US 6,618,490 B1Grant
Method for efficiently registering object models in images via dynamic ordering of features
Issue Date:2003-09-09
•28 Claims
•17 Drawing Sheets
Abstract
An object model, having a plurality of features and described by a model state, is registered in an image. Unregistered features of the object model are dynamically selected such that the cost function of each feature search is minimized. A search is performed for a match of the selected model feature to the image, or to features within the image, to register the feature, and the model state is updated accordingly. These steps are repeated until all features have been registered. The search is performed in a region of high probability of a match. The cost function for a feature is based on the feature's basin of attraction, and in particular can be based on the complexity of the search process at each basin of attraction. A search region is based on a projected state probability distribution. In particular, the cost function is based on the “matching ambiguity,” or the number of search operations required to find a true match with some specified minimum probability. For feature-to-feature matching, the number of search operations is preferably the number of target features located within each search region. For feature-to-image matching, the matching ambiguity is computed, for each search region, by dividing the region into minimally-overlapping volumes which have the same size and shape as a basin of attraction associated with the feature, and then counting the number of volumes required to cover the regions. The model state is updated according to a propagated state probability distribution. Preferably, the propagation of the probability distribution is based on successive registered features.
Metadata
Assignee
- Hewlett-Packard Development Company, L.P.
Inventors
- Tat-Jen Cham
- James Matthew Rehg
Application Information
Application Number:US 09/466,975
Filing Date:1999-12-20
Priority Date:1999-09-16
Art Unit:7
Classifications
IPC:
G06K 900
Field of Search:
382192382312382100382118382103382228382151382289382291382294382305382107382175382282369 301636917801369 43712234712222712 4712 3342 25342 93704232707 3345420
Patent Drawings (17 sheets)
Description
RELATED APPLICATIONS
[0002] This Application claims the benefit of U.S. Provisional Application No. 60/154,385, filed Sep. 16, 1999, the entire teachings of which are incorporated herein by reference.
[0003] This application is also related to application Ser. No. 09/466,970 filed entitled “A Method for Object Registration via Selection of Models with Dynamically Ordered Features” by Tat-Jen Chain and James M. Rehg, filed on the even day herewith, the entire teachings of which are incorporated herein by reference.
BACKGROUND OF THE INVENTION
[0004] There is a large class of applications that depend upon the ability to localize a model of an object in an image, a task known as “registration.” These applications can be roughly categorized into detection, alignment, and tracking problems.
[0005] Detection problems involve, for example, finding objects in image databases or finding faces in surveillance video. The model in a detection problem is usually generic, describing a class of objects. For example, in a prior art face detection system, the object model is a neural network template that describes all frontal, upright faces. See Rowley et al., “Neural network-based face detection”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 20(1), pages 23-38, January 1998. Another example is locating armored vehicles in images for a military targeting system.
[0006] An example of an alignment application is mosaicing, in which a single large image is constructed from a series of smaller overlapping images. In this application, each model is simply an image to be added incrementally to the mosaic. The alignment goal is to position each new image so that it is consistent with the current mosaic wherever the two overlap. A description is given in Irani et al., “Mosaic based representations of video sequences and their applications,” Proceedings of Int. Conference on Computer Vision, pages 605-611, Cambridge, Mass., 1995.
[0007] Another example is the alignment of plural images obtained from different sensors, e.g. aligning remote-sensed images obtained via normal and infra-red photography, or aligning MRI and SPECT medical images. This allows different regions of an image to be analyzed via multimodal (i.e., vector) measurements instead of scalar pixel intensities. These and other applications are further discussed in the survey on image registration, Brown, “A survey of image registration techniques,” ACM Computing Surveys, 24(4), pages 325-376, 1992.
[0008] In tracking applications, the models are typically specific descriptions of an image object that is moving through a video sequence. Examples include tracking people for surveillance or user-interface purposes. In figure tracking for surveillance, a stick-figure model of a person evolves over time, matched to the location of a person in a video sequence. A representative prior method is Cham et al., “A multiple hypothesis approach to figure tracking,” Proceedings Computer Vision and Pattern Recognition, pages 239-245, Fort Collins, Colo., 1999. In user-interface applications, the user's gaze direction or head pose may be tracked to determine their focus-of-attention. A prior method is described in Oliver et al., “LAFTER: Lips and face real time tracker,” Proceedings Computer Vision and Pattern Recognition, pages 123-129, San Juan, PR, Jun. 17-19, 1997.
[0009] In each of these application areas, there is a desire to handle increasingly sophisticated object models, which is fueled by the increasing demand for sensing technologies. For example, modern user interfaces may be based on tracking the full-body pose of a user to facilitate gesture recognition. As the complexity of the model increases, the computational cost of registration rises dramatically. A naive registration method such as exhaustive search would result in a slow, inefficient system for a complex object like the human figure. However a fast and reliable solution would support advanced applications in content-based image and video editing and retrieval, surveillance, advanced user-interfaces, and military targeting systems.
[0010] Therefore, there is a need for a registration method which is computationally efficient in the presence of complex object models.
SUMMARY OF THE INVENTION
[0011] The present invention registers a model in an image sequentially, that is, one feature at a time. Until now, sequential feature registration has been done in an order predetermined before any registration begins. The Applicants have found that the process of registration can be optimized by determining a feature registration order dynamically, that is, at the beginning of each registration step, selecting the feature whose registration will be most cost effective and searching for that feature.
[0012] Accordingly, in a preferred method of registering an object model in an image, where the object model has a plurality of features and is described by a model state, an unregistered feature of the object model is selected such that the cost function of a subsequent search is minimized. A search is performed for a match of the selected model feature to the image to register the feature, and the model state is updated accordingly. These steps are repeated until all features have been registered.
[0013] Preferably, the search is performed in a region of high probability of a match. The cost function for a feature is based on the feature's basin of attraction, and in particular can be based on the complexity of the search process at each basin of attraction.
[0014] A search region can be based on a projected state probability distribution. A search is preferably based on maximizing a comparison function.
[0015] Selecting and searching are preferably responsive to a propagated state probability distribution. The state probability distribution is projected into feature space.
[0016] For each unregistered feature, the number of search operations required to find a match with at least a predetermined probability is determined, and the feature requiring a least number of search operations is selected.
[0017] The number of required search operations is determined by first finding search regions within a feature space, where each region has an associated probability density which exceeds some predetermined threshold. A total probability is then formed by summing the probabilities associated with each of the found search regions. If the total probability is less than the predetermined probability, the threshold is lowered and new regions are found and the probabilities summed. This process repeats until the total probability is greater or equal to the predetermined probability. Finally, the number of required search operations is computed, based on the found search regions.
