Edge Detection Method and Apparatus for an Image Processing System

The present invention relates to an image processing system and more particularly to an edge detection method and apparatus of an image processing system using multistate linear threshold logic elements.

In a motion detection system, which is one of the most important application areas of the present invention, is preprocessing is recommended because it can improve the accuracy in detecting motion vectors by removing unwanted factors in the image such as noise. Preprocessing can also reduce the computational load by mapping a full resolution image, usually represented by 8 bits per pixel, to a different type image represented by less than 8 bits per pixel.

Several kinds of preprocessing have been proposed for the above mentioned purpose. For example, Band Extract Representative Point (BERP) Method which was used by Umori et. al in "Automatic Image stabilizing system by Full-Digital Signal Processing", on IEEE Transactions on Consumer Electronics Vol. 36, No.3 published in Aug., 1990, can be thought of as a kind of bandpass filtering method. Although BERP method can efficiently filter out both the extremely high spatial frequency components such as noise and the low frequency components such as the flat area in intensity, it still needs more than two bits per pixel to represent the BERP image. The detected edge information can be represented by one bit per pixel. Accordingly, the edge detection method can simplify the hardware. There are various approaches for edge detection such as: (i) the use of image spatial gradients, (ii) the use of the Laplacian, (iii) the use of differences of averages, (iv) matching or fitting to a prespecified pattern, and (v) the detection of the zero-crossings filtered by the Laplacian of the Gaussian (LOG) in the image. The two major drawbacks of the edge detectors enumerated in (i)-(iv) are that they perform well only with some images and that performance of edge detection is prominently degraded when noise is present. On the other hand, approach (v) reduces the noise effect through the convolution with a Gaussian-shaped kernel. This operation may also improve the connectivity of extracted image and it guarantees that the zero crossings of the second derivative are preserved. However, the LOG operator has the potential drawback that the mask size is not constant and it becomes very large with a large amount of noise.

Accordingly, it is an object of the present invention to provide an edge detection method which can reduce noise without increasing window size.

It is another object of the present invention to provide an edge detection apparatus which can simplify an implementation of hardware and do a real time operation.

To achieve the first object, an edge detection method of the present invention comprises the steps of;

converting the pixel data into a set of multi-state values;

performing an inner product of the set of multi-state values and a set of prespecified values; and making a decision according to the result of said inner product.

To achieve the second object, an edge detection apparatus of the present invention comprises:

a conversion means for converting the input pixel data into a set of multi-state values;

a matching means for performing an inner product of the set of multi-state values and a set of prespecified values; and

a decision means for making a decision according to the result of said inner product.

FIG. 1 is a flow chart which shows the signal flow of an edge detection apparatus of an image processing system according to the present invention.

FIG. 2 is a block diagram showing the edge detection apparatus according to the present invention.

FIG. 3 is a block diagram showing a preferred embodiment of the edge detection apparatus according to the present invention.

FIG. 4 is a block diagram showing the encoding circuit of the edge detection apparatus according to the present invention.

FIG. 5 shows prespecified edge patterns used for the inner product of the present invention.

FIG. 6A is a block diagram for the inner-product W.sub.1 .multidot.V of a matching means of the edge detection apparatus according to the present invention.

FIG. 6B is a block diagram for the inner product W.sub.2 .multidot.V of the matching means of the edge detection apparatus according to the present invention.

FIG. 6C is a block diagram for the inner product W.sub.3 .multidot.V of the matching means of the edge detection apparatus according to the present invention.

FIG. 6D is a block diagram for the inner product W.sub.4 .multidot.V of the matching means of the edge detection apparatus according to the present invention.

FIG. 7 is a truth table for the inner product output of W and V of the edge detection apparatus according to the present invention.

FIG. 8 is a Karnaugh's map for the simplification of the inner product circuit of the edge detection apparatus according to the present invention.

FIG. 9 shows a logic circuit diagram of the absolute value circuit of the matching means of the edge detection apparatus according to the present invention.

FIG. 10 shows a logic circuit diagram of the decision circuit of the edge detection apparatus according to the present invention.

FIG. 11 is a timing diagram for explaining the operation of the edge detection apparatus according to the present invention.

