- Email: [email protected]
Contour extraction of gait recognition based on improved GVF Snake model
Computers and Electrical Engineering 38 (2012) 882–890
Contents lists available at SciVerse ScienceDirect
Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
Contour extraction of gait recognition based on improved GVF Snake model q Fan Zhang a,b,⇑, Xinhong Zhang c, Kui Cao b, Rui Li b a
Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475001, China College of Computer and Information Engineering, Henan University, Kaifeng 475001, China c Computing Center, Henan University, Kaifeng 475001, China b
a r t i c l e
i n f o
Article history: Received 13 July 2010 Received in revised form 13 March 2012 Accepted 13 March 2012 Available online 7 April 2012
a b s t r a c t Contourlet transform can be used to captures smooth contours and edges at any orientation. In order to solve the initial active contour problem of Snake model, Contourlet transform is introduced into the GVF (Gradient Vector Flow) Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. The multi-scale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. Firstly, the contours of the object in images can be obtained based on Contourlet transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. Experimental results show that the proposed method can extract the edge feature accurately and efficiently. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Feature extraction and description is the key steps for gait recognition. How to extract the motion contour effectively is most important in the gait recognition, and it is the main point of this paper. Currently, the main methods of motion segmentation and contour extraction include background subtraction method [1], frame difference method and approximate motion field method [2]. The frame difference method is the most commonly used method, which is fast but sensitive to noise. Some researches have been done and have received good segmentation results through combining the background subtraction method and the frame difference method [3,4]. The feature extraction methods of gait recognition include ellipse model method [5] and graph model method [6] etc. The ellipse model method expresses different parts of binary image of human profile using ellipses. The graph model expresses different parts of human body using curves, and it tracks the angle-swing of every part of human body in the image sequence and takes the angles as the feature for gait recognition. The matching algorithms of gait recognition include Dynamic Time Warping (DTW) and Hidden Markov Model (HMM) etc. The DTW can complete pattern matching when the test sequences and reference sequences are not accordant. DTW is widely used in speech recognition fields. Hidden Markov model is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters from the observable parameters. The extracted model parameters can then be used to perform further analysis, for example for pattern recognition applications. Active contour model is also a powerful tool to solve the contour extraction in gait recognition [7].
q
Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.
⇑ Corresponding author at: Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475001, China. E-mail address: [email protected] (F. Zhang). 0045-7906/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compeleceng.2012.03.007
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2. Active contour model Active contour model, also called snakes, is a framework for delineating an object outline from a possibly noisy 2D image [8]. This framework attempts to minimize an energy associated to the current contour as a sum of an internal and external energy. The external energy is supposed to be minimal when the snake is at the object boundary position. The most straightforward approach consists in giving low values when the regularized gradient around the contour position reaches its peak value. The internal energy is supposed to be minimal when the snake has a shape which is supposed to be relevant considering the shape of the sought object. The most straightforward approach grants high energy to elongated contours (elastic force) and to bended/high curvature contours (rigid force), considering the shape should be as regular and smooth as possible. In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model to restrict the shape range to an explicit domain learned from a training set. Snakes have multiple advantages over classical feature attraction techniques. Snakes are autonomous and self-adapting in their search for a minimal energy state. They can be easily manipulated using external image forces. They can be made sensitive to image scale by incorporating Gaussian smoothing in the image energy function. They can be used to track dynamic objects in temporal as well as the spatial dimensions. However, the traditional Snake model has some drawbacks. (1) Initialization. The initial curve must be placed close to the object boundary. The initial curve and the desired object boundary differ greatly in size and shape. The model must be reparameterized dynamically to recover the object boundary. This process requires some additional computation. (2) Minimization. A local minimum of energy, such as spurious edges caused by noise, may stop the evolution of the snake unexpectedly. (3) Topology. This method is difficult when dealing with topological changes. If multiple objects appear in the image and an initial curve surrounds them, all the objects cannot be detected. Additional splitting and merging approaches are needed to solve this problem. These increase the complexity of the snake implementation significantly [9–11]. Snake models minimize the energy functional and restrain to the target object contour. A traditional snake is a curve XðsÞ ¼ ðxðsÞ; yðsÞÞs 2 ½0; 1 , its minimizing energy function is as follows,
E¼
Z
1 0
1 ½ajX 0 ðsÞj2 þ bjX 00 ðsÞj2 þ Eext ðXðsÞÞds; 2
ð1Þ
where a and b are parameters which control the snake’s tension and rigidity respectively. The first term is the internal force, which controls the curve changes, while the second term Eext is the external force, which pulls the curve to desired features. Different Eext can be constructed in different models. To analyze the movement of snake model curve from the aspect of force balance, the minimized E of a snake musta satisfy the Euler equation:
aX 00 ðsÞ bX 0000 ðsÞ rEext ¼ 0: To add additional flexibility to the snake model, it is possible to start from the force balance equation directly, F int þ where F int ¼ aX 00 ðSÞ bX 0000 ðSÞ and F 1ext ¼ rEext . As the Snake contour is dynamic, the XðsÞ can be viewed as the function of t and s , then,
X t ðs; tÞ ¼ aX 00 ðsÞ bX 0000 ðsÞ rEext :
ð2Þ F 1ext
¼0,
ð3Þ
Once getting solution of the Eq. (3), we will find a solution of Eq. (2). 3. GVF Snake model Snake model is sensitive to the initial position. An initial contour should be placed close to the real contour, otherwise the result is often unsatisfied. Continuous image information is often used to obtain the initial contour of an image when Snake model is used in the image sequences. But sometimes the initial contour is not close to the true profile. As the traditional Snake model is difficult to determine the contours of the initial position and to deal with topological changes, Xu et al. proposed GVF (Gradient Vector Flow) concept [12,13]. The snake is developed based on new type of external field, called Gradient Vector Flow, or GVF. This computation causes diffuse forces to exist far from the object, and crisp force vectors near the edges. Combining these forces with the usual internal forces yields a powerful computational object: the GVF snake (2D), or the GVF deformable model (N-D). Even though this snake is started far from the object, it still gets attracted towards the object. Especially, GVF active contours can handle broken object edges and subjective contours. The GVF external forces are what make snake inherently different from previous snakes. Because the GVF forces are derived from a diffusion operation, they tend to extend very far away from the object. This extends the ‘capture range’ so that snakes can find objects that are quite far away from the snake’s initial position. This same diffusion creates forces which can pull active contours into concave regions. Because of this property, they cannot be derived from the energy minimization framework of traditional snakes. In [14], the GVF (Gradient Vector Flow) field replaces the potential force field in Eq. (3). Defining a new snake, GVF Snake, is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. GVF Snake has
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the better performance than snake in many fields. GVF Snake expands the capture region of the curve, and can force the curve into the concave regions. Assuming f ðx; yÞ is the contour image of a grayscale image Iðx; yÞ , then rf is the vector field. If rf is iterative diffused to the edge of image, it will form a gradient vector flow field (GVF), Vðx; yÞ ¼ ðuðx; yÞ; v ðx; yÞÞ . Then we minimize the energy function of contour. The energy function is as follows,
e¼
ZZ
lðu2x þ u2y þ v 2x þ v 2y Þþ j rf j2 j V rf j2 dxdy:
ð4Þ
The parameter l is the control parameters, which is set according to the image noise. The parameter l provides the tradeoff between the first part and the second part of the energy function. When rf is small, the curve is away from the target edge, the partial derivatives dominate the energy function. When rf is large, the energy is mainly depends on the second term of the integrand. Energy minimization is achieved by iterative approximation to the target edge, and the following Euler equations must be satisfied:
lr2 v ðv fy Þðfx2 þ fy2 Þ ¼ 0:
ð5Þ
lr2 u ðu fx Þðfx2 þ fy2 Þ ¼ 0:
ð6Þ
2
where r is the Laplacian operator. fx2 þ fy2 is the maximum in edge regions, and is zero in homogeneous regions. So this can be controlled edge gradient only in the boundary, and it will avoid the effect of the diffusion weaken. Eqs. (5) and (6) can be solved by view u and v as the function of time t , then,
u ¼ lr2 uðx; y; tÞ ½uðx; y; tÞ fx ðx; yÞ ½fx ðx; yÞ2 þ fy ðx; yÞ2 : 2
v ¼ lr v ðx; y; tÞ ½v ðx; y; tÞ fy ðx; yÞ ½fx ðx; yÞ 2
2
2
þ fy ðx; yÞ :
ð7Þ ð8Þ
2
Let div ½cðj rU jÞrU replaces r u and r v of GVF Snake in Eqs. (5) and (6). It is an improved GVF Snake model. A nonlinear diffusion function is added between the divergence operator and the gradient operator to control the diffusion.
cðj rU jÞ ¼ exp
j rUj2
! ð9Þ
:
K2
where U is the edge gradient image, K is the gradient sensitivity parameter. In the same size gradient regions, the smaller K represents the slow diffusion, otherwise the strong diffusion. In particular, the performance of the method is superior to GVF Snake in narrow concave boundary specially. Then the new anisotropic diffusion model can be build, the Euler equation is as follows,
" u ¼ l div ½cðj ru jÞru 1 exp
j fx2 þ fy2 j2
"
v ¼ l div ½cðj rv jÞrv
1 exp
K2 j fx2 þ fy2 j K2
!# ðu fx Þ:
ð10Þ
!# 2 ðv fy Þ:
ð11Þ
4. Contourlet transform The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In 2002, Do and Vetterli proposed a ‘true’ two-dimensional transform, Contourlet transform, which is called pyramidal directional filter bank [15,16]. The resulting image expansion is a directional multiresolution analysis framework composed of contour segments, and thus is named Contourlet. This will overcome the challenges of wavelet and curvelet transform. Contourlet transform is a double filter bank structure. It is implemented by the pyramidal directional filter bank (PDFB) which decomposes images into directional subbands at multiple scales. In terms of structure the Contourlet transform is a cascade of a Laplacian pyramid and a directional filter bank. In essence, it first uses a wavelet-like transform for edge detection, and then a local directional transform for contour segment detection. The Contourlet transform provides a sparse representation for two-dimensional piecewise smooth signals that resemble images. Fig. 1 shows that Contourlet transform can captures smooth contours and edges at any orientation. Contourlet coefficients of natural images exhibit the following properties: 1. 2. 3. 4.
Non-Gaussian marginally. Dependent on generalized neighborhood. Conditionally Gaussian conditioned on generalized neighborhood. Parents are (often) the most influential.
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Fig. 1. Contourlet transform can captures smooth contours and edges at any orientation.
Fig. 2. The transform decouples the multiscale and the directional decompositions.