[0018] Searching can comprise feature-to-feature matching. In this case, the number of search operations is preferably the number of target features located within each search region. The number of target features located within the search region can be based on Mahalanobis distances to potential target features.
[0019] In a preferred embodiment, target features are approximately uniformly distributed, and the number of features is proportional to the search region's size. Thus, the features can be ranked according to the sizes of the associated search regions.
[0020] Alternatively, searching can comprise feature-to-image matching. Here, the number of required search operations is computed, for each search region, by first dividing the region into minimally-overlapping volumes which have the same size and shape as a basin of attraction associated with the feature, and then by counting the number of volumes required to cover the regions.
[0021] In a preferred embodiment, counting the volumes is approximated by obtaining eigenvalues and eigenvectors to a covariance matrix associated with the feature search region. A basin of attraction span is calculated for each eigenvector direction, and a count is approximated from the eigenvalues and the spans.
[0022] The model state is updated according to a propagated state probability distribution. Preferably, the propagation of the probability distribution is based on successive registered features.
[0023] The present invention is thus a method and apparatus for sequential feature registration in which features are selected dynamically so as to minimize total matching ambiguity, based on a propagated state probability model. The method can be applied both to feature-to-feature matching and to feature-to-image matching.
[0024] The computation of matching ambiguity is based on a state probability model projection from model space to feature space, and on the feature or image data.
[0025] In the preferred embodiment of feature-to-feature matching, matching ambiguity is given by the number of target features located inside the search region of a source feature.
[0026] In the preferred embodiment of feature-to-image matching, matching ambiguity is given by the minimum number of attractor regions which are required to span the search region of a source feature.
[0027] In the preferred embodiment, the state probability model is a Gaussian distribution and is propagated using the Kalman filter update step. Matching ambiguity is defined in terms of a feature search region, i.e., a high probability region in feature space.
[0028] In another preferred embodiment, not all of the available features are matched. Matching continues until a desired level of certainty in the estimate has been achieved.
[0029] In yet another preferred embodiment, optimal feature orders are computed over a corpus of examples of registration tasks. A single fixed ordering is obtained from the training set of optimal orderings.
BRIEF DESCRIPTION OF THE DRAWINGS
[0030] The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention.
[0031] FIG. 1 is a schematic diagram illustrating the projection of a polygonal object model into an image by a transform.
[0032] FIG. 1A is a schematic diagram illustrating edge extraction.
[0033] FIG. 2A is a schematic diagram illustrating the transform of an object model into the image.
[0034] FIG. 2B is an illustration showing the result of successful registration.
[0035] FIG. 3 is a block diagram illustrating static sequential feature registration as is well-known in the art.
[0036] FIGS. 4A and 4B are diagrams illustrating the registering of a kinematic model with known features.
[0037] FIG. 5 is a graph illustrating sequential feature registration times with different feature ordering.
[0038] FIG. 6 is a block diagram of a feature-to-image matching embodiment of the present invention.
[0039] FIG. 7 is a block diagram of a feature-to-feature matching embodiment of the present invention.
[0040] FIGS. 8A and 8B are conceptual diagrams illustrating matching ambiguity for feature-to-feature matching and feature-to-image matching, respectively.
[0041] FIG. 9 is a flow diagram for the feature selection module of FIGS. 6 and 7.
[0042] FIG. 10A is a diagram illustrating the dynamic feature ordering, by an embodiment of the present invention, for the image of FIGS. 4A and 4B
[0043] FIGS. 10B and 10C are diagrams illustrating, respectively, an initial state and a dynamic feature ordering for another image.
[0044] FIGS. 11A-11D are diagrams which illustrate initial states and resulting dynamic feature ordering for the images of FIGS. 10A-10C when some strong prior knowledge is used.
[0045] FIG. 12 is a graph comparing quantitative results for three different feature orderings using the image of FIGS. 11C and 11D.
DETAILED DESCRIPTION OF THE INVENTION
[0046] The present invention comprises a new class of sequential feature registration methods for efficient model-to-image matching. This new class has four advantages over sequential registration methods known in the prior art.
[0047] First, features are selected dynamically at each stage of a multi-stage registration process so as to minimize the required number of search operations.
[0048] Second, feature selection is based on both propagated prior state probabilities and image or feature data. Thus all available information is taken into account when ordering features.
[0049] Third, the present invention applies to both feature-to-feature and feature-to-image matching problems.
[0050] Finally, the method is automatic and can produce different feature orders for different registration problems without the intervention of the user.
[0051] The problem of object registration has three main components: 1) an “object model” which describes a target to be located in an input image; 2) a “comparison function” that determines how well a specific instantiation of the object model matches the image data; and 3) a “search strategy” that specifies how to systematically identify occurrences of the object model in the image.
[0052] The object model can be further decomposed into two main components: 1) a set of “features,” such as templates, edge features, corner features, etc., that describe the visual signature of the object; and 2) a vector of parameters, called the “model state,” that encodes the configuration of the features in the image.
[0053] Registration can be defined as the search for the model state that minimizes the cost function between the projection of the model features onto image or feature space, and the image itself.
[0054] FIG. 1 illustrates an exemplary object model 10 for the task of registering a known 2D polygonal shape in an image 13. The model parameters comprising the model state w 15 in this example encode four degrees of freedom: translation in x 15A and y 15B, rotation 15C, and scaling 15D. FIG. 1 illustrates the projection 12 of the object model features 11 into the image 13 by transform G(w) according to model state w 15. Model features define, for example, edges and corners in the input edge image.
[0055] In this example, edges are used as the registration features and the cost function measures the distance between projected model edges 14A and the extracted image edges 14B.
[0056] FIG. 1A illustrates an extracted edge image 13B resulting from the application of a standard edge detection algorithm 5 to an intensity image 13A containing the target object 14. The presence of spurious lines 7 and corners in the extracted edge image 13B or the input image 13A itself is a major source of difficulty in registration. FIGS. 2A and 2B show the desired result. FIG. 2A shows how, under the action of some optimal state w*, the polygonal model 11 is scaled 8A, rotated 8B and translated 8C such that it is aligned 8D with its corresponding image edges 14B.
[0057] FIG. 2B shows the result of successful registration. Optimal state w* has aligned the polygon model 14C (shaded) with its corresponding image edges 14B.