The present invention is based on linear separability of multi-state linear threshold logic which can be explained by the following definition and theorem. Linear separability of binary input has been discussed in P. M. Lewis II and C. L. Coates, Threshold Logic, John Wiley and Sons, 1967. The definition of a linearly separable function of multi-state input is given here first.

Let P be a set of L-dimensional vectors. Each component of any vector in P takes on of M=j+k+1 values in {-j, . . . , -1,0,1, . . . , k}, that is,

Then the maximum number of different vectors in P becomes M.sup.L and we call -j and k the extreme values of the input state. Let P.sub.0 and P.sub.1 be two mutually exclusive subsets of P such that P.sub.0 UP.sub.1 =P.

Given the weight vector w, a logical function F defined by ##EQU1## where .theta. is a threshold value, is of the linearly separable class if and only if

The analysis of multi-state linear separability is in general a complicated task. However, a special class of logical functions, which will be use in the proposed edge detector, can be shown to be linearly separable, according to the following theorem.

Let x be an L-dimensional input vector whose components are all extreme values and let P.sub.1 ={X} and P.sub.0 =P-{X}, i.e.,

P.sub.1 ={X.vertline.X.sub.i .epsilon.{-j, k}, i=1, . . . , L} and P.sub.0 =P-P.sub.1, where P, -j, and k are given in the above definition. Then there exists a linearly separable function F which separates the input vector X from others.

The proof of the above theorem is as follows. We prove this theorem, by using the above definition and showing that there exists a weight vector W which satisfies

Let us consider the following weight vector ##EQU2## Then the following inequality holds

By summing these inequalities for i=1, . . . ,L, we have

because for at least one i, the equality should not hold.

We can also consider a set P.sub.-1 ={-X}, where X and W are defined in the above equation respectively. Then we have a kind of multicategory discriminant function of multi-state inputs such as

In order to use the multi-state linear threshold logic for edge detection, we have to map the continuous intensity value of a pixel to several discrete states.

Let us use an 1.times.1 local window for detecting an edge at a given pixel location. We assume that the image size is n=n.sub.1 Xn.sub.2. Let X.sub.i, i=1, . . . ,n, be the i-th pixel value in the lexicographically ordered image and Z.sub.j, j=1, . . . ,r, the j-the pixel value in the lexicographically ordered pixel values inside the local window centered by Xi, where r=1.times.1. Then for the local window corresponding to X.sub.i, Z.sub.j can be obtained by the mapping

The notation 1/2 denotes the integer part of the resulting division, and i mod 1 equals the value of the residual of the division of the integer i by the integer 1.

After the one dimensional array Z.sub.j is obtained, the local mean corresponding to the i-th pixel is equal to ##EQU3## Then the state for the j-th input to the multi-state linear threshold logic, V.sub.j, is defined by ##EQU4## where .epsilon. is the safeguard against noisy data. The larger the amount of noise to be suppressed, the larger .epsilon. should be.

We define four pairs of bidirectional edges whose directions are 0 and 180, 90 and 270, 45 and 225, and 135 and 315 degrees, respectively. First, a right edge is defined by ascending input states from right to left in the local window. For 1=3, for example, the right edge and its bidirectional counterpart, the left edge, are respectively given by ##EQU5## where x represents the don't care state. The second pair of edges, the upper and the down edges are defined in the same way, that is ##EQU6## The third pair of edges denoted by right-upper and left-down edges are given by ##EQU7## Finally, the pair of edges denoted by left-upper and right-down edges are given by ##EQU8## For 1=5, the riHxt edge, for example, has 1 in the first column, -1 in the last column, and x (don't care) in the remaining columns.

Using the multicategory discriminant function given in the equation both the right and left edges can be detected by the same weight vector, denoted by W.sub.--, because they are composed by extreme values and the left edge is equal to the right edge with the sign inverted. In the same manner, the upper and down edges, the right-upper and left-down edges, and the left-upper and right-down edges are detected by W.sub.1, W.sub./, and W , respectively. As shown by the above described therorem, one possible weight vector for detecting the right or the left edge, for example, for 1=3, is equal to

Clearly, based on this equation, the rest of the weight vectors, that is, W.sub..vertline., W.sub./, and W , can be obtained by appropriately arranging the elements of W.sub.--.

Alternatively, the LMS algorithm can also be used to obtain the weight vector.

