Gait recognition via optimally interpolated deformable contours

Pattern Recognition Letters 34 (2013) 663–669

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Pattern Recognition Letters journal homepage: www.elsevier.com/locate/patrec

Gait recognition via optimally interpolated deformable contours Chin Poo Lee a,⇑, Alan W.C. Tan b, Shing Chiang Tan a a b

Faculty of Information Science and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450 Bukit Beruang, Melaka, Malaysia Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, Bukit Beruang, 75450 Melaka, Malaysia

a r t i c l e

i n f o

a b s t r a c t

Article history: Received 24 April 2012 Available online 4 February 2013

Gait as a biometric was inspired by the ability to recognize an acquaintance by his manner of walking even when seen at a distance. In this paper, we describe a novel Fourier descriptor based gait recognition method that models the periodic deformation of human contours. A new measure of similarity using the product of Fourier coefficients is proposed as a distance measure between closed curves. In order to maximize the similarity between subsequent closed curves, the assembly of contours in gait