[0058] While the choice of object model and cost function depends greatly on the intended application, the search strategies used in a registration method are often quite general. Thus an improved search algorithm could have a significant impact on a broad range of applications.
[0059] The search can be performed either in state space or in feature space. The difficulty of the search problem depends to a large extent on the amount of prior information available about the state. Prior information in state space can be conveniently expressed as a probability distribution, which describes probabilities for the range of possible states.
[0060] For example, in a tracking application, the posterior state estimate from the previous frame can provide a strong constraint on the current state, i.e., a state prediction with a small variance. In this case, the state space volume that must be searched will be small, and the possible configurations of the object in the image will be tightly constrained.
[0061] Search strategies can update the state vector either sequentially or in parallel. Parallel updates modify all of the state parameters simultaneously to improve the quality of the match. The classical gradient descent algorithm is an example of parallel search. For registration problems with strong prior constraints, gradient-based optimization methods perform well, achieving quadratic convergence rates in many cases.
[0062] However, when prior information is weak or nonexistent, as in an object detection problem, sequential search strategies are often more efficient. Sequential search can take place in either state space or feature space. In this approach, subsets of state variables or features are processed in sequence, resulting in incremental updates of the state estimate. A chief advantage is that the search space becomes successively smaller, and the search problem easier, as more features or states are processed.
[0063] A classical example of sequential feature search is coarse-to-fine processing using an image pyramid. Starting at the coarsest level, the pyramid is processed sequentially, resulting in a series of state estimates of increasing accuracy.
[0064] In contrast to sequential feature search, sequential state space search has been employed in domains such as image mosaicing. For example, it is common in mosaicing to estimate the translation parameters before computing rotation and scale.
[0065] In most vision applications the model parameters interact strongly through the image features and it is not possible to optimize them independently when the prior information is weak. Thus the sequential state space method is primarily useful in domains such as mosaicing or visual tracking where there is a strong prior constraint. In contrast, sequential feature methods have much broader applicability. This suggests that an improved algorithm for sequential feature registration could impact many application domains.
1. Static Sequential Feature Registration
[0066] The methods of sequential feature registration that are known in the prior art are based on a predetermined, fixed ordering of features. FIG. 3 is a block diagram illustrating the general process 30 for this registration method. In particular, FIG. 3 depicts the case where features are matched directly with the image known as feature-to-image matching.
[0067] The process is iterative. It starts with an input image 35, an initial state distribution typically gleaned from prior knowledge, more commonly known in the art as a prior state distribution p0(x) 37, and a predefined sequence of features {Fi}ni=1. It ends when an acceptable state estimate 39 has been obtained. Processing steps for the ith iteration are as follows:
[0068] 1. The search operation module 31 identifies the optimal position or configuration 38 for feature Fi. For example, in template registration using an image pyramid, Fiwould be the template model for the ith level of the pyramid. Under a translational state model, the search would begin at xi=n xi−1and yi=n yi−1, where n is the sampling rate for the pyramid and (xi−1,yi−1) is the final state estimate from the previous level. Local exhaustive search could be used for a translational model, or gradient-based optimization if the model were more complex. The final state estimate for iteration i would be chosen to minimize the cost function.
[0069] 2. The state update module 33 uses the result 38 from the search operation module 31 to compute a new probability distribution 39 for the model state. Because an additional feature whose position or configuration has now been determined is now registered, the state probability distribution will be more sharply peaked, representing increased accuracy of the model parameters. In an exemplary implementation, a Gaussian model can be used for the probability distribution. The state update module 33 then involves a Kalman update step as described in Anderson et al., “Optimal Filtering,” Prentice-Hall, 1979, incorporated by reference herein, in which the mean and covariance of the state are computed.
[0070] 3. Steps 1 and 2 are repeated. The search operation module 31 uses the updated probability distribution 39 from the state update module 33, until the process converges or achieves the desired accuracy.
[0071] In some cases, searching is more efficiently carried out by matching the model features directly to features extracted from the image (image features). The features applicable for this form of matching are typically discrete features such as corners, edges and contours. In these instances, the feature extraction is done as an independent process whereby the relevant feature-detector is applied on the image. For example if edge, corner or contour features are to be matched, corresponding edge detectors, corner detectors or B-spline fitting algorithms are used for feature extraction.
[0072] Edge detectors are described in Canny, “A computational approach to edge detection,” IEEE Trans. Pattern Analysis and Machine Intelligence, vol 8, pages 679-698, 1986. Comer detectors are described in Noble, “Finding corners,” Image and Vision Computing, 6(2), pages 121-128, 1988. B-spline feature extraction is described in Cham et al., “Automated B-spline curve representation incorporating MDL and error-minimizing control point insertion strategies,” IEEE Trans. Pattern Analysis and Machine Intelligence, 21(1), 1999.
[0073] Prior methods for static sequential feature registration have employed a variety of fixed, heuristic feature-ordering schemes. One of the most popular schemes is simply to order the features a priori based on feature size. For example, in one prior method the components of an object (e.g. a cabinet) are sequentially registered based on a pre-determined hierarchical decomposition (e.g. progressing from the overall cabinet frame to the cabinet drawers). See Hauck et al., “Hierarchical recognition of articulated objects from single perspective views,” Proceedings Computer Vision and Pattern Recognition, pages 870-876, San Juan, PR, 1997.
[0074] Another class of prior methods for size-based feature-ordering is multi-resolution search. The search begins at the lowest image resolution level and hence the coarsest features which survive at this resolution are used first. While the low resolution reduces the amount of search required to find the correspondences, the accuracy of estimation is poor. However once an approximate model state is computed, the search progresses to the next resolution level. At this level smaller features are used. Because an estimate of the model state is known, the search can be confined to smaller regions of the image where these features are expected to be found. The state estimate after incorporating the smaller features becomes more accurate, and thus this routine progresses through the other levels with heuristically minimal search. A method which uses a multi-resolution approach for registration is described in Cham et al., “A statistical framework for long-range feature matching in uncalibrated image mosaicing,” Proc. IEEE Conference on Computer Vision and Pattern Recognition, pages 442-447, Santa Barbara, Calif., 1998.
[0075] In another prior method, the search for a small object is directed by its known probability of being located in a vicinity of larger objects (e.g., a spoon on table). Hence search is done indirectly by first looking for the large object followed by the desired smaller object. See Wixson et al., “Using intermediate objects to improve the efficiency of visual search,” Int. Journal of Computer Vision, 12(2/3), pages 209-230, 1994.