Based on the definition of edges given in the previous section, the edge is detected by ORing the outputs of four multi-state linear threshold logic with properly trained weight vectors. The complete edge detection procedure is described by the following algorithm.

1. Choose the size of the local window 1.

2. For i=1, . . . ,n do

2.1 Form Z

2.2 Compute the input state V set V.sub.0 :=1.

2.3 Compute the four inner products, W.sub.--.sup.T V, W.sub..vertline..sup.T V, W.sub./.sup.T V and W.sub. .sup.T V. If at least one of them is greater than or equal to the output threshold .theta., or less than or equal to -.theta., in which case the output of the OR gate is equal to 1, an edge is detected at location i, otherwise, there is no edge.

In implementing the above algorithm, the nonlinear function g(.multidot.) given as following is used, ##EQU9## where .theta. is a threshold value, .theta. was set equal to six when the above weight vector was used.

Regarding the choice of the mask size, the following issues should be taken into account. The larger mask size, better the noise control due to the local averaging operation in step (2.2) in the above algorithm. However, there are two drawbacks in increasing the mask size, that is, (i) it becomes more difficult to detect edges in directions different form 0, 45, 90, 135, 180, 225, 270, and 315 degrees and (ii) since more inputs are needed for the multi-state linear threshold logic, more interconnections and computation are required. The mask size of 1=3 has been shown to be very effective based not only on window is the most sensitive one to edges in any direction, because it is the smallest symmetric window.

FIG. 1 is a flow chart showing a signal flow in the edge detection method according to the present invention. By using FIG. 1, software implementation can directly be realized. In the first step, index i represents the lexicographically ordered pixel position. In the second step, get neighbors, Z.sub.j, j=1, . . . ,m, of the local image pattern centered by an i-th pixel Xi. In the third step, Z.sub.j represents a set of pixels in a local window including the i-th pixel X.sub.i and m the number of pixels in the local window. Also, in the third step, Z.sub.j 's, j=1, . . . ,m, are mapped to corresponding multi-state values V.sub.j, j=1, . . . ,m. In the fourth step, V=[V.sub.1, . . . ,V.sub.m ].sup.T is compared with a prespecified edge patterns, W.sub.1, W.sub.2, W.sub.3 and W.sub.4, respectively. In the fifth step, if V matches at least one among the prespecified edge patterns W.sub.1, W.sub.2, W.sub.3 and W.sub.4, in sixth step, the i-th pixel X.sub.i is decided to be an edge. Otherwise, in the seventh step, the i-th pixel X.sub.i is decided not to be an edge. In the eighth step, if the i-th pixel X.sub.i is not total pixel, in the ninth step, i is increased by 1 and the process returns to the second step and performs a main loop repeatedly. Otherwise, in the eighth step, the operation stops.

FIG. 2 shows a general block diagram of an edge detection apparatus according to the present invention. The construction and function of the apparatus are as follows.

FIG. 2 consists of three blocks, an encoding block for converting the lexicographical ordered data Z.sub.l, . . . ,Z.sub.m into a multi-state V.sub.l, . . . ,V.sub.m after an original image data X.sub.i is ordered lexicographically by using a local window, a matching block for performing an inner-product a multi-state data V.sub.l, . . . ,V.sub.m and the prespecified edge patterns W.sub.1, W.sub.2, W.sub.3 and W.sub.4 corresponding to W.sub.--, W.sub..vertline., W and W , respectively, and a decision block for comparing the respective resulting data of the inner-product with an output threshold value and deciding whether the original image data X.sub.i is an edge or not.

The above three blocks perform functions as follows.

First, a concept of window is needed to decide whether the original image data X.sub.i is an edge or not by correlation of a neighboring pixels. Thus the encoding block arranges the neighboring pixels, Z.sub.1, Z.sub.2, . . . ,Z.sub.m, one-dimensionally and gets a mean value having an intensity value and converts the neighboring pixels, Z.sub.1, Z.sub.2, . . . ,Z.sub.m, into the corresponding multi-state values, V.sub.1, V.sub.2, . . . ,V.sub.m.