The Contourlet transform expresses image by first applying a multi-scale transform, followed by a local directional transform to gather the nearby basis functions at the same scale into linear structures. In the first stage of Contourlet transform, the Laplacian pyramid (LP) is used for sub-band decomposition. The resulting image is subtracted from the original image to obtain the bandpass image. This process can be iterated repeatedly on the coarser version of the image. The LP decomposition at each step generates a sampled lowpass version of the original image and the difference between the original and the prediction, resulting in a bandpass high frequency image. Directional filter bank (DFB) is used in the second stage to link the edge points into linear structures, which involves modulating the input image and using quincunx filter banks (QFB) with
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diamond-shaped filters. Fig.2 shows that the transform decouples the multiscale and the directional decompositions. In the practical application, the direction of number increase generally along with the scale of number increase. Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The Contourlet transform has a fast implementation based on a Laplacian pyramid decomposition followed by directional filterbanks applied on each bandpass subband. Contourlet transform can be used to capture smooth contours and edges at any orientation. The transform decouples the multiscale and the directional decompositions. The multiscale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. In order to solve the initial active contour problem of Snake model, in this paper, Contourlet transform is introduced into the GVF Snake model, which will provide a new way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. 5. Contour extraction based on GVF Snake and Contourlet transform In the GVF field, some points have an important influence to the initial contour setting. When these points within the target, the initial contour must contain these points; and when these points outside the target, the initial contour do not contain these points, otherwise it will not converge to correct results. We call these points the critical points. The creation of critical points has the following factors: (1) critical points are associated with the image gradient Df . By minimizing the energy functional, Df will be spread out, the impact of noise generated by the local minima will produce the critical points. (2) Critical points are associated with the smoothing coefficient l . The higher the value l is, the greater the smoothing effect is. The critical points will reduce, and GVF performance will reduce. Choosing a large-scale Gaussian smoothing and a smaller l value will get good results. (3) Critical points are associated with iterations number of solving equations. When the number of iterations is more than a thousand times, GVF field has changed dramatically. Although we require the final converged solution, but in the actual image processing applications, an intermediate result is acceptable. Therefore, the initial contour should contain the critical points as much as possible. So we can reduce the need of capture and reduce the amount of computation. Contourlet transform offers a much richer sub-band set of different directions and shapes, which helps to capture geometric structures in images much more efficiently [17–19]. The Laplacian pyramid (LP) is first used to capture the point discontinuities, and then followed by a direction filter banks (DFB) to link point discontinuities into linear structures. In particular, Contourlets have elongate supports at various scales, directions, and aspect ratios. The Contourlets satisfy anisotropy principle and can capture intrinsic geometric structure information of images and achieve better a sparser expression image than discrete wavelet transform (DWT). In order to solve the initial active contour problem of Snake model, in this paper, Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improve the edge detection results of GVF Snake model effectively. Firstly, the contours of the object in images can be obtained based on Contourlet Transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. The proposed algorithm is described as follows: ðlÞ
(1) Applying Contourlet transform in the original image. The Contourlet transform coefficients, C j;k ½nð0 6 l 6 J; 0 6 j 6 J; 0 6 k 6 2l Þ , and approximate sub-band coefficients C 0 ½n , can be obtained in different scale and different directions, where 2j denotes the scale of LP, l denotes the DFB decomposition levels, k denotes the direction serial number. ðlÞ (2) Let the approximate sub-band coefficient C 0 ½n ¼ 0, and let C j;k ½n remains unchanged. ðlÞ (3) Processing C j;k ½n using a threshold. ðlÞ ðlÞ (4) Detecting the maximum point of C j;k ½n , and other non-maximum points are assigned to 0. Then the matrix M j;k ½n , the ðlÞ modulus maximum matrix of Contourlet transform coefficients C j;k ½n is obtained. ðlÞ (5) Applying the Contourlet inverse transform to Mj;k ½n and C 0 ½n , getting a single pixel wide edge of object in images. (6) Using the edge that obtained by Contourlet transform as the initial contour of the GVF Snake model. Applying GVF snake model control the movement of contour until get the target profile. (7) Decomposing the each level of LP decomposition of low-pass images. Setting the upper contours as the initial goal of edge contours, searching the target edge contours continually until the ultimate goal edge is detected. Then the iteration is terminated. 6. Experimental results In this paper, the edge contours of human motion gait are used as the experimental objects. Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour to the edge extraction. Experimental implementations are based on the MATLAB 7.0. Experimental images come from Biometrics and Security Research Center of gait recognition database [20]. This algorithm is based on the GVF Snake model and Contourlet Transform processing, GVF Snake model l = 0.2, the number of iterations is 120 times. The body contour extracted image shown in Fig. 3.
F. Zhang et al. / Computers and Electrical Engineering 38 (2012) 882–890
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Fig. 3. (a) The background image. (b) The moving human image in the same background image.
Fig. 4. (a) The rough contour image. (b) The moving human contour extraction.
Fig. 3a is the background image, Fig. 3b is the moving human body image in the same background. Using the proposed algorithm, the rough contour is extracted from the background as shown in Fig. 4a. Then the GVF Snake model is used to extract the body contour of motion human. We compute the GVF field, where l = 0.2 and iteration number is 120 times. The experimental results show that the Contourlet transform based GVF Snake model can extract the body contour accurately. The extracted body contour is shown in Fig. 4b. Fig. 5 shows the head force field of Fig. 4b. Some of the characteristics of GVF Snake model can be found according to the balance perspective of force field. When the initial contour is not setting in false zero force field, we can get very good results. The calculating of the number of iterations does not affect the GVF force field. GVF force field not only keeps the diffusivity
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Fig. 5. The head force field of Fig. 4b.
Fig. 6. The comparison of extracted body contour using GVF Snake model (a) and Contourlet transform based GVF Snake model (b), respectively.
and the smoothness of Laplacian force field, but also maintains the characteristics that the gradient force field locates in the real contours and points to the real contours. In Fig. 5, we can see that the gradient force field locates in the real contours and points to the real contours in the direct neighborhood of the real contour. The GVF force field smoothly spreads and points to the real contour in the homogeneous regions of image. In the GVF, the center is the neighborhood of real contour, and the force field smoothly diamond diffuses out according to the number of iterations. The direction of diffusion is same as the gradient force field center and the diffusion area is proportional to the number of iterations. Fig. 6 is the comparison of extracted body contour using GVF Snake model and Contourlet transform based GVF Snake model, respectively. The parameters of both two models are l = 0.2, and the number of iteration is 100 times. Fig. 6a is the final result of contour using GVF Snake model. When we increase the number of iterations continually, and it mains increase the computing time, the edge contour still can not deeper recessed area of body, the search is terminated. Fig. 6b is the final result of contour using the Contourlet transform based GVF Snake model. Body crotch area usually is difficult to track. GVF Snake model can not get a good result. Contourlet transform based GVF Snake model uses the edge which is obtained by Contourlet transform as the initial contour of the GVF Snake model. Applying GVF snake model, we can control the movement of contour until getting the target profile. Guaranteed point boundary gradient vector flow field and boundary gradient strength is better preserved, well into the recessed area, extracting the external continuous contour of the body without affect by the influence of various complexity factors of body, and gaining a better body contour. Fig. 7a and b are the rough contour segmented from the background in a continuous images, and the extracted body contour using the Contourlet transform based GVF Snake model (l = 0.2, the number of iterations is 80 times). Experimental results show that using GVF Snake model can not accurately detect the crotch position of body. While the Contourlet transform based GVF Snake model can produce a better Concavities fitting effect. 7. Conclusions The background subtraction method and the symmetry differential method can be effectively combined for the moving target detection. The moving target detection is the key step in gait recognition. In order to solve the initial active contour
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Fig. 7. (a) The rough contour segmented from the background. (b) The extracted body contour using the improved GVF Snake model.