[0076] As an alternative to feature size, other prior methods use the a priori robustness of features to order their selection during tracking. See Toyama et al. in “Incremental focus of attention for robust visual tracking,” Proceedings Computer Vision and Pattern Recognition, pages 189-195, San Francisco, Calif., 1996. A face-tracking system based on this method uses a fixed hierarchy of tracking methods. At the start, tracking is carried out using the coarsest but most robust method, e.g., skin-color sensor. If the sensor output is deemed to be stable, higher-level methods are used which increase both estimation accuracy and computational cost, e.g. template feature matching. Failure of higher-level methods return the tracker to lower-level methods.
[0077] In related prior art by Coutaz et al. a finite state machine is used to determine which feature detectors to apply during visual tracking. See Coutaz et al., “Coordination of perceptual processes for computer mediated communication,” Proceedings of 2nd Int. Conference Automatic Face and Gesture Recognition, pages 106-111, 1996. The processes are selected according to an overall confidence measure in tracking obtained from the previous image frame. As in the prior method of Toyama et al. the hierarchy of processes is fixed and manually specified. The difference in these two prior methods is that the finite state machine allows some levels to be bypassed based on a confidence measure.
[0078] Another prior art proposes a fixed feature ordering strategy for registering articulated objects which can be described by kinematic chains. See Hel-Or et al., “Constraint fusion for recognition and localization of articulated objects,” Int. Journal of Computer Vision, 19(1), pages 5-28, 1996. In this method, features along a kinematic chain are successively matched in linear order from end to end. A linear Gaussian estimation method is used to incrementally improving the model state and covariance estimates.
[0079] Another prior method addresses the question of using a predefined subset of the total features in order to achieve a prespecified accuracy. See Akra et al., “Sampling of images for efficient model-based vision,” IEEE Trans. Pattern Analysis and Machine Intelligence, 21(1), pages 4-11, 1999. This method addresses image sub-sampling for efficient registration. This is an example of the statistical problem of optimal stopping.
[0080] In all the above cases, the ordering of the features are manually fixed prior to the registration process. For example in registering a human kinematic model using template features, the ordering of features may be pre-specified as {torso→face→hair→upper-arm→lower-arm→ . . . }. However, having a fixed feature ordering is sub-optimal for two reasons.
[0081] First, prior knowledge of the model state is ignored. For example, in tracking problems, a common occurrence is partial tracking failure. A person tracker may mistrack various limbs due to distractors such as shadows, background clutter and occlusion, yet accurately track other parts of the body. Consider the situation in which a person's lower leg is accurately tracked, but tracking has failed on the rest of the body. The reinitialization process should be able to exploit the accurate localization of the lower leg in registering the rest of the body. This is achieved by a feature order which starts at the lower leg, as described below in Section 3. This clearly demonstrates the need for dynamic feature ordering, since failure modes cannot be predicted in advance.
[0082] Second, image data is ignored. Consider a different example in which a computer has an attached camera and is running a vision-based head-detection system as part of an advanced user interface. The system has two low-level sensors for independently detecting skin-color and motion. A person's head can be further localized by using two high-level features: (i) a face feature or (ii) a head-silhouette feature. These features can be detected with significant computational cost, using either a face-detection algorithm which analyzes image regions containing skin-color pixels, or a head-silhouette analysis algorithm which operates on image regions containing motion.
[0083] If the computer were used in a room with skin-colored walls, the skin-color sensor would output large candidate image regions, while the motion sensor would produce only a small candidate region. In this case, the person's head would be more efficiently localized using the head-silhouette analysis algorithm first before the face-detector.
[0084] Conversely, if the location was a factory floor with moving machinery, there would be large candidate regions for the motion-sensor but a small candidate region for the skin-color sensor. Here it would be more efficient to use the face-detector first. As demonstrated in these examples, the most efficient feature ordering is dependent on the image data and cannot be predicted in advance.
[0085] Experimental evidence underscores the importance of selecting the optimal feature ordering for a registration problem. Consider an exemplary task of registering a human kinematic model in an image.
[0086] FIGS. 4A and 4B illustrate the registering of a high-degree of freedom (DOF) kinematic model with known features, but without prior knowledge of the model state, using a template-based feature model known in the art as a scaled prismatic model (SPM). FIG. 4A shows the initial model state of the model 41 compared to the image 43, while FIG. 4B shows the desired feature registration 45. If the model is highly detailed and if the initial feature used was a hand template feature, the search process would take much longer than if the initial feature was the torso template feature.
[0087] FIG. 5 is a graph 50 which illustrates this problem by comparing the amount of time required in Applicants' experiments to register the model using: (a) random ordering of features 51, (b) worst ordering 53, i.e., ordering of features which take the longest registration time, and (c) best ordering of features 55.
[0088] The results show that the sequential feature registration time is very sensitive to the ordering of features used. In particular, Applicants are able to achieve a speedup of 24 using an optimal ordering compared to the worst ordering. Hence, when designing an algorithm for sequential feature registration, finding an efficient ordering of the features is critical.
2. Dynamic Sequential Feature Registration
[0089] FIG. 6 is a block diagram of a feature-to-image matching embodiment 30A of the present invention. The sub-optimality of fixed feature ordering is avoided by adding a model feature selector module 34 in the sequential feature registration process 30A. The model feature selector module 34 analyzes the remaining unmatched model features to determine which feature to search next.
[0090] In this manner, the feature ordering is determined dynamically during the registration process. Both prior knowledge and the image data are allowed to influence the feature ordering.
[0091] FIG. 7 is a block diagram 30B for a feature-to-feature matching embodiment. Here, the image 35 is replaced by a set of image features 35B created by a feature extractor 35A which extracts features from the image 35.
[0092] In the next two sections, 2.1 and 2.2, some mathematical notation is established for this framework, and formally describe feature-matching. Section 2.3 explains how the amount of search operations required to match each feature, called the “matching ambiguity,” can be determined. Section 2.4 describes the feature-selection module 34 of FIGS. 6 and 7, which orders features dynamically during the matching process. Other components of search initialization, registration and state-update are then discussed.
[0093] 2.1 Spatial Registration Framework
[0094] The spatial registration framework is expressed as follows. Start with an object model M comprising a set of known “source” features F and a set of transformation functions {G1, G2, . . . }, each of which maps an associated feature into the image. This is described in more detail below. Then, given a target image I, the goal is to match these features to their correct locations in the image and also to recover the parameters of M denoted as a vector w. These features can either be prior knowledge as part of the model specification, or in the case of registering two images, they can represent extracted features.