If V.sub.j, j=1, . . . ,m, have M-states (M>2), log.sub.2.sup.M is required to represent V.sub.j. The notation log.sub.2.sup.M denotes log.sub.2.sup.M if M is a multiple of 2, and otherwise, it denotes the integer part of log.sub.2.sup.M +1. Here, by inserting the mean value and a noise control parameter .epsilon., the matching block separates the respective pixels into three levels which have a value over mean+.epsilon., a value below mean-.epsilon., and a value between mean+.epsilon. and mean-.epsilon. respectively. Here, the noise reduction effect prominently appears according to the parameter .epsilon..

A matching block outputs the degree of matching of the converted image data and four prespecified edge patterns respectively. That is, the matching block performs the inner product of the converted image data, V.sub.1, V.sub.2, . . . ,V.sub.m, and the respective four prespecified edge patterns, W.sub.1, W.sub.2, W.sub.3, and W.sub.4 which are expected with respect to a horizontal, vertical and two diagonal directions. Here, W.sub.1.sup.T .multidot.V represents the inner product of the converted image data, V.sub.1, V.sub.2, . . . , V.sub.m, and the prespecified edge patterns W.sub.1 which is expected with respect to the horizontal direction.

A real time process can be realized, which is based on the image processing system by performing the operation of the four inner products simultaneously.

A decision block performs a function which compares an output value of the inner products, W.sub.1.sup.T .multidot.V,W.sub.2.sup.T .multidot.V,W.sub.3.sup.T .multidot.V, W.sub.4.sup.T .multidot.V, respectively with a given constant and decides to be an edge if at least one among the output values and the converted image data, V.sub.1, V.sub.2, . . . ,V.sub.m, match. And the given constant for comparing with the output values of the inner products can be controlled by user by using a microcomputer.

FIG. 3 shows of the a preferred embodiment edge detection apparatus according to the present invention. The construction and the function of the apparatus are as follows.

An encoding means comprises a first delay device 10 for outputting one horizontal scanned line delayed signal, a second delay device 20 which is serially connected to the first delay device 10, for outputting two horizontal scanned line delayed signal, a 3.times.3 window circuit 30 for storing nine pixel data in the 3.times.3 local window circuit, a mean calculation circuit 40 for getting a mean value of an eight pixel data except the center pixel in 3.times.3 local window, and a tri-state encoder 50 for separating the respective eight pixel data from three levels by using the mean value and the given value and converting the eight pixel data into codes corresponding to three levels.

A matching means comprises the inner product circuits 60, 61, 62, 63 for performing inner product of the respective prespecified edge patterns, W.sub.1, W.sub.2, W.sub.3 and W.sub.4, and the outputs of the tri-state encoder 50.

A decision means comprises comparators 70, 71, 72, 73 for comparing the outputs of the respective inner product circuit 60, 61, 62, 63 with the given constant and outputting the matching signal, and OR gate for summing logically the outputs of the comparators 70, 71, 72, 73.

FIG. 4 shows a preferred embodiment of the encoding means. The 3.times.3 window circuit 30 comprises three registers 90, 91, 92 respectively including a set of eight parallel connected D-type flip-flops and serially connected to an input terminal for inputting a sequentially scanned digital video signal represented by eight bits, and three registers 100, 101, 102 respectively including a set of eight parallel connected D-type flip-flops and serially connected to an output terminal of the first delay device 10, and three registers 110, 111, 112 respectively including a set of eight parallel connected D-type flip-flops and serially connected to the output terminal of the second delay device 20 for inputting the output signal of the second delay device 20. The 3.times.3 window circuit 120 comprises adders 121, 122, 123, 124 for adding by twos the output signals of the eight registers 90, 91, 92, 100, 102, 110, 111, 112, except the output signal of the one register 101, and adders 130, 131 for adding by twos the signals remaining after discarding the least significant bit LSB from output signals of the adders 121, 122, 123, 124, and an adder 140 for adding signals remaining after discarding on least significant bit LSB from output signals of the adders 130, 131 and for outputting a signal remaining after discarding one least significant bit LSB of its output signal.

The output signals of the eight registers 90, 91, 92, 100, 102, 110, 111, 112 and the output signal of the adder 140 are temporarily stored in registers (not shown) for inputting in the following stage. That is, the mean calculation circuit 120 calculates a means value as follows.

