representing the GMM parameters is based on the concept of reference points (also referred to as control grid points), which were described above. According to that representation, an n-parameter GMM model requires n/2 reference points. At each reference point a motion vector may need to be sent in order to reconstruct the parameters at the decoder side. The accuracy of the encoded motion vectors at reference points determines the GMM parameter approximation accuracy. In some implementations herein, the accuracy may be set to a ¼-pel precision.

[0390] The locations of the reference points are defined as follows:
z₀=(x₀,y₀)
z₁=(x₁,y₁)=(x₀+W,y₀)
z₂=(x₂,y₂)=(x₀,y₀+H)
z₃=(x₃,y₃)=(x₀+W,y₀+H)
z₄=(x₄,y₄)=(x₀−W,y₀)
z₅=(x₅,y₅)=(x₀,y₀−H)

[0391] For 4-parameter model, points z₀ and z₃ are used. Applying translational global motion model g₄ on z₀ and z₃ yields globally moved points g₄(z₀)=(g₄(x₀), g₄(y₀))=(a₀x₀+a₁, a₂y₀+a₃), and g₄(z₃)=(a₀x₃+a₁, a₂y₃+a₃). On the other hand, for 6-parameter model points z₀, z₁, and z₂ are used. Applying affine global motion model g₆ on z₀, z₁, and z₂ yields globally moved points g₆(z_i)=(g₆(x_i), g₆(y_i))=(a₀x_i+a₁y_i+a₂, a₃x_i+a₄y_i+a₅), i=0, 1, 2. For 8-parameter model points z₀, z₁, z₂, and z₃ are used. Applying pseudo-perspective global motion model g₈ on z₀, z₁, z₂ and z₃ yields globally moved points g₈(z_i)=(g₈(x_i), g₈(y_i))=(a₀x_i²+a₁x_iy_i+a₂x_i+a₃y_i+a₄, a₁y_i²+a₀x_iy_i+a₅x_i+a₆y_i+a₇), i=0, 1, 2, 3. Finally, for a 12-parameter model all 6 points are used (z₀, z₁, z₂, z₃, z₄ and z₅). Applying 12-parameter bi-quadratic global motion model g₁₂ on z₀, z₁, z₂, z₃, z₄ and z₅ yields globally moved points g₁₂ (z_i)=(g₁₂(x_i), g₁₂(x_i)=(a₀x_i²+a₁y_i²+a₂x_iy_i+a₃x_i+a₄y_i+a₅, a₆x_i²+a₇y_i²+a₈x_iy_i+a₉x_i+a₁₀y_i+a₁₁), i=0, 1, 2, 3, 4, 5.

[0392] As discussed earlier, the motion vectors at reference points define a system of equations whose solution determines the reconstructed global motion model parameters. In order to allow for fast processing, the reconstructed parameters may be approximated with a ratio of two integers, with denominator being a power of 2. This way, applying GMM on any pixel location in the frame can be achieved with a multiplication and binary shifting operations.

[0393] For example, to obtain the reconstructed 4-parameter model {ā₀, ā₁, ā₂, ā₃} from the given model g₄ (applied at 1/s-th pixel precision) the following equation may be used:

[0394] ${\stackrel{\_}{a}}_0=\frac{g_4\left(x_3\right)-g_4\left(x_0\right)}{\mathrm{sW}},{\stackrel{\_}{a}}_1=\frac{g_4\left(x_0\right)}{s},{\stackrel{\_}{a}}_2=\frac{g_4\left(y_3\right)-g_4\left(y_0\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_3=\frac{g_4\left(y_0\right)}{s}$

[0395] This equation may be modified to allow for fast global motion modeling as follows:

[0396] ${\stackrel{\_}{a}}_0=\frac{d_0}{2^k},{\stackrel{\_}{a}}_1=\frac{d_1}{2^k},{\stackrel{\_}{a}}_2=\frac{d_2}{2^l},{\stackrel{\_}{a}}_3=\frac{d_3}{2^l}$

[0397] Where d₀=(2^k/(sW))×(g₄(x₃)−g₄(x₀)), d₁=(2^k/s)×g₄(x₀), k=┌log₂ SW┐, d₂=(2^l/(sH))×(g₄(y₃)−g₄(y₀)), d₃=(2^l/s)×g₄(y₀), l=┌log₂ sH┐.