problem of Snake model, this paper introduces the Contourlet transform into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. Contourlet transform can be used to captures smooth contours and edges at any orientation. In order to solve the initial active contour problem of Snake model, Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. The multiscale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. Firstly, the contours of the object in images can be obtained based on Contourlet Transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. Based on Contourlet transform, the contours of object are identified as the initial contour in GVF Snake model. The human motion gait images are used as experimental objects. Experimental results show that the proposed method can extract the edge feature accurately and efficiently. Acknowledgments This research was supported by the Foundation of Education Bureau of Henan Province, China grants No. 2010B520003, and the key scientific and technological projects of Public Health Department of Henan Province, China Grants No. 2011020114. References [1] Lin Hong-wen, Yao Z-L, Tu D, Li G-H. The Research of Background-subtraction Based Moving Objects Detection Technology. J Nat Univ Defense Technol 2003;25(3):66–9. [2] A Murat Tekalp. Digital Video Processing. M. Prentice-Hall Press 1996. [3] Kim JB, Kim HJ. Efficient region-based motion segmentation from a video monitoring system. Pattern Recognit Lett. 2003;24:113–28. [4] Zhou Xihan, Liu Bo, Zhou Heqin. A motion detection algorithm based on background subtraction and symmetrical differencing. J Comput Simul 2005;22(4):117–9. [5] Lily L. Gait analysis for classification. R. AI Technical Report 2003-014, Massachusetts Institute of Technology-artificial Intelligence Laboratory, 2003. [6] Yoo JH, Nixon MS, Harris CJ. Extracting gait signatures based on anatomical knowledge. In: Proceedings of BMVA Symposium on Advancing Biometric Technologies, 2002. [7] Tian Guang-jian, Zhao Rong-chun. Survey of gait recognition. Appl Res Comput 2005;22(5):17–9. [8] Kass M, Witkin A, Terzopoulos D. Snake: active contour models. Int J Comput Vision 1988;1(4):321–31. [9] Zosso D, Bresson X, Thiran J. Geodesic active fields – a geometric framework for image registration. IEEE Trans Image Process 2011;20(5):1300–12. [10] Wenbo Song, Keller J, Haithcoat T, Davis C. Automated geospatial conflation of vector road maps to high resolution imagery. IEEE Trans Image Process 2010;18(2):388–400. [11] Xutong Niu. A semi-automatic framework for highway extraction and vehicle detection based on a geometric deformable model. Photogrammetry Remote Sens 2006;61:170–86. [12] Chenyang Xu, Prince J.L. Gradient Vector Flow: a new external force for Snakes. A. In: Proceeding of IEEE International Conference on CVPR, pp. 66–71 (1997).
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[13] Chenyang Xu, Prince JL. Snakes, shapes, and gradient vector flow. IEEE Trans Image Process 1998;7(3):359–69. [14] Wang Yu, Li Ming, Li Ling. New GVF model based on non-linear diffusion. J Comput Eng 2010;36(4):215–7. [15] Do M, Vettedi M. Contourlets: a directional multi-resolution image representation. IEEE International Conference on Image Processing, 2002, pp. 357– 360. [16] Do M, Vettedi M. The contourlet transform: an efficient directional multi-resolution image representation. IEEE Trans Image Process 2005;14(12):2091–106. [17] Yang Y, Dai Q. Contourlet-based image quality assessment for synthesised virtual image. Electron Lett 2010;46(7):492–4. [18] Xinbo Gao, Wen Lu, Dacheng Tao, Xuelong Li. Image quality assessment based on multiscale geometric analysis. IEEE Trans Image Process 2009;18(9):1409–23. [19] Nguyen T, Chauris H. Uniform discrete curvelet transform. IEEE Trans Signal Process 2010;58(7):3618–34. [20] Center for Biometrics and Security Research, http://www.cbsr.ia.ac.cn/. Fan Zhang received the B.S degree from North China University, China, in 1989, the M.S degree from Jiangsu University, China, in 2001, and the Ph. D. degree in Computer Science from Beijing University of Technology, China, in 2005. Now, He is the Professor of Henan University, China. His research interests include pattern recognition, image processing. Xinhong Zhang received the B.S. degree in Computer Science in 1990 from Henan University, China. She is now the Associate Professor of Henan University. Her current research interests include pattern recognition, image processing and computer vision. Kui Cao received the Ph. D. degree in Computer Science from Huazhong University of science and technology, China, in 2001. His current research interests include image processing and computer vision. He is the Professor of Henan University. Rui Li received the M.S. degree in Computer Science in 2010 from Henan University, China. Her current research interests is image processing.