[0095] The amount of searching required in the registration process depends significantly on the a priori knowledge of the model parameters. For example if w has a small prior covariance, such as in video-based tracking applications, feature-to-feature matching may simply involve mapping the source features into the image and searching for the nearest target features. The model parameters may then be computed directly from these correspondences. Similarly, if template features are used instead, registration may be carried out in the model state-space by locally minimizing the pixel residual error. Registration in these problems which have strong priors do not have significant search complexities and all features can be matched simultaneously.
[0096] In the case of registering a kinematic model of the figure to an image, F may be the set of template features associated with the links in the model, and M is parameterized by a vector of joint angles and link lengths. These features are not necessarily limited to a single class, as F can simultaneously include templates, corners and edges. It can also include features from different levels of resolution.
[0097] 2.2 Analysis of Spatial Features A feature f ∈ F is described by a number of attributes:
[0098] 1. A function Gi:w→u which maps the model state w to a feature state u for feature fiin a common feature space. This feature space is common to all features of the same type. For example, if the feature is a point, the common feature space is simply the image space. For more complex features such as templates or edges, the feature space may be further parameterized by including additional rotation, scaling or skew dimensions if necessary.
[0099] 2. A property vector p which allows a feature to be compared with another feature, or compared to the image, using a comparison function. Examples of such properties are color, shape, etc.
[0100] 3. Additionally for image-based features such as templates, we specify the dimensions for a “basin of attraction” in feature space. A basin of attraction for a particular feature is a region bounded by the maximum displacement or perturbation between the true and predicted locations of the feature in feature space for which local optimization of the estimated location (via the maximization of a comparison function) guarantees convergence toward the true location.
[0101] In the case of feature-to-feature matching, a feature comparison function Cff(pi,pj) generates a similarity measure for comparing feature pairs. In the case of feature to image matching, the comparison function Cfl(pi,ui,I) measures the compatibility between the feature in its current feature state piwith the image I—it is through the maximization of this function by which the image-based features can be optimally localized.
[0102] Finally, we assume that the correct feature pair or feature state maximizes the relevant comparison functions, i.e., once all candidate features or states are tested, the correct solution will be obtained.
[0103] 2.3 Matching Ambiguity of a Feature
[0104] In order to compute the cost of matching a particular feature, we introduce the concept of “matching ambiguity.” The matching ambiguity of a feature fi, denoted by αi, is defined as the number of search operations required to find the true match with some specified minimum probability.
[0105] Computation of the matching ambiguity for a particular feature can be done in the following way. Starting with the probability distribution of the model state and some specified minimum probability p for finding the true match of the feature:
[0106] 1. Find the regions in the feature space within which the probability density exceeds some threshold.
[0107] 2. If the total probability within these regions is less than p, lower the threshold and return to step 1.
[0108] 3. Compute the number of search operations required to find the match within these regions. For feature-to-feature matching, this is done by counting the number of target features located within the regions. For feature-to-image matching, the regions are divided into volumes which are the size and shape as the basin-of-attraction of the feature. The number of such volumes required to fully cover the regions is then counted.
[0109] The number of search operations computed in step 3 is the matching ambiguity.
[0110] To illustrate this process, consider an exemplary implementation which assumes that the probability of the model state is based on a Gaussian distribution. We can employ the idea of a search region such as the “validation gate” used in extended Kalman filters and described in Bar-Shalom et al., “Tracking and Data Association,” Academic Press, 1988, incorporated by reference herein, to compute the matching ambiguity. This is shown below.
[0111] Assume that the estimated model state has a mean μ and a covariance Σ. Linearizing the mapping Gi(w) about μ, the covariance Siin feature space is expressed as
[0112] Si=JiΣJiT (1)
[0113] where
[0114] Ji=∇Gi|w=μ (2)
[0115] is the Jacobian. The validation gate is then the volume bounded by an isoprobability surface which may be specified as a factor ψ of standard deviations.
[0116] For feature-to-feature matching, the matching ambiguity is then the number of target features which lie within the validation gate. This may be obtained by evaluating the Mahalanobis distances to potential target features and counting. Unfortunately, this is a potentially intensive computation because it would involve pair-wise comparisons of features. A reasonable approximation which can be used when target features are approximately uniformly distributed is that the matching ambiguity is proportional to the size of the validation gate, i.e.
[0117] αi∝(∥Si∥)½ (3)
[0118] Since in the algorithm proposed later the matching ambiguities are used to sort the features, the exact values of the matching ambiguities need not be evaluated as long as they can be ranked in the right order.
[0119] For feature-to-image matching, the matching ambiguity is the number of minimally-overlapping regions which have the same dimensions as the basin of attraction that would fit into the validation gate. This can be approximated by first obtaining the eigenvalues ejand eigenvectors vjto the covariance matrix Si, and then calculating the span of the basin of attraction bjalong each of the vjdirections. Finally, the matching ambiguity is computed as
[0120] where ceil(·) rounds fractional values up to the next integer.
[0121] Matching ambiguity can also be based on further complexity, in the search process.
[0122] FIGS. 8A and 8B illustrate the concept of matching ambiguity for the two separate cases in this exemplary implementation. Because a Gaussian probability model is assumed here, the validation gate 81 is elliptical.
[0123] FIG. 8A shows, for feature-to-feature matching, the target features 83 located within the validation gate 81 of a source feature. The matching ambiguity in this case is the number of candidates to be searched, which here is six. The regions having the same span of the basin of attraction indicated in FIG. 8B are referred to as “attractor regions” 85.
[0124] FIG. 8B shows, for feature-to-image matching, minimally overlapping regions 85 with the span of the basin of attraction covering the validation gate 81. The matching ambiguity is the number of regions required, which here is ten.
[0125] 2.4 Dynamic Feature Ordering and Selection
[0126] As each feature is used in the estimation step during sequential search, the model state probability distribution becomes more sharply peaked, reflecting the increased accuracy in the model parameters. This means as each feature is used in the registration process, the high probability regions in feature space become smaller for the remaining unmatched features, thereby leading to a reduction in their matching ambiguities.
[0127] First we assume that the intention is to use all available features in the registration process. Then the total number of search operations involved can be minimized by selecting each successive feature to be the feature requiring the smallest number of search operations to be matched, among all remaining features. This ordering of features can only be done at run-time, hence the term “dynamic feature ordering” is used.
[0128] Based on this principle of search minimization, an efficient feature selection method is described below which is to be used in the feature selector module 34 of FIG. 6.
[0129] FIG. 9 is a flow-chart 90 for this feature selection method.
