Hybrid image object tracking method

Abstract

A hybrid image object tracking method contains the steps of; S1: reading a video sequence picture, and performing bounding box selection on an object to be tracked in a picture; S2: filtering all part

Description

FIELD OF TECHNOLOGY

[0001] The present invention relates to the technical field of computer vision object tracking, and in particular to a hybrid image object tracking method. BACKGROUND

[0002] Vision object tracking plays an important role in computational vision, and has been found in various applications such as a man-machine interface, road traffic control, video monitoring and so on. But so far, object tracking is still a challenging problem. In an outdoor environment, because a background and an object may be quite complex and changeable, it will involve some problems such as a brightness change, a scale change, a posture change, background clutter, etc. Visual object tracking is still confronted with challenges.

[0003] At present, many scholars have also done related research on object tracking. For example, Chinese patent CN114998392A discloses a video multi-object tracking method based on particle filtering, which detects an object in the video sequence through deep learning and predicts a position of the object by using a particle filter. Although this method can solve a nonlinear problem of object tracking, what is used for object detection is a YOLO model. Model training needs a large number of prior samples, which becomes infeasible in an unknown environment. And this method does not solve the problem of particle degradation of the filter. Chinese patent CN107273905A discloses an object active contour tracking method with motion information combined. This method mainly uses an active contour tracking result of a previous frame image as an initial contour of curve evolution. Although this method uses superpixels, a tracking framework cannot solve the nonlinear problem of tracking. Chinese patent CN115015907A discloses a particle filter pre-detection tracking method based on sparse representation. Although this method uses a nonlinear framework of the particle filter, it is mainly used for point object tracking, and in terms of the object tracking of a video sequence, the problems of object deformation and scale change cannot be solved.

[0004] From the above researches, it can be found that an existing video object tracking algorithm mainly aims at the object tracking problem under a condition that an image is clear and unobstructed, and cannot solve the object tracking problems in a complex environment including factors such as serious clutter, a low-resolution image, an unstable camera, an uncertain multi-feature and regular object, and the problem of particle degradation. Therefore, a hybrid image object tracking method is urgently needed to solve the above problems. SUMMARY

[0005] The present invention provides a method of hybrid image object tracking, which can deal with the object tracking problems in a complex environment including factors such as serious clutter, a low-resolution image, an unstable camera, a multi-feature and regular object s, etc.

[0006] In order to achieve the above objectives, the present invention provides the following technical solution: a computer implemented method of hybrid image object tracking including the following steps:

[0007] SI: reading a video sequence picture, and performing bounding box selection on an object to be tracked in the picture;

[0008] S2: filtering all particles in the object region with preset threshold parameters, and establishing a rough initial object contour around the remaining particles by using an a-shape method;

[0009] S3: evolving the initial object contour through a C-V algorithm, wherein

[0010] a Hausdorff distance is calculated to measure a boundary contour similarity between a candidate contour and the initial contour of the object;

[0011] a mean value and a histogram based on a signed distance function <p are calculated for the candidate contour, and a mean value likelihood and a histogram likelihood are calculated;

[0012] a current candidate object velocity vector is obtained by smoothing a past velocity vector, and a velocity vector similarity between the candidate contour and the initial contour of the object is calculated; and

[0013] the contour with a largest likelihood value is selected as a final object contour in combination with a boundary contour similarity, a mean value likelihood, a histogram likelihood and a velocity vector similarity.

[0014] Preferably, in step S2, all particle weights in the object region are calculated, and all the weight particles are filtered by the threshold parameters, the particles with the weights greater than the threshold parameters are retained, and the remaining particles are discarded.

[0015] Preferably, the calculation of the weights of the particles specifically includes:

[0016] initializing the particles and endowing each particle with an initial coordinate value;

[0017] performing state transition on the initial particles by using a state transition equation, to generate a particle state at next time;

[0018] setting a coverage region of the particle with a position of the particle state at the next time as a center, and calculating the pixel gray level histogram of the color space corresponding to the coverage region;

[0019] calculating a pixel gray level histogram of the object region, calculating a Bhattacharyya coefficient value between the pixel gray level histogram of the coverage region and the pixel gray level histogram of the object region, taking the Bhattacharyya coefficient value as a weight of the corresponding particle, and repeating a particle weight calculation process until all particle weights are calculated.