Contents lists available at SciVerse ScienceDirect
Computers and Electrical Engineering journal homepage: www.elsevier.com/locate/compeleceng
Contour extraction of gait recognition based on improved GVF Snake model q Fan Zhang a,b,⇑, Xinhong Zhang c, Kui Cao b, Rui Li b a
Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475001, China College of Computer and Information Engineering, Henan University, Kaifeng 475001, China c Computing Center, Henan University, Kaifeng 475001, China b
a r t i c l e
i n f o
Article history: Received 13 July 2010 Received in revised form 13 March 2012 Accepted 13 March 2012 Available online 7 April 2012
a b s t r a c t Contourlet transform can be used to captures smooth contours and edges at any orientation. In order to solve the initial active contour problem of Snake model, Contourlet transform is introduced into the GVF (Gradient Vector Flow) Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. The multi-scale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. Firstly, the contours of the object in images can be obtained based on Contourlet transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. Experimental results show that the proposed method can extract the edge feature accurately and efficiently. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Feature extraction and description is the key steps for gait recognition. How to extract the motion contour effectively is most important in the gait recognition, and it is the main point of this paper. Currently, the main methods of motion segmentation and contour extraction include background subtraction method [1], frame difference method and approximate motion field method [2]. The frame difference method is the most commonly used method, which is fast but sensitive to noise. Some researches have been done and have received good segmentation results through combining the background subtraction method and the frame difference method [3,4]. The feature extraction methods of gait recognition include ellipse model method [5] and graph model method [6] etc. The ellipse model method expresses different parts of binary image of human profile using ellipses. The graph model expresses different parts of human body using curves, and it tracks the angle-swing of every part of human body in the image sequence and takes the angles as the feature for gait recognition. The matching algorithms of gait recognition include Dynamic Time Warping (DTW) and Hidden Markov Model (HMM) etc. The DTW can complete pattern matching when the test sequences and reference sequences are not accordant. DTW is widely used in speech recognition fields. Hidden Markov model is a statistical model in which the system being modeled is assumed to be a Markov process with unknown parameters, and the challenge is to determine the hidden parameters from the observable parameters. The extracted model parameters can then be used to perform further analysis, for example for pattern recognition applications. Active contour model is also a powerful tool to solve the contour extraction in gait recognition [7].
q
Reviews processed and approved for publication by Editor-in-Chief Dr. Manu Malek.
⇑ Corresponding author at: Institute of Image Processing and Pattern Recognition, Henan University, Kaifeng 475001, China. E-mail address: [email protected] (F. Zhang). 0045-7906/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compeleceng.2012.03.007
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2. Active contour model Active contour model, also called snakes, is a framework for delineating an object outline from a possibly noisy 2D image [8]. This framework attempts to minimize an energy associated to the current contour as a sum of an internal and external energy. The external energy is supposed to be minimal when the snake is at the object boundary position. The most straightforward approach consists in giving low values when the regularized gradient around the contour position reaches its peak value. The internal energy is supposed to be minimal when the snake has a shape which is supposed to be relevant considering the shape of the sought object. The most straightforward approach grants high energy to elongated contours (elastic force) and to bended/high curvature contours (rigid force), considering the shape should be as regular and smooth as possible. In two dimensions, the active shape model represents a discrete version of this approach, taking advantage of the point distribution model to restrict the shape range to an explicit domain learned from a training set. Snakes have multiple advantages over classical feature attraction techniques. Snakes are autonomous and self-adapting in their search for a minimal energy state. They can be easily manipulated using external image forces. They can be made sensitive to image scale by incorporating Gaussian smoothing in the image energy function. They can be used to track dynamic objects in temporal as well as the spatial dimensions. However, the traditional Snake model has some drawbacks. (1) Initialization. The initial curve must be placed close to the object boundary. The initial curve and the desired object boundary differ greatly in size and shape. The model must be reparameterized dynamically to recover the object boundary. This process requires some additional computation. (2) Minimization. A local minimum of energy, such as spurious edges caused by noise, may stop the evolution of the snake unexpectedly. (3) Topology. This method is difficult when dealing with topological changes. If multiple objects appear in the image and an initial curve surrounds them, all the objects cannot be detected. Additional splitting and merging approaches are needed to solve this problem. These increase the complexity of the snake implementation significantly [9–11]. Snake models minimize the energy functional and restrain to the target object contour. A traditional snake is a curve XðsÞ ¼ ðxðsÞ; yðsÞÞs 2 ½0; 1 , its minimizing energy function is as follows,
E¼
Z
1 0
1 ½ajX 0 ðsÞj2 þ bjX 00 ðsÞj2 þ Eext ðXðsÞÞds; 2
ð1Þ
where a and b are parameters which control the snake’s tension and rigidity respectively. The first term is the internal force, which controls the curve changes, while the second term Eext is the external force, which pulls the curve to desired features. Different Eext can be constructed in different models. To analyze the movement of snake model curve from the aspect of force balance, the minimized E of a snake musta satisfy the Euler equation:
aX 00 ðsÞ bX 0000 ðsÞ rEext ¼ 0: To add additional flexibility to the snake model, it is possible to start from the force balance equation directly, F int þ where F int ¼ aX 00 ðSÞ bX 0000 ðSÞ and F 1ext ¼ rEext . As the Snake contour is dynamic, the XðsÞ can be viewed as the function of t and s , then,
X t ðs; tÞ ¼ aX 00 ðsÞ bX 0000 ðsÞ rEext :
ð2Þ F 1ext
¼0,
ð3Þ
Once getting solution of the Eq. (3), we will find a solution of Eq. (2). 3. GVF Snake model Snake model is sensitive to the initial position. An initial contour should be placed close to the real contour, otherwise the result is often unsatisfied. Continuous image information is often used to obtain the initial contour of an image when Snake model is used in the image sequences. But sometimes the initial contour is not close to the true profile. As the traditional Snake model is difficult to determine the contours of the initial position and to deal with topological changes, Xu et al. proposed GVF (Gradient Vector Flow) concept [12,13]. The snake is developed based on new type of external field, called Gradient Vector Flow, or GVF. This computation causes diffuse forces to exist far from the object, and crisp force vectors near the edges. Combining these forces with the usual internal forces yields a powerful computational object: the GVF snake (2D), or the GVF deformable model (N-D). Even though this snake is started far from the object, it still gets attracted towards the object. Especially, GVF active contours can handle broken object edges and subjective contours. The GVF external forces are what make snake inherently different from previous snakes. Because the GVF forces are derived from a diffusion operation, they tend to extend very far away from the object. This extends the ‘capture range’ so that snakes can find objects that are quite far away from the snake’s initial position. This same diffusion creates forces which can pull active contours into concave regions. Because of this property, they cannot be derived from the energy minimization framework of traditional snakes. In [14], the GVF (Gradient Vector Flow) field replaces the potential force field in Eq. (3). Defining a new snake, GVF Snake, is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. GVF Snake has
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the better performance than snake in many fields. GVF Snake expands the capture region of the curve, and can force the curve into the concave regions. Assuming f ðx; yÞ is the contour image of a grayscale image Iðx; yÞ , then rf is the vector field. If rf is iterative diffused to the edge of image, it will form a gradient vector flow field (GVF), Vðx; yÞ ¼ ðuðx; yÞ; v ðx; yÞÞ . Then we minimize the energy function of contour. The energy function is as follows,
e¼
ZZ
lðu2x þ u2y þ v 2x þ v 2y Þþ j rf j2 j V rf j2 dxdy:
ð4Þ
The parameter l is the control parameters, which is set according to the image noise. The parameter l provides the tradeoff between the first part and the second part of the energy function. When rf is small, the curve is away from the target edge, the partial derivatives dominate the energy function. When rf is large, the energy is mainly depends on the second term of the integrand. Energy minimization is achieved by iterative approximation to the target edge, and the following Euler equations must be satisfied:
lr2 v ðv fy Þðfx2 þ fy2 Þ ¼ 0:
ð5Þ
lr2 u ðu fx Þðfx2 þ fy2 Þ ¼ 0:
ð6Þ
2
where r is the Laplacian operator. fx2 þ fy2 is the maximum in edge regions, and is zero in homogeneous regions. So this can be controlled edge gradient only in the boundary, and it will avoid the effect of the diffusion weaken. Eqs. (5) and (6) can be solved by view u and v as the function of time t , then,
u ¼ lr2 uðx; y; tÞ ½uðx; y; tÞ fx ðx; yÞ ½fx ðx; yÞ2 þ fy ðx; yÞ2 : 2
v ¼ lr v ðx; y; tÞ ½v ðx; y; tÞ fy ðx; yÞ ½fx ðx; yÞ 2
2
2
þ fy ðx; yÞ :
ð7Þ ð8Þ
2
Let div ½cðj rU jÞrU replaces r u and r v of GVF Snake in Eqs. (5) and (6). It is an improved GVF Snake model. A nonlinear diffusion function is added between the divergence operator and the gradient operator to control the diffusion.
cðj rU jÞ ¼ exp
j rUj2
! ð9Þ
:
K2
where U is the edge gradient image, K is the gradient sensitivity parameter. In the same size gradient regions, the smaller K represents the slow diffusion, otherwise the strong diffusion. In particular, the performance of the method is superior to GVF Snake in narrow concave boundary specially. Then the new anisotropic diffusion model can be build, the Euler equation is as follows,
" u ¼ l div ½cðj ru jÞru 1 exp
j fx2 þ fy2 j2
"
v ¼ l div ½cðj rv jÞrv
1 exp
K2 j fx2 þ fy2 j K2
!# ðu fx Þ:
ð10Þ
!# 2 ðv fy Þ:
ð11Þ
4. Contourlet transform The limitations of commonly used separable extensions of one-dimensional transforms, such as the Fourier and wavelet transforms, in capturing the geometry of image edges are well known. In 2002, Do and Vetterli proposed a ‘true’ two-dimensional transform, Contourlet transform, which is called pyramidal directional filter bank [15,16]. The resulting image expansion is a directional multiresolution analysis framework composed of contour segments, and thus is named Contourlet. This will overcome the challenges of wavelet and curvelet transform. Contourlet transform is a double filter bank structure. It is implemented by the pyramidal directional filter bank (PDFB) which decomposes images into directional subbands at multiple scales. In terms of structure the Contourlet transform is a cascade of a Laplacian pyramid and a directional filter bank. In essence, it first uses a wavelet-like transform for edge detection, and then a local directional transform for contour segment detection. The Contourlet transform provides a sparse representation for two-dimensional piecewise smooth signals that resemble images. Fig. 1 shows that Contourlet transform can captures smooth contours and edges at any orientation. Contourlet coefficients of natural images exhibit the following properties: 1. 2. 3. 4.
Non-Gaussian marginally. Dependent on generalized neighborhood. Conditionally Gaussian conditioned on generalized neighborhood. Parents are (often) the most influential.
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Fig. 1. Contourlet transform can captures smooth contours and edges at any orientation.
Fig. 2. The transform decouples the multiscale and the directional decompositions.