[0130] 1. Set the list of used features L as empty, and initialize the “best” feature index.
[0131] That is, set (database index ib, matching ambiguity αb) (−1,∞). (Step 91)
[0132] 2. Check if L is full, i.e. if it contains all features in the model feature database. Go to step 8 if full. (Step 92)
[0133] 3. Retrieve the next model feature fiin the database 94, and add fito L. (Step 93)
[0134] 4. Based on the current model state probability distribution 95, compute, in a matching ambiguity calculator, the matching ambiguity αifor the feature, using the method described previously in section 2.3. (Step 96)
[0135] 5. If αi>αb, return to step 2 (Step 92). (Step 97)
[0136] 6. Otherwise feature fiis currently the “best” feature with the smallest matching ambiguity. Update the best feature index 99: (ib, αb)=(i, αi). (Step 98)
[0137] 7. Return to step 2 (Step 92).
[0138] 8. The feature with the smallest matching ambiguity has been found. Extract feature with index ibfrom the database and pass to the next module in the system (i.e. the search initialization module). (Step 100)
[0139] 2.5 Search Initialization and Registration
[0140] Once the feature selection has been carried out, the search initialization and registration processes for matching a feature is straightforward. Once again this is different for matching to features or directly to the image:
[0141] 1. For feature-to-feature matching, each image feature which is found within the desired high probability regions in feature space represents a target for the matching the model feature. Registration then involves mapping the model feature to each image feature, and selecting the mapping to the image feature which maximizes the feature-to-feature comparison function Cff.
[0142] 2. For feature-to-image matching, the method of computing the matching ambiguity involves dividing the high probability regions into volumes which are the size and shape as the basin-of-attraction. Hence the initial search points, or “seeds,” in the matching process are simply the center points of each basin-of-attraction. Registration then involves mapping the model feature to each of the seeds, locally maximizing the comparison function Cflwithin the basin-of-attraction, and selecting the optimal mapping of model feature to image.
[0143] 2.6 State Update
[0144] State update involves computing the new probability distribution of the model parameters based on matching the previous feature. State update may be achieved using different methods depending on the probability representation used. For example, probability representations using histogramming, Parzens window, mixture-of-Gaussians, or particle distributions have well-documented methods of updating the probabilities based on additional observations. Parzens window is described in Therrien, “Decision, Estimation and Classification: An Introduction to Pattern Recognition and Related Topics,” John Wiley, 1989. Mixture-of-Gaussians is described in Bar-Shalom et al., “Tracking and Data Association,” Academic Press, 1988. For particle distributions, see Isard et al., “CONDENSATION—conditional density propagation for visual tracking,” Int. Journal of Computer Vision, 29(1), pages 5-28, 1998.
[0145] The simple example we will show here is based on the Gaussian model which is parameterized by a mean and covariance. This employs the Kalman filter update step. The updated model mean state μkand covariance Σkcan be computed from the optimally registered feature state ubwith observation covariance Sbvia the following equations:
[0146] μk=μk−1+Kk(ub−Jkμk−1) (5)
[0147] Σk=Σk−1−KkJk-Σk−1 (6)
[0148] where the subscript k denote the sequential update index and Kkis the Kalman gain given by
[0149] Kk=Σk−1JT(JΣk−1JT+Sb)−1 (7)
[0150] Combining all the components discussed in the previous sections, we arrive at a sequential registration method employing the novel feature selection mechanism based on dynamic feature ordering.
[0151] Again using an exemplary implementation where a Gaussian probability distribution model is assumed, the complete algorithm is illustrated below:
[0152] 1. Set the hierarchy list of used features LHas empty.
[0153] 2. Compute the matching ambiguities αifor all unused features, using either equations (3) or (4).
[0154] 3. Select the feature fbfor which αbis the smallest matching ambiguity. Note that this step and step 2 above are described in more detail with respect to FIG. 6.
[0155] 4. Carry out the necessary αbsearch operations to recover the optimal feature state ub. This is the minimum number of search operations which have to be performed to register a feature.
[0156] 5. The optimal feature state uband the associated observation covariance Sbis used to improve the model state and covariance by applying the standard Kalman filter update steps (5) and (6).
[0157] 6. Append fbto the LH.
[0158] 7. If all features have been used, stop; otherwise return to step 2.
[0159] At the end of the registration process, the hierarchy list of features LHcontains the “feature hierarchy.” The feature hierarchy represents the optimal sequential ordering of features and is dependent on the prior model state and covariance, as well as the accuracy of registering each feature. The feature hierarchy must be formed dynamically as part of the estimation process. While the predefined feature orderings used in the algorithms may be reasonably efficient in typical situations, the optimal feature hierarchy can often be found at negligible cost using the 2DYFOR algorithm. Furthermore, the dynamic feature ordering copes even when the prior knowledge changes significantly—using the original predefined feature ordering may not take full advantage of the additional prior knowledge for increasing search efficiency.
3 Experimental Results
[0160] An exemplary use of this algorithm is in figure registration. Here we attempt to register a 2D Scaled-Prismatic Model (SPM) to a person in a test image, based on known template features. The SPM model is further described in Morris et al., “Singularity analysis for articulated object tracking”, Proc. IEEE Conference Computer Vision and Pattern Recognition, pages 289-296, Santa Barbara, Calif., 1998. A Gaussian probability representation is also used here.
[0161] In our experiments which involve localizing the figure with minimal prior knowledge, the model state is initialized as denoted by the pose of the stick figure in the images of FIGS. 4A and 10B. The prior covariance is set as a diagonal matrix with standard deviations of 50 pixels for global x translation, 20 pixels for global y translation, 2 radians for joint angles and 10 pixels for link lengths. The only strong prior is that the torso is approximately upright as we wish to restrict our search to upright figures. For each template, the basin of attraction for the refinement step is set to be its minimum dimension at present, although a more formal analysis may be applied in the future based on the spatial frequency content of the templates.
[0162] FIG. 10A illustrates the feature ordering that arises in the registration process for the image of FIGS. 4A and 4B. The ordering is indicated alphabetically, “A” indicating the first ordered feature, “B” the second, and so on. The feature ordering obtained in these instances is similar to a size-based ordering, except that in the algorithm employed by the preferred embodiment of the present invention, the ordering is done both automatically and dynamically. The registration localizes the figure well despite the high dimensionality of the figure model and the weak prior knowledge.