Let Z.sub.1, Z.sub.2, Z.sub.3, Z.sub.4, Z.sub.6, Z.sub.7, Z.sub.8 and Z.sub.9 be the outputs from the registers 90, 91, 92, 100, 102, 110, 111, 112 and A, B, C, D are represented by

Here, let E, F, G, and H be the remaining after discarding one LSB bit of the values A, B, C, D.

Then, E, F, G, and H are represented by ##EQU10## And, let I and J be the outputs of the addition of E and F, and G and H, respectively, such as, ##EQU11## Here, let k and L be the remaining values after discarding LSB from I and J, respectively, then K, L are represented by ##EQU12## And, suppose that the value resulted from adding K and L and discarding one LSB bit of the resultant value is M.

M is represented by ##EQU13## The obtained mean value M is not an exact one. But the difference between the exact mean value and the obtained mean value doesn't degrade the quality of a resulting edge because the obtained mean value is used for tri-state encoding of the following stage.

And, the tri-state encoder circuit 150 comprises the adder 160 for adding the mean value M and a parameter .epsilon. having a noise reduction effect and for producing a value M+.epsilon.; the adder 161 for adding the mean value M and the parameter-.epsilon. and for producing a value M-.epsilon.; a comparators 170 for comparing the respective pixel data, Z.sub.1, Z.sub.2, . . . ,Z.sub.9 except the center pixel data, Z.sub.5, with the value M+.epsilon.; comparators 171 for comparing the respective pixel data, Z.sub.1, Z.sub.2, . . . , Z.sub.9 except the center pixel data, Z.sub.5, with the value M-.epsilon.; and inverters 180 for outputting a most significant bit MSB signals V.sub.11, V.sub.21, . . . , V.sub.91, of the comparators 170; and OR gates for outputting least significant bit LSB signals V.sub.10, V.sub.20, . . . , V.sub.90, of the tri-state signals and logically summing the outputs of the comparators 171. That is, the tri-state encoder 150 outputs a value 11 if the respective pixel data is smaller than the value M-.epsilon., and a value 01 if the respective pixel data are larger than the value M+.epsilon., and otherwise, a value 00. Here, suppose that the most significant bit MSB is a sign bit and the least significant bit LSB is a magnitude bit. Then, the values 11, 00, 01, correspond to the tri-state, -1, 0, 1, respectively.

FIG. 5 shows the four prespecified edge patterns, W.sub.1, W.sub.2, W.sub.3 and W.sub.4.

FIGS. 6A, 6B, 6C, 6D show the circuits for performing the inner products of the matching means of the present invention.

The matching means performs the inner products between two's complement of elements of the respective four prespecified edge patterns, W.sub.1, W.sub.2, W.sub.3 and W.sub.4, and the coverted values, V.sub.11 V.sub.10 V.sub.21 V.sub.20, . . . ,V.sub.91 V.sub.90.

FIG. 7 shows a truth table for the inner product.

FIG. 8 shows a Karnaugh's map for the simplification of the inner product circuit.

The simplified logic equations from FIG. 8 are

These logic equation can be further simplified by using the properties of the four prespecified edge patterns.

First, in case that W.sub.j1 =W.sub.j0 =1,

Second, in case that W.sub.j1 =W.sub.j0 =0,

That is, the inner product output is always "0" regardless of the image data and then doesn't have influence on the resulting edge.

Third, in case that W.sub.j1 =0, W.sub.j0 =1,

As a result, in implementing a hardware, the four prespecified edge patterns exist implicitly, and only tri-state values look like having an influence on the output of the inner product. Also, the obtained inner product outputs are represented by two bits and only six pixels out of nine pixels are used for each matching with a corresponding prespecified edge patterns.

A hardware implementation using the above logic equations is as follows.

First, the matching circuit of W.sub.1 .multidot.V outputs (V.sub.11 .multidot.V.sub.10)V.sub.10, (V.sub.31)V.sub.30, (V.sub.41 .multidot.V.sub.40)V.sub.40, V.sub.61 V.sub.60, (V.sub.71 .multidot.V.sub.70)V.sub.70, V.sub.91 V.sub.90.

Second, the matching circuit of W.sub.2 .multidot.V outputs (V.sub.11 .multidot.V.sub.10)V.sub.10, V.sub.71 V.sub.70, (V.sub.21 .multidot.V.sub.20)V.sub.20, V.sub.81 V.sub.80, (V.sub.31 .multidot.V.sub.30)V.sub.30, V.sub.91 V.sub.90.