The Contourlet transform expresses image by first applying a multi-scale transform, followed by a local directional transform to gather the nearby basis functions at the same scale into linear structures. In the first stage of Contourlet transform, the Laplacian pyramid (LP) is used for sub-band decomposition. The resulting image is subtracted from the original image to obtain the bandpass image. This process can be iterated repeatedly on the coarser version of the image. The LP decomposition at each step generates a sampled lowpass version of the original image and the difference between the original and the prediction, resulting in a bandpass high frequency image. Directional filter bank (DFB) is used in the second stage to link the edge points into linear structures, which involves modulating the input image and using quincunx filter banks (QFB) with
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diamond-shaped filters. Fig.2 shows that the transform decouples the multiscale and the directional decompositions. In the practical application, the direction of number increase generally along with the scale of number increase. Contourlets form a multiresolution directional tight frame designed to efficiently approximate images made of smooth regions separated by smooth boundaries. The Contourlet transform has a fast implementation based on a Laplacian pyramid decomposition followed by directional filterbanks applied on each bandpass subband. Contourlet transform can be used to capture smooth contours and edges at any orientation. The transform decouples the multiscale and the directional decompositions. The multiscale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. In order to solve the initial active contour problem of Snake model, in this paper, Contourlet transform is introduced into the GVF Snake model, which will provide a new way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. 5. Contour extraction based on GVF Snake and Contourlet transform In the GVF field, some points have an important influence to the initial contour setting. When these points within the target, the initial contour must contain these points; and when these points outside the target, the initial contour do not contain these points, otherwise it will not converge to correct results. We call these points the critical points. The creation of critical points has the following factors: (1) critical points are associated with the image gradient Df . By minimizing the energy functional, Df will be spread out, the impact of noise generated by the local minima will produce the critical points. (2) Critical points are associated with the smoothing coefficient l . The higher the value l is, the greater the smoothing effect is. The critical points will reduce, and GVF performance will reduce. Choosing a large-scale Gaussian smoothing and a smaller l value will get good results. (3) Critical points are associated with iterations number of solving equations. When the number of iterations is more than a thousand times, GVF field has changed dramatically. Although we require the final converged solution, but in the actual image processing applications, an intermediate result is acceptable. Therefore, the initial contour should contain the critical points as much as possible. So we can reduce the need of capture and reduce the amount of computation. Contourlet transform offers a much richer sub-band set of different directions and shapes, which helps to capture geometric structures in images much more efficiently [17–19]. The Laplacian pyramid (LP) is first used to capture the point discontinuities, and then followed by a direction filter banks (DFB) to link point discontinuities into linear structures. In particular, Contourlets have elongate supports at various scales, directions, and aspect ratios. The Contourlets satisfy anisotropy principle and can capture intrinsic geometric structure information of images and achieve better a sparser expression image than discrete wavelet transform (DWT). In order to solve the initial active contour problem of Snake model, in this paper, Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improve the edge detection results of GVF Snake model effectively. Firstly, the contours of the object in images can be obtained based on Contourlet Transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. The proposed algorithm is described as follows: ðlÞ
(1) Applying Contourlet transform in the original image. The Contourlet transform coefficients, C j;k ½nð0 6 l 6 J; 0 6 j 6 J; 0 6 k 6 2l Þ , and approximate sub-band coefficients C 0 ½n , can be obtained in different scale and different directions, where 2j denotes the scale of LP, l denotes the DFB decomposition levels, k denotes the direction serial number. ðlÞ (2) Let the approximate sub-band coefficient C 0 ½n ¼ 0, and let C j;k ½n remains unchanged. ðlÞ (3) Processing C j;k ½n using a threshold. ðlÞ ðlÞ (4) Detecting the maximum point of C j;k ½n , and other non-maximum points are assigned to 0. Then the matrix M j;k ½n , the ðlÞ modulus maximum matrix of Contourlet transform coefficients C j;k ½n is obtained. ðlÞ (5) Applying the Contourlet inverse transform to Mj;k ½n and C 0 ½n , getting a single pixel wide edge of object in images. (6) Using the edge that obtained by Contourlet transform as the initial contour of the GVF Snake model. Applying GVF snake model control the movement of contour until get the target profile. (7) Decomposing the each level of LP decomposition of low-pass images. Setting the upper contours as the initial goal of edge contours, searching the target edge contours continually until the ultimate goal edge is detected. Then the iteration is terminated. 6. Experimental results In this paper, the edge contours of human motion gait are used as the experimental objects. Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour to the edge extraction. Experimental implementations are based on the MATLAB 7.0. Experimental images come from Biometrics and Security Research Center of gait recognition database [20]. This algorithm is based on the GVF Snake model and Contourlet Transform processing, GVF Snake model l = 0.2, the number of iterations is 120 times. The body contour extracted image shown in Fig. 3.
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Fig. 3. (a) The background image. (b) The moving human image in the same background image.
Fig. 4. (a) The rough contour image. (b) The moving human contour extraction.
Fig. 3a is the background image, Fig. 3b is the moving human body image in the same background. Using the proposed algorithm, the rough contour is extracted from the background as shown in Fig. 4a. Then the GVF Snake model is used to extract the body contour of motion human. We compute the GVF field, where l = 0.2 and iteration number is 120 times. The experimental results show that the Contourlet transform based GVF Snake model can extract the body contour accurately. The extracted body contour is shown in Fig. 4b. Fig. 5 shows the head force field of Fig. 4b. Some of the characteristics of GVF Snake model can be found according to the balance perspective of force field. When the initial contour is not setting in false zero force field, we can get very good results. The calculating of the number of iterations does not affect the GVF force field. GVF force field not only keeps the diffusivity
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Fig. 5. The head force field of Fig. 4b.
Fig. 6. The comparison of extracted body contour using GVF Snake model (a) and Contourlet transform based GVF Snake model (b), respectively.
and the smoothness of Laplacian force field, but also maintains the characteristics that the gradient force field locates in the real contours and points to the real contours. In Fig. 5, we can see that the gradient force field locates in the real contours and points to the real contours in the direct neighborhood of the real contour. The GVF force field smoothly spreads and points to the real contour in the homogeneous regions of image. In the GVF, the center is the neighborhood of real contour, and the force field smoothly diamond diffuses out according to the number of iterations. The direction of diffusion is same as the gradient force field center and the diffusion area is proportional to the number of iterations. Fig. 6 is the comparison of extracted body contour using GVF Snake model and Contourlet transform based GVF Snake model, respectively. The parameters of both two models are l = 0.2, and the number of iteration is 100 times. Fig. 6a is the final result of contour using GVF Snake model. When we increase the number of iterations continually, and it mains increase the computing time, the edge contour still can not deeper recessed area of body, the search is terminated. Fig. 6b is the final result of contour using the Contourlet transform based GVF Snake model. Body crotch area usually is difficult to track. GVF Snake model can not get a good result. Contourlet transform based GVF Snake model uses the edge which is obtained by Contourlet transform as the initial contour of the GVF Snake model. Applying GVF snake model, we can control the movement of contour until getting the target profile. Guaranteed point boundary gradient vector flow field and boundary gradient strength is better preserved, well into the recessed area, extracting the external continuous contour of the body without affect by the influence of various complexity factors of body, and gaining a better body contour. Fig. 7a and b are the rough contour segmented from the background in a continuous images, and the extracted body contour using the Contourlet transform based GVF Snake model (l = 0.2, the number of iterations is 80 times). Experimental results show that using GVF Snake model can not accurately detect the crotch position of body. While the Contourlet transform based GVF Snake model can produce a better Concavities fitting effect. 7. Conclusions The background subtraction method and the symmetry differential method can be effectively combined for the moving target detection. The moving target detection is the key step in gait recognition. In order to solve the initial active contour
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Fig. 7. (a) The rough contour segmented from the background. (b) The extracted body contour using the improved GVF Snake model.