[0163] FIGS. 4A and 10B each show the respective initial, or prior states of their kinematic models, represented by stick FIGS. 43, 43A, respectively. Weak generic priors are used in these two test cases. As the coupled dynamic feature ordering algorithm is iterated, the next template feature selected is the one requiring the least amount of search operations for registration. FIGS. 10A and 10C show, in alphabetic order, the feature ordering.
[0164] FIGS. 11A and 11C show the initial models used when various forms of strong prior knowledge are available which is captured in the prior covariance. For the image 43 of FIG. 11A, the feet template positions are accurately positioned; while for the image 43A of FIG. 11C, the front shin template position is accurately positioned. A 5-pixel standard deviation is used for these constraints. The feature ordering for these instances, shown respectively in FIGS. 11B and 11D, differs significantly from the ordering obtained in FIGS. 10A and 10C. Also notice, for example in FIG. 11D, that the optimal feature ordering does not propagate along the articulated chains which contradicts the proposed heuristic of Hel-Or et al.
[0165] In FIG. 11A, the positions of the two foot templates are assumed to be known accurately. In FIG. 11C, the position of the front shin template is known accurately. As can be seen by comparing FIG. 1B with FIG. 10A, and FIG. 11D with FIG. 10C, the feature ordering obtained when strong prior knowledge is available can be significantly different from the ordering with weak generic priors. Although not shown, the initial registration of some feature such as the left leg in the case of FIGS. 11A and 11C can be corrected as more features are integrated into the estimation.
[0166] The first sequence images generally took approximately forty to fifty seconds for the localization, while the second sequence images took approximately five to twenty seconds because of the simpler model used. In both instances the number of samples used for initializing the search of individual templates appears to be significantly more than is necessary, which is due to the conservative estimates for the span of the basins of attraction in the refinement process. More accurate estimates could easily be substituted.
[0167] FIG. 12 is a graph 120 showing quantitative results for a comparison of three different feature orderings using the sequence of FIG. 11D.
[0168] The left bar 121 shows, for weak prior ordering, the number of search operations and computation time required to complete the registration without prior knowledge of the location of the shin. The center bar 123, corresponding to a heuristic ordering, shows the result obtained when the shin position is known, but a heuristic-based fixed ordering of largest to smallest template is used. The right bar 125 shows the result obtained when the shin position is known and the present invention's dynamic feature ordering is used. The result provides empirical evidence that dynamic feature ordering is superior to heuristic-based fixed orderings, especially when partial prior knowledge is available.
4 Use of the Invention
[0169] Since registration is a basic problem in computer vision, an improved registration technique could impact many application domains. In particular, this invention could increase the efficiency of detection and tracking systems, making it possible to use more complex object models or process larger data sets with fixed computational resources.
Computing Optimal Fixed Feature Orderings
[0170] One use of the invention is to automatically precompute fixed feature orderings that have been tuned to a particular class of registration problems. This could be helpful in situations where the cost of computing the optimal feature ordering on-line is prohibitively expensive. It is worth mentioning that this has not been the case for the examples we have considered.
[0171] In a preferred embodiment of this method, a representative training data set consisting of a multiplicity of examples of registration problems is constructed. These examples are chosen to characterize the range of problems that a fixed ordering would need to address. An optimal feature ordering is constructed for each of the examples using the method described above. The matching ambiguities for each distinct feature are compared across the set of optimal feature orders. The result is an average matching ambiguity for each feature. Sorting the feature list on the basis of the average matching ambiguity gives a static feature order. Of course, many alternative schemes for constructing the fixed feature order could be employed.
Application to Visual Tracking
[0172] Tracking systems work by propagating an initial registration between a model and an image target over time. As each new frame arrives, the state of the model is updated in order to maintain its correspondence with the image. Before tracking can take place, the tracker must be initialized by identifying a state that places it in correspondence with an initial image. Subsequent re-initialization may be necessary to recover from failures during tracking.
[0173] Figure tracking is an important task in surveillance, user-interface, and video editing applications. It is challenging due to the complexity of the object model and its large number of degrees of freedom. This is a domain which could particularly benefit from our framework, as evidenced by the experiments in Section 3.
[0174] Tracking using detailed kinematic models of humans is computationally intensive and difficult to run in real-time, and hence simplified models are often used. This invention could enable tracking applications based on more complex models, as well as improve computational performance in tracking with simple models. Improved performance could result from automatically “tuning” the search strategy to the constraints of a particular video clip.
[0175] For example, the limited range of motion of an actor in a TV weather program can be exploited during tracking by registering the torso features first. In contrast, in sports footage such as gymnastics, alternative search orders will be more effective. In tracking a gymnast's performance on the rings, for example, the hands are the most stationary feature and would be registered first. The present invention makes it possible to perform this tuning process automatically, without the need for additional context from the footage itself.
[0176] Furthermore, tracking systems may periodically lose track of the target due to distractors such as shadows, occlusion, and background clutter. Our invention would allow trackers with complex models to be re-initialized efficiently. This would facilitate real-time tracking for applications such as a smart conference room, which could detect and initialize tracking on new entrants as well as reinitialize tracks that become lost when individuals temporarily occlude one another.
Application to Object Detection
[0177] Object detection problems arise in video and image retrieval applications, as well as in military targeting and surveillance problems. These problems are characterized by a wide range of potential sensing cues and demanding computational requirements. Efficient feature ordering could improve performance by choosing features so as to maximize the gain from each sensing operation.
[0178] For example, an interesting problem for image retrieval is the detection of figures in single images. This problem is challenging because of the wide range in human appearance and the lack of motion cues which are present, for example, in video content. A wide range of cues can be employed, including skin and hair color, silhouette edges, texture models for clothing and hair, and template models for faces, hands, and feet. The present invention makes it possible to automatically deduce the correct order in which to apply these cues, based on the contents of a given image.
[0179] While one could imagine building a dynamic feature order by hand for a specific problem like figure detection, the true potential of our invention becomes apparent when you consider the wide range of objects such as cars, buildings, etc. that may be of interest for retrieval purposes. The present invention provides a general mechanism for efficient search that is not limited to a specific type of target.
Additional Embodiments
[0180] While the method of dynamic feature ordering determines the optimal sequence of matching all available features, the total computational cost may exceed the budget allocated. For example, this can happen in a real-time tracking system where registration of the object in each image frame must be achieved within the given frame interval. In this case, as many features as possible are matched within the frame interval, while remaining unmatched features after the frame interval has elapsed are ignored. By using the sequence of dynamically ordered features, the system will match the largest number of features within the frame interval compared to other methods of feature ordering.