[0020] Preferably, an object region and a background region with twice object area are taken as a calculation region, R. G, B, RGB, H, S, V and HSV spaces are selected as candidate features, the space with a largest block ratio value is determined as a feature space, the color space is taken as a histogram region, and a gray level pixels histogram is made for the color feature region, thereby obtaining a pixel gray level histogram of the object region;

[0021] Preferably, in step S3, the C-V algorithm is specifically as follows: E(C, q,c2) = fiLength(C) + vArea(inside(C')) +2 I I(x, y) — c, I2 dxdy + 2, I I(x, y)-c7 I2 dxdy yJinsid^cY 1 'AoutsiMeY

[0022] where, C is an active contour curve; gLength(C) is a length of a closed contour curve, and vArea(mside(Cy) is an area term of an internal region surrounded by the closed contour curve, which together constitute internal energy of the model and keep the smoothness of the curve in an evolution process; g = 1 , v >0 and ^=^ = 1 are determined parameters; Cr represents a mean value of gray levels of pixels in the initial contour of the object; C2 represents a mean value of gray levels of remaining pixels in a part of a region with an area two times that of the initial object contour region, with the initial object contour region being removed from the region.

[0023] Preferably, in step S3, the boundary contour similarity is calculated as follows: D(A,B) = max(h(A,B),h(B,A)'):

[0024] where, h(A,B) = maxmin\\a — b\\, h(B,A) = max min\\b — a\\; a£A bEB bGB a£A

[0025] a contour similarity is defined as: Lcontour(ycontow.|x) oc exp( - DtCcan'C°b^ ; Ccan and Cobj represent a candidate contour and an object contour respectively; and ad 's a Gaussian variance.

[0026] Preferably, in step S3, the calculation of the mean value likelihood and histogram likelihood includes:

[0027] firstly, integrating a signed distance into each pixel: w0 (*, y) = m0 Cf J;) * eWO> y));

[0028] then calculating the mean value likelihood and the histogram likelihood: —2 ^meanCYmecml-^) GXp( 2 ), mean

[0029] where, = mean(uAx,y)), u^x^) represents a contour inner region; ffmean is a mean value likelihood variance. Lhist(.ytiist\x) 6Xp( — 2 ), ^hist

[0030] where, p represents a Bhattacharyya coefficient of the histogram. is a histogram likelihood variance.

[0031] Preferably, in step S3, the calculation of the velocity vector similarity includes: v*mv LveiocitytyM K exp(sign(v • mv)) * exp{ -

[0032] where, "v represents the current velocity vector and mv represents a mean value of the past N velocity vectors.

[0033] Preferably, a nonparametric Parzen window density estimator is used to estimate continuous state distribution of particles in the object contour; 1 1 x-x, TV j — [ fl fl

[0034] where, N represents a number of samples, K represents a kernel function and hN is a bandwidth of the kernel function; x is an independent variable of the function expression, j represents a certain position in a discrete space, and Xj is a particle sample number.

[0035] Preferably, a Dirac 8 kernel is replaced by a general kernel, and the particles are resampled from a continuous state space by a stratified sampling strategy.

[0036] Compared with the prior art, the present invention has the beneficial effects that:

[0037] 1. A traditional video object tracking algorithm mainly aims at the object tracking problem under a condition that an image is clear and unobstructed, and cannot solve the object tracking problems in a complex environment including factors such as serious clutter, a low-resolution image, an unstable camera, an uncertain multi-feature and regular object. In view of this situation, the present invention provides a novel hybrid image object tracking method. The present invention is not a simple addition of two algorithms, but an endogenous mechanism that conforms to mutual promotion, that is, particle filtering and the active contour are mutually improved and promoted in algorithm, and the object tracking performance is improved; the particle filtering is selected to estimate an object state vector of a non-Gaussian nonlinear system, and the object contour is initialized by weight particles; a geometric active contour is used to solve local deformation and topological structure changes of a deformed object, and results of curve evolution are used to eliminate invalid particles to maintain the diversity of resampled particles.