problem of Snake model, this paper introduces the Contourlet transform into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. Contourlet transform can be used to captures smooth contours and edges at any orientation. In order to solve the initial active contour problem of Snake model, Contourlet transform is introduced into the GVF Snake model, which will provides a way to set the initial contour, as a result, will improves the edge detection results of GVF Snake model effectively. The multiscale decomposition is handled by a Laplacian pyramid. The directional decomposition is handled by a directional filter bank. Firstly, the contours of the object in images can be obtained based on Contourlet Transform, and this contours will be identified as the initial contour of GVF Snake model. Secondly, then GVF Snake model is used to detect the contour edge of human gait motion. Based on Contourlet transform, the contours of object are identified as the initial contour in GVF Snake model. The human motion gait images are used as experimental objects. Experimental results show that the proposed method can extract the edge feature accurately and efficiently. Acknowledgments This research was supported by the Foundation of Education Bureau of Henan Province, China grants No. 2010B520003, and the key scientific and technological projects of Public Health Department of Henan Province, China Grants No. 2011020114. References [1] Lin Hong-wen, Yao Z-L, Tu D, Li G-H. The Research of Background-subtraction Based Moving Objects Detection Technology. J Nat Univ Defense Technol 2003;25(3):66–9. [2] A Murat Tekalp. Digital Video Processing. M. Prentice-Hall Press 1996. [3] Kim JB, Kim HJ. Efficient region-based motion segmentation from a video monitoring system. Pattern Recognit Lett. 2003;24:113–28. [4] Zhou Xihan, Liu Bo, Zhou Heqin. A motion detection algorithm based on background subtraction and symmetrical differencing. J Comput Simul 2005;22(4):117–9. [5] Lily L. Gait analysis for classification. R. AI Technical Report 2003-014, Massachusetts Institute of Technology-artificial Intelligence Laboratory, 2003. [6] Yoo JH, Nixon MS, Harris CJ. Extracting gait signatures based on anatomical knowledge. In: Proceedings of BMVA Symposium on Advancing Biometric Technologies, 2002. [7] Tian Guang-jian, Zhao Rong-chun. Survey of gait recognition. Appl Res Comput 2005;22(5):17–9. [8] Kass M, Witkin A, Terzopoulos D. Snake: active contour models. Int J Comput Vision 1988;1(4):321–31. [9] Zosso D, Bresson X, Thiran J. Geodesic active fields – a geometric framework for image registration. IEEE Trans Image Process 2011;20(5):1300–12. [10] Wenbo Song, Keller J, Haithcoat T, Davis C. Automated geospatial conflation of vector road maps to high resolution imagery. IEEE Trans Image Process 2010;18(2):388–400. [11] Xutong Niu. A semi-automatic framework for highway extraction and vehicle detection based on a geometric deformable model. Photogrammetry Remote Sens 2006;61:170–86. [12] Chenyang Xu, Prince J.L. Gradient Vector Flow: a new external force for Snakes. A. In: Proceeding of IEEE International Conference on CVPR, pp. 66–71 (1997).
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[13] Chenyang Xu, Prince JL. Snakes, shapes, and gradient vector flow. IEEE Trans Image Process 1998;7(3):359–69. [14] Wang Yu, Li Ming, Li Ling. New GVF model based on non-linear diffusion. J Comput Eng 2010;36(4):215–7. [15] Do M, Vettedi M. Contourlets: a directional multi-resolution image representation. IEEE International Conference on Image Processing, 2002, pp. 357– 360. [16] Do M, Vettedi M. The contourlet transform: an efficient directional multi-resolution image representation. IEEE Trans Image Process 2005;14(12):2091–106. [17] Yang Y, Dai Q. Contourlet-based image quality assessment for synthesised virtual image. Electron Lett 2010;46(7):492–4. [18] Xinbo Gao, Wen Lu, Dacheng Tao, Xuelong Li. Image quality assessment based on multiscale geometric analysis. IEEE Trans Image Process 2009;18(9):1409–23. [19] Nguyen T, Chauris H. Uniform discrete curvelet transform. IEEE Trans Signal Process 2010;58(7):3618–34. [20] Center for Biometrics and Security Research, http://www.cbsr.ia.ac.cn/. Fan Zhang received the B.S degree from North China University, China, in 1989, the M.S degree from Jiangsu University, China, in 2001, and the Ph. D. degree in Computer Science from Beijing University of Technology, China, in 2005. Now, He is the Professor of Henan University, China. His research interests include pattern recognition, image processing. Xinhong Zhang received the B.S. degree in Computer Science in 1990 from Henan University, China. She is now the Associate Professor of Henan University. Her current research interests include pattern recognition, image processing and computer vision. Kui Cao received the Ph. D. degree in Computer Science from Huazhong University of science and technology, China, in 2001. His current research interests include image processing and computer vision. He is the Professor of Henan University. Rui Li received the M.S. degree in Computer Science in 2010 from Henan University, China. Her current research interests is image processing.