[0181] The cost of computing the feature ordering dynamically is typically small compared to the cost of feature matching. However, there may be rare cases when this is not true, or there may be cases when even the small computational cost of dynamic feature ordering cannot be afforded. In these cases, an attempt can be made to predict the optimal feature ordering from example runs of the registration task. Dynamic feature ordering is applied by obtaining the computed feature orderings while executing these example runs, and at the end of the runs storing the computed orderings in a training set.
[0182] The predicted optimal feature ordering can be, for example, the most common feature ordering in the training set, i.e., the mode of the set. This predetermined feature ordering is then used in the actual registration task with zero computational cost, in place of dynamic feature ordering. Learning the predicted optimal ordering from training examples is preferable to using ad hoc heuristics to guess this optimal ordering.
[0183] While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.
Claims
What is claimed is:
1. A method of registering an object model in an image, the object model comprising a plurality of features, the object model described by a model state, comprising:
selecting an unused model feature based initially on a prior state probability model, and subsequently on a propagated state probability model;
searching for a match of the selected model feature to the image to register the feature;
updating the state probability model based on the optimal configuration, the updated state probability model being propagated for a next iteration; and
repeating the steps of selecting, searching and updating.
2. The method of claim 1 wherein selecting an unused model feature comprises:
determining, for each unregistered feature, a number of search operations required to find a match with at least a predetermined probability, wherein a feature requiring a least number of search operations is selected.
3. The method of claim 2, wherein, for each unregistered feature, determining a number of search operations comprises:
determining search regions within a feature space, each search region having an associated probability density, such that a total probability equal to the sum of the search regions' associated probability densities exceeds a predetermined probability, wherein the number of required search operations is based on the found search regions.
4. The method of claim 3, wherein determining search regions comprises:
iteratively finding search regions such that each search region's associated probability density exceeds a predetermined threshold, lowering the predetermined threshold each iteration until the total probability exceeds the predetermined probability.
5. The method of claim 3, wherein searching comprises:
performing feature-to-feature matching, such that the number of required search operations is related to the number of target features located within the search regions.
6. The method of claim 5 wherein the number of features which lie within the search region is based on Mahalanobis distances to potential target features.
7. The method of claim 6 wherein, when target features are approximately uniformly distributed, the number of features is proportional to the search region's size, such that selecting a feature comprises ranking the features according to the sizes of their associated search regions.
8. The method of claim 3 wherein searching comprises:
performing feature-to-image matching, such that the number of required search operations is related to a number of minimally-overlapping volumes having a same size and shape as a basin of attraction associated with the feature, the volumes being sufficient to cover the regions.
9. The method of claim 8, wherein the number of volumes is approximated with a count responsive to eigenvalues and basin of attraction spans, the eigenvalues associated with a covariance matrix associated with the feature search region, and each span based associated with an eigenvector direction.
10. The method of claim 1, wherein the state probability model has a Gaussian distribution.
11. The method of claim 10, wherein the state probability model is propagated using a Kalman filter update step.
12. The method of claim 1, wherein the step of repeating continues only until a predetermined level of certainty in an estimate of the model is achieved, such that some of the available features are not registered.
13. The method of claim 1, further comprising:
providing a training set of registration tasks;
for each registration task, determining an optimal feature ordering by performing the steps of selecting, searching, updating and repeating;
responsive to the optimal feature orderings, determining a fixed ordering; and
registering the object model in the image using the fixed ordering.
14. A system for registering an object model in an image, the object model comprising a plurality of features, the object model described by a model state, comprising:
a selection module which selects an unregistered model feature based initially on a prior state probability model, and subsequently on a propagated state probability model;
a search module which searches the image and finds an optimal configuration for the selected model feature; and
an update module which updates the state probability model based on the optimal configuration, the updated state probability model being propagated to the selection module.
15. The system of claim 14 wherein the selection module comprises:
a matching ambiguity calculator which determines, for each unregistered feature, a number of search operations required to find a match with at least a predetermined probability, the selection module selecting a feature requiring a least number of search operations.
16. The system of claim 15, wherein, for each unregistered feature, the matching ambiguity calculator determines search regions within a feature space, each search region having an associated probability density, such that a total probability equal to the sum of the search regions' associated probability densities exceeds a predetermined probability, and wherein the matching ambiguity calculator computes the number of required search operations based on the found search regions.
17. The system of claim 16, wherein the matching ambiguity calculator determines search regions by iteratively finding search regions such that each search region's associated probability density exceeds a predetermined threshold, lowering the predetermined threshold each iteration until the total probability exceeds the predetermined probability.
18. The system of claim 16, wherein the searching module performs feature-to-feature matching, such that the number of required search operations is related to the number of target features located within the search regions.
19. The system of claim 18 wherein the number of features which lie within the search region is based on Mahalanobis distances to potential target features.
20. The system of claim 19 wherein, when target features are approximately uniformly distributed, the number of features is proportional to the search region's size, such that the feature selection module ranks the features in order corresponding to their associated search regions.
21. The system of claim 16 wherein the searching module performs feature-to-image matching, such that the number of required search operations is related to a number of minimally-overlapping volumes having a same size and shape as a basin of attraction associated with the feature, the volumes being sufficient to cover the regions.
22. The system of claim 21, wherein the number of volumes is approximated with a count responsive to eigenvalues and basin of attraction spans, the eigenvalues associated with a covariance matrix associated with the feature search region, and each span based associated with an eigenvector direction.
23. The system of claim 14, wherein the state probability model has a Gaussian distribution.
24. The system of claim 23, wherein the state probability model is propagated using a Kalman filter update step.
25. The system of claim 14, wherein only some of the available features, sufficient to achieve a predetermined level of certainty in an estimate of the model, are registered.
26. The system of claim 14, wherein for each registration task in a training set of registration tasks, an optimal feature ordering is determined by the selection module, the search module and the update module, and wherein a fixed ordering is determined responsive to the optimal feature orderings, such that the object model is registered in the image using the fixed ordering.
27. A computer program product for registering an object model in an image, the object model comprising a plurality of features, the object model described by a model state, the computer program product comprising a computer usable medium having computer readable code thereon, including program code which iteratively:
selects an unused model feature based initially on a prior state probability model, and subsequently on a propagated state probability model;
searches for a match of the selected model feature to the image to register the feature; and
updates the state probability model based on the optimal configuration, the updated state probability model being propagated for a next iteration.
28. The computer program product of claim 27 wherein, in selecting an unregistered feature, the program code further:
determines, for each unregistered feature, a number of search operations required to find a match with at least a predetermined probability; and
selects a feature requiring a least number of search operations.
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