[0038] 2. The present invention is different from the prior art in that the present invention adopts the following key steps: (1) the object differential histogram is defined by the present invention, and this histogram is used to calculate the similarity of statistical characteristics of the object; the object region and the background region with an area two times that of the object region are taken as the calculation region, eight color spaces such as R, G, B, RGB, H, S, V and HSV are selected as candidate features, the space with the largest block ratio value is determined as the feature space, and the color block region is taken as the histogram region; (2) boundary initialization is performed, wherein the particles are filtered by a threshold value, and a rough object initial contour is established around the remaining particles by using an a-shape method; (3) multi-clue likelihoods are calculated, wherein single likelihoods based on the mean value, based on the histogram, based on the boundary contour and based on the velocity vector are calculated respectively, and then the mixed similarity is calculated; and (4) particle resampling based on evolution curve is performed. An object curve contour is evolved through a C-V algorithm, wherein the contour of the object divides the particles into two types, namely contour inside particles and contour outside particles; the continuous state distribution of the object particles is estimated by using the nonparametric Parzen window density estimator; the particles are resampled from a continuous state space by adopting a stratified sampling strategy. Therefore, the robustness of object tracking in the low-resolution complex environment is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this description, illustrate embodiments of the present invention and together with embodiments of this description serve to explain the principles of the present invention and not to limit the present invention.

[0040] In the drawings:

[0041] Fig. 1 is an overall flow chart of the present invention. DESCRIPTION OF THE EMBODIMENTS

[0042] The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it should be understood that they are presented herein only to illustrate and explain the present invention and not to limit the present invention.

[0043] Embodiment: As shown in Fig. 1, a hybrid image object tracking method includes the following steps:

[0044] 1. Selecting an object

[0045] Firstly, a video sequence picture is read, and an object to be tracked in the picture is manually selected with a rectangular box.

[0046] In this embodiment, let Ro represent an object region with C as an object center and with a width of w and a height of h; Rb represents a background region centered on C, with a width of 2w and a height of 2h, but the Ro region should be removed.

[0047] 2. Calculating an object differential histogram, that is, a gray level histogram of the object

[0048] In this embodiment, a number of histogram containers is set to B=8, 8 spaces such as R, G, B, RGB, H, S, V and HSV are selected as candidate feature spaces, the space with a highest block ratio value is selected as a final color feature space, and a calculation formula is as follows: . , ,obhist(i) max = arg max (-----— kbins bghist(j) ) bins = [1,2,...B] ;

[0049] where, obhist and bghist respectively represent an object frequency histogram and a background frequency histogram; after a container value corresponding to the color space is selected, a gray level histogram is calculated for pixels in the container value, and the gray level histogram serves as an object feature.

[0050] 3. Performing particle initialization

[0051] In this embodiment, N (which is equal to 150) particles are randomly and evenly distributed in a region with a center of C and a radius of r (r is generally greater than a maximum value of w or h, but less than a whole image size), with a weight oy of each particle being and a state of each particle being a current coordinate value.

[0052] 4. Performing state prediction of particles

[0053] The particles generated in step 3 are subjected to state prediction, and a particle at time t is subjected to state transition by using a state transition equation to generate a particle state at next time (t+1), namely Xt+1 = TXt + dt * <a(t), which is a new state;

[0054] where, dt=l, a>(t) is Gaussian white noise with a mean value of 0 and a variance of a2, and a state variable and a state transition matrix are X = [x,y,x,y] and T = 1 0 0 .0 0 1 0 0 1 0 1 0 0 1 0 1. respectively; x and y are coordinate axis values of the particle in an image coordinate system. x,y are particle velocities in the corresponding coordinate system.

[0055] 5. Performing particle weight calculation

[0056] A position of each particle at current time (t+1) is taken as a center, a particle coverage region with a width of w and a height of h is obtained, and then a pixel gray level histogram of a corresponding color space of the region is calculated; a Bhattacharyya coefficient value between the current histogram and the object histogram is calculated, and is taken as the particle weight; a particle weight calculation process is repeated until weights of the N particles are calculated completely; and

[0057] in this embodiment, all the obtained weight particles are filtered by a threshold parameter p = 0.5, and the particles with weights greater than p are retained and the remaining particles are discarded.