[0398] Therefore, in order to apply the reconstructed global motion model g₄ to a pixel location (x, y), the following equation without division may be used:

[0399] ${\stackrel{\_}{g}}_4\left(x\right)={\stackrel{\_}{a}}_{0}x+{\stackrel{\_}{a}}_1=\frac{d_0}{2^k}x+\frac{d_1}{2^k}=\left(d_{0}x+d_1\right)\text{>>}k$ $\mathrm{And}$ ${\stackrel{\_}{g}}_4\left(y\right)={\stackrel{\_}{a}}_{2}y+{\stackrel{\_}{a}}_3=\frac{d_2}{2^l}y+\frac{d_3}{2^l}=\left(d_{2}x+d_3\right)\text{>>}l$

[0400] Where >> denotes bitwise shift to the right.

[0401] To obtain the reconstructed 6-parameter model {ā₀, ā₅} from the given model g₆ (applied at 1/s-th pixel precision) the following equation may be used:

[0402] ${\stackrel{\_}{a}}_0=\frac{g_6\left(x_1\right)-g_6\left(x_0\right)}{\mathrm{sW}},{\stackrel{\_}{a}}_1=\frac{g_6\left(x_2\right)-g_6\left(x_0\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_2=\frac{g_6\left(x_0\right)}{s},{\stackrel{\_}{a}}_3=\frac{g_6\left(y_1\right)-g_6\left(y_0\right)}{\mathrm{sW}},{\stackrel{\_}{a}}_4=\frac{g_6\left(y_2\right)-g_6\left(y_0\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_5=\frac{g_6\left(y_0\right)}{s}$

[0403] This equation may be modified to allow for fast global motion modeling as follows:

[0404] ${\stackrel{\_}{a}}_0=\frac{d_0}{2^k},{\stackrel{\_}{a}}_1=\frac{d_1}{2^k},{\stackrel{\_}{a}}_2=\frac{d_2}{2^k},{\stackrel{\_}{a}}_3=\frac{d_3}{2^k},{\stackrel{\_}{a}}_4=\frac{d_4}{2^k},{\stackrel{\_}{a}}_5=\frac{d_5}{2^k}$

[0405] Where d₀=(2^k/(sW))×(g₆(x₁)−g₆(x₀)), d₁=(2^k/(sH))×(g₆(x₂)−g₆(x₀)), d₂=(2^k/s)×g₆(x₀), d₃=(2^k/(sW))×g₆(y₁)−g₆(y₀)), d₄=(2^k/(sH))×(g₆(y₂)−g₆(y₀)), d₅=(2^k/s)×g₆(y₀), k=┌log₂(s² W H)┐.

[0406] Therefore, in order to apply the reconstructed global motion model g₆ to a pixel location (x, y), the following equation without division may be used:

[0407] ${\stackrel{\_}{g}}_6\left(x\right)={\stackrel{\_}{a}}_{0}x+{\stackrel{\_}{a}}_{1}y+{\stackrel{\_}{a}}_2=\frac{d_0}{2^k}x+\frac{d_1}{2^k}y+\frac{d_2}{2^k}=\left(d_{0}x+d_{1}y+d_2\right)\text{>>}k$ $\mathrm{And}$ ${\stackrel{\_}{g}}_6\left(y\right)={\stackrel{\_}{a}}_{3}x+{\stackrel{\_}{a}}_{4}y+{\stackrel{\_}{a}}_5=\frac{d_3}{2^k}x+\frac{d_4}{2^k}y+\frac{d_5}{2^k}=\left(d_{3}x+d_{4}y+d_5\right)\text{>>}k$

[0408] In case of pseudo-perspective model, in order to obtain the reconstructed 8-parameter model {ā₀, . . . , ā₇} from the given model g₈ (applied at 1/s-th pixel precision) the following equation may be used:

[0409] ${\stackrel{\_}{a}}_0=\frac{g_8\left(y_0\right)-g_8\left(y_1\right)-g_8\left(y_2\right)+g_8\left(y_3\right)}{s^2\mathrm{WH}},{\stackrel{\_}{a}}_1=\frac{g_8\left(x_0\right)-g_8\left(x_1\right)-g_8\left(x_2\right)+g_8\left(x_3\right)}{s^2\mathrm{WH}},{\stackrel{\_}{a}}_2=\frac{\begin{array}{c}-{\mathrm{sHg}}_8\left(x_0\right)-{\mathrm{sWg}}_8\left(y_0\right)+{\mathrm{sHg}}_8\left(x_1\right)+\\ {\mathrm{sWg}}_8\left(y_1\right)+{\mathrm{sWg}}_8\left(y_2\right)-{\mathrm{sWg}}_8\left(y_3\right)\end{array}}{s^2\mathrm{WH}},{\stackrel{\_}{a}}_3=\frac{g_8\left(x_2\right)-g_8\left(x_0\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_4=\frac{g_8\left(x_0\right)}{s},{\stackrel{\_}{a}}_5=\frac{g_8\left(y_1\right)-g_8\left(y_0\right)}{\mathrm{sW}},{\stackrel{\_}{a}}_7=\frac{g_8\left(y_0\right)}{s}$ ${\stackrel{\_}{a}}_6=\frac{\begin{array}{c}-{\mathrm{sHg}}_8\left(x_0\right)-{\mathrm{sWg}}_8\left(y_0\right)+{\mathrm{sHg}}_8\left(x_1\right)+\\ {\mathrm{sHg}}_8\left(x_2\right)+{\mathrm{sWg}}_8\left(y_2\right)-{\mathrm{sHg}}_8\left(x_3\right)\end{array}}{s^2\mathrm{WH}}$

[0410] Like in the previous cases of simpler models, this equation may be expressed as follows:

[0411] ${\stackrel{\_}{a}}_i=\frac{d_i}{2^k},i=0,\dots ,7$

[0412] To apply the reconstructed global motion model g₈ to a pixel location (x, y), the following equation without division may be used:
g₈(x)=(d₀x²+d₁xy+d₂x+d₃y+d₄)>>k
And
g₈(y)=(d₁y²+d₀xy+d₅x+d₆y+d₇)>>k

[0413] Where k=┌log₂(s² W H)┐.

[0414] Finally, in the case of bi-quadratic model, in order to obtain the reconstructed 12-parameter model {ā₀, . . . , ā₁₁} from the given model g₁₂ (applied at 1/s-th pixel precision) the following equation may be used:

[0415] ${\stackrel{\_}{a}}_0=\frac{-2g_{12}\left(x_0\right)+g_{12}\left(x_1\right)+g_{12}\left(x_4\right)}{2s^2{W}^2},{\stackrel{\_}{a}}_1=\frac{-2g_{12}\left(x_0\right)+g_{12}\left(x_2\right)+g_{12}\left(x_5\right)}{2s^2{H}^2},{\stackrel{\_}{a}}_2=\frac{g_{12}\left(x_0\right)-g_{12}\left(x_1\right)-g_{12}\left(x_2\right)+g_{12}\left(x_3\right)}{s^2\mathrm{WH}},{\stackrel{\_}{a}}_3=\frac{g_{12}\left(x_1\right)-g_{12}\left(x_4\right)}{\mathrm{sW}}$ ${\stackrel{\_}{a}}_3=\frac{g_{12}\left(x_{12}\right)-g_{12}\left({\mathrm{x5}}_4\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_5=\frac{g_{12}\left(x_0\right)}{s}$ ${\stackrel{\_}{a}}_6=\frac{-2g_{12}\left(y_0\right)+g_{12}\left(y_1\right)+g_{12}\left(y_4\right)}{2s^2{W}^2},{\stackrel{\_}{a}}_7=\frac{-2g_{12}\left(y_0\right)+g_{12}\left(y_2\right)+g_{12}\left(y_5\right)}{2s^2{H}^2},{\stackrel{\_}{a}}_8=\frac{g_{12}\left(y_0\right)-g_{12}\left(y_1\right)-g_{12}\left(y_2\right)+g_{12}\left(y_3\right)}{s^2\mathrm{WH}},{\stackrel{\_}{a}}_9=\frac{g_{12}\left(y_1\right)-g_{12}\left(y_4\right)}{\mathrm{sW}}$ ${\stackrel{\_}{a}}_{10}=\frac{g_{12}\left(y_2\right)-g_{12}\left(y_5\right)}{\mathrm{sH}},{\stackrel{\_}{a}}_{11}=\frac{g_{12}\left(y_0\right)}{s}$