Third, the matching circuit of W.sub.3 .multidot.V outputs (V.sub.11 .multidot.V.sub.10)V.sub.10, V.sub.61 V.sub.60, (V.sub.21 .multidot.V.sub.20)V.sub.20, V.sub.81 V.sub.80, (V.sub.41 .multidot.V.sub.40)V.sub.40, V.sub.91 V.sub.90.

Fourth, the matching circuit of W.sub.4 .multidot.V outputs (V.sub.21 .multidot.V.sub.20)V.sub.20, V.sub.41 V.sub.40, (V.sub.31 .multidot.V.sub.30)V.sub.30, V.sub.71 V.sub.70, (V.sub.61 .multidot.V.sub.60)V.sub.60, V.sub.81 V.sub.80.

These logic equations are implemented by using an inverters 200 and a AND gates 210 as shown in FIGS. 6A, 6B, 6C and 6D.

Next, the outputs of the AND gates 210 and the outputs of the inverters 200 in the corresponding matching circuits are added for inner product.

Here, the addition is implemented by using adders 220 because the outputs of the AND gates 210 are represented by two's complement, and by adding an absolute circuit 230 to obtain the same edge result in case that the final value of the addition has a negative value. Also, the addition of the outputs of the AND gates 210 and the outputs of the inverters 200 use sign extension method.

The absolute circuit 230 shown in FIGS. 6A, 6B, 6C and 6D for obtaining the absolute value is shown in FIG. 9 in more detail.

In FIG. 9, suppose that an input data are A.sub.3 A.sub.2 A.sub.1 A.sub.0 and an output data is B.sub.2 B.sub.1 B.sub.0. The absolute circuit 230 consists of OR gate 240 for ORing the input data A.sub.1 and A.sub.0, and NAND gate 250 for providing "0" when the output of the OR gate 240 and the input data A.sub.3 are all "1", NAND gate 260 for providing "0" when the input data A.sub.3 and A.sub.0 are all "1", and EXNOR gate 270 for outputting "1" when the input data A.sub.2 and the output of the NAND gate 250 are not the same values, and EXNOR gate 280 for outputting "1" when the input data A.sub.1 and the output of the NAND gate 260 are not the same values. And the output values of the EXNOR gates 270, 280 and an input data, respectively, become the output B.sub.2 B.sub.1 B.sub.0 of the absolute circuit 230.

FIG. 10 shows a preferred embodiment of the decision means of the edge detection apparatus of the invention. The decision means consists of four comparators 190 input signals, OUT1, OUT2, OUT3, and OUT4 from the matching means and a threshold value "110" of an edge, and two OR gates 300 for ORing the first two output signals of the four comparators 290, and OR gates 300 for ORing the other two output signal of the two OR gates 300. And, if at least one among the output signals, OUT1, OUT2, OUT3 and OUT4 is larger than or equal to "6", the output of the OR gate 310 becomes "1", that is, an edge.

FIG. 11 shows a timing diagram of the operation of the edge detection circuit.

Suppose that the input image data 90, 91, 92, 100, 101, 102, 110, 111, and 112 shown in FIG. 11 are stored in the 3.times.3 window circuit 30. Here, .epsilon. is set equal to 10. And the tri-state values, V.sub.1, V.sub.2, V.sub.3, V.sub.4, V.sub.6, V.sub.7, V.sub.8, V.sub.9, are shown in FIG. 11. Here, the input patterns in the two dotted square areas are equal to the corresponding prespecified edge pattern. That is, the first dotted square area is equal to W.sub.1 and the second dotted square area is equal to W.sub.2. Accordingly, the output signal EDGE becomes "1" when at least one of the output signals, OUT1 and OUT2 is "1".

The edge detection apparatus according to the present invention has the following advantages.

First, by using the present multi-state encoding method, it can greatly reduce noise effect without using additional lowpass filters.

Second, it can greatly reduce noise effect with 3.times.3 neighboring pixels, which is the smallest number of pixels for a two dimensional symmetric local window.

Third, by using several linear threshold logics at the same time it can utilize the rotation invariant properties of multi-layered linear threshold logics.