[0058] 6. Performing boundary initialization

[0059] For the retained particles, adjacent points of a convex hull boundary are determined by an a - shape method according to their particle coordinates, and then the adjacent points of the boundary are connected by line segments to form a polygon; according to the variance c2 of particle distribution, an a - shape model parameter is set as a = so that a real object boundary can be approached by using an adaptive method; and the polygon is a rough initial contour established around the object.

[0060] 7. Performing curve evolution based on a C-V algorithm

[0061] The C-V algorithm is specifically as follows: E(C, c,, c2) = fiLength(C) + vArea(inside (C)) +2 | I(x,y)-c{ |2 dxdy + 22 | I(x,y)—c212 dxdy ]Jinside(c) Joutsiddc)

[0062] where, C is an active contour curve; pLength(C) is a length of a closed contour curve, and vArea(mside(Cy) is an area term of an internal region surrounded by the closed contour curve, which together constitute internal energy of the model and keep the smoothness of the curve in an evolution process; p = 1 , v >0 and ^ = ^ = 1 are determined parameters; Q represents a mean value of gray levels of pixels in the initial object contour; C2 represents a mean value of gray levels of remaining pixels in a part of a region with an area two times that of the initial object contour region, with the initial object contour region being removed from the region; inside refers to an interior of the curve, outside refers to an exterior of the curve, dxdy refers to an integral variable, and E refers to an energy function.

[0063] In the process of curve evolution, a definition domain of the curve is located in the whole image, and ranges of Q and C2 are also the whole image. The performance of image segmentation mainly depends on the accuracy of Q and C2. In this embodiment, dynamic Cx and C2 are replaced by calculating a static statistical mean value of a local region.

[0064] 8. Performing likelihood calculation based on multiple clues

[0065] Since the C-V algorithm model generates a large number of redundant contours and the object segmentation will undergo processes of splitting and merging, a fusion strategy based on multiple clues is used to obtain the most similar object contour. The strategy specifically includes:

[0066] calculating a Hausdorff distance to measure a similarity between a candidate contour (a current contour) and an object contour (an object contour calculated in a previous frame): D(A,B) = max(h(A,B),h(B,A));

[0067] where, D represents the calculated Hausdorff distance; max represents a maximum value taken; min represents a minimum value taken; A and B represent two sets of elements, - max minlla - fell and h(B,A) - max minllb - all; a represents a position aeA bEB beB aeA r r element in set A; and b represents a position element in set B.

[0068] A contour likelihood is defined as: Lcontour(ycontour|%) <x exp{ - D(Ccan^ob^ • 2°c Ccan and Cobj represent a candidate contour and an object contour respectively; ac is a Gaussian variance; D is the Hausdorff distance; oc represents being in direct proportion to, and the following same symbols have the same meanings. The larger the value of Lcontour is, the more similar the candidate contour is to an object template contour, and the greater the possibility that the candidate contour is a real object contour.

[0069] Calculation of mean value likelihood and histogram likelihood: since the contour may be any shape and a kernel distance is inconvenient to calculate any shape, the kernel distance is replaced by a signed distance function to reduce the influence of boundary pixels;

[0070] firstly, a signed distance is integrated into each pixel: (x,y) = u0(x,y)*exp«r,y));¢)(x, y) is the signed distance function, u0(x,y) on a right side of the formula is a pixel gray value of the corresponding position, and u0(x,y) on a left side is a pixel integrated with spatial position information; exp is a natural constant e, exp() is an exponential function of the natural constant e, and all exp below have the same meaning;

[0071] then the mean value likelihood Lmean and the histogram likelihood Lhist are calculated: —2 ^meanCfmeanlx) ), mean

[0072] where, Cr = mean(ui(x,y)), ur(x,y) represents a contour inner region, and &mean is a mean value likelihood variance, which is given according to actual situations; x is a current image, ymean is a mean value of pixels in the currently selected contour region; Lmeantymean\x) is a conditional probability expression, which is an expression form to implement the unity of a likelihood formula; a real calculated value is calculated by the exp expression after the direct proportional sign «=; Lhist&histlx) ^expt~ ^hist

[0073] where, p represents a Bhattacharyya coefficient of the histogram and a^ist is a histogram likelihood variance, which is given according to actual situations. In the above formula, x is a current image and yhlst is a histogram calculated in the currently selected contour region; LhjSt(yhiSt|x) is a conditional probability expression, which is an expression form to implement the unity of a likelihood formula; a real calculated value is calculated by the exp expression after the direct proportional sign 00;

[0074] a current object velocity vector is obtained by smoothing the past velocity vector; then the current velocity vector is applied to calculate a velocity vector likelihood Lvelocity of the candidate contour and the object contour: v*mv LveiocitytyM x exptsigntv • mv)) * expt - ^r);

[0075] where, 1? represents the current velocity vector; mv represents a mean value of the past N velocity vectors; x represents a current image; yv represents a current contour velocity of the current object; sign is a sign function, with a value of 1 or -1; and represents a velocity likelihood variance, which is given according to actual situations.

[0076] In the above, by combining the velocity vector likelihood and the other three likelihoods, the final object likelihood is calculated and obtained: ifrtkt) — ^contour * ^velocity * ^hist * ^mean’

[0077] A contour with a maximum likelihood value is selected as the final object contour. The final object contour region is a tracking result of an object tracking algorithm.

[0078] A mean value of coordinates of all pixels contained in the contour curve is calculated, and this mean value is taken as a final contour center coordinate, and a coordinate position of a contour center replaces a state estimation method of summing the products of particle states and particle weights and serves as a final output value of state estimation.

[0079] 9. Performing particle filter resampling and state estimation based on the contour

[0080] A nonparametric Parzen window density estimator is used to estimate continuous state distribution of object particles in the object contour; 1 1 x — x- TV j—[ rl fa

[0081] where, N represents a number of samples, K represents a kernel function and hN is a bandwidth of the kernel function; where, N represents a number of samples, x is an independent variable of the function expression, j represents a certain position in a discrete space, and xj is a particle sample number;

[0082] where, in order to approximate posterior probability distribution more effectively, a Dirac 8 kernel is replaced by a general kernel, and the particles are resampled from a continuous state space by a stratified sampling strategy.

[0083] Finally, it should be explained that the described above are only preferred embodiments of the present invention, and not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, it is still possible for a person skilled in the art to modify the technical solutions recited in the foregoing embodiments or to replace some of the technical features with equivalents. Any modification, equivalent substitution, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A computer implemented method of hybrid image object tracking, the method comprising:S1: reading a video sequence picture, and performing bounding box selection on an object to be tracked in a picture;wherein, an object differential histogram is calculated by: taking an object region and a background region with an area two times that of the object region as a calculation region, selecting R, G, B, RGB, H, S, V and HSV spaces as candidate feature spaces, determining the space with a largest block ratio value as a feature space, taking the feature space as a histogram color space region, and making a gray level histogram for pixels in the histogram region, to obtain a pixel gray level histogram of the object region;S2: filtering all particles in the object region with preset threshold parameters;wherein, weights of all particles of the object region are calculated, and all the weight particles are filtered by the threshold parameters, the particles with the weights greater than the threshold parameters are retained, and the remaining particles are discarded:the calculation of the weights of the particles specifically comprises:initializing the particles and endowing each particle with an initial coordinate value;performing state transition on the initial particles by using a state transition equation, to generate a particle state at next time;setting a coverage region of the particle with a position of the particle state at the next time as a center, and calculating the pixel gray level histogram of the color space corresponding to the coverage region;calculating a pixel gray level histogram of the object region, calculating a Bhattacharyya coefficient value between the pixel gray level histogram of the coverage region and the pixel gray level histogram of the object region, taking the Bhattacharyya coefficient value as a weight of the corresponding particle, and repeating a particle weight calculation process until the weights of all particles are calculated completely;establishing a rough initial contour of the object around the remaining particles by using an a-shape method, which specifically comprises the steps that:for the retained particles, adjacent points of a convex hull boundary are determined by the a - shape method according to their particle coordinates, and then the adjacent points of theboundary are connected by line segments to form a polygon; according to the variance a2 of particle distribution, an a - shape model parameter is set as a = and the polygon is a rough initial contour established around the object;S3: evolving the initial object contour through a C-V algorithm, whereina Hausdorff distance is calculated to measure a boundary contour similarity between a candidate contour and the initial object contour;a mean value of the pixels inside object contour and a histogram based on a signed distance function <p are calculated for the candidate contour, and a mean value likelihood and a histogram likelihood are calculated;a current candidate object velocity vector is obtained by smoothing a past velocity vector, and a velocity vector similarity between the candidate contour and the initial object contour is calculated; andthe contour with a largest likelihood value is selected as a final object contour in combination with a boundary contour similarity, a mean value likelihood, a histogram likelihood and a velocity vector similarity; andS4: estimating continuous state distribution of particles inside the object contour by using a nonparametric Parzen window density estimator;1 1 x-x.Jy ,^i n ft. / —*where, N represents a number of samples, K represents a kernel function and hN is a bandwidth of the kernel function; x is an independent variable of the function expression, j represents a certain position in a discrete space, and Xj is a particle sample number;a Dirac 8 kernel is replaced by a general kernel, and the particles are resampled from a continuous state space by a stratified sampling strategy.

2. The method according to claim 1, wherein in step S3, theC-V algorithm is specifically as follows:E(C, q, c2) = ^iLength(C) + vArea{inside (C))+2 I | I(x, y) - q |2 dxdy + | | I(x.y) c2 |2 dxdy£ Joutsiddt )where, C is an active contour curve; pLength^C) is a length of a closed contour curve,and vArea^inside^Q) is an area term of an internal region surrounded by the closed contour curve, which together constitute internal energy of the model and keep the smoothness of the curve in an evolution process; = 1, v >0 and = d2 = 1 are determined parameters;represents a mean value of gray levels of pixels in the initial object contour; C2 represents a mean value of gray levels of remaining pixels in a part of a region with an area two times that of the initial object contour region, with the initial object contour region being removed from the region; inside refers to an interior of the curve, outside refers to an exterior of the curve, dxdy refers to an integral variable, and E refers to an energy function.

3. The method according to claim 1, wherein in step S3, the boundary contour similarity is calculated as follows:D(A,B) = max(h(A,B),h(B,AJ);where, h(A,B} = max min\\a - b\\, MB.A} = max min\\b — all; aEA bEB bEB aEAD represents the calculated Hausdorff distance; max represents a maximum value taken; min represents a minimum value taken; A and B represent two sets of elements; a represents a position element in set A; b represents a position element in set B;a contour similarity is defined as: Leontour(ycontour\x) <x exp( - D(Ccan’^ob^ ■ ccatl and Cob]- represent a candidate contour and an object contour respectively; and <tc2 is Gaussian variance;D is a Hausdorff distance; « represents being in direct proportion to; the greater the value of Lcontour is, the more similar the candidate contour is to an object template contour, and the greater the possibility that the candidate contour is a real object contour.

4. The method according to claim 1, wherein in step S3, thecalculation of the mean value likelihood and the histogram likelihood comprises:firstly, integrating a signed distance into each pixel: u0(x, y) = u0(x,y) * exp(^(x,y)) ;where, u0(x,y) on a right side of the formula is a pixel gray value of the corresponding position, and u0(x,y) on a left side is a pixel integrated with spatial position information; exp is a natural constant e, and cxp() is an exponential function of the natural constant e; andthen calculating the mean value likelihood and the histogram likelihood:—2Lmeantymeanlx) 6Xp( 2 ),meanwhere, = mean(u1(x,y')), u^x^) represents a contour inner region; dmean is a mean value likelihood variance; x is a current image, ymeari is a mean value of pixels in the currently selected contour region; imean(y,nra is a conditional probability expression, which is an expression form to implement the unity of a likelihood formula; a real calculated value is calculated by the exp expression after the direct proportional sign 0(2;LhistCyhist 1-^) — 2 )»^histwhere, p represents a Bhattacharyya coefficient of the histogram and is a histogram likelihood variance; x is a current image, and yhist is a histogram calculated in the currently selected contour region; Lhist(yhist\x') is a conditional probability expression, which is an expression form to implement the unity of a likelihood formula; a real calculated value is calculated by the exp expression after the direct proportional sign .

5. The method according to claim 1, wherein in step S3, thevelocity vector similarity is calculated as follows:LVeiocity(yv\x) K exp(sign(v • mv)) * exp( - ^J);where, v represents the current velocity vector; mv represents a mean value of the past N velocity vectors; x represents a current image; yv represents a current object contour velocity; sign is a sign function, with a value of 1 or -1; and o„ represents a velocity likelihood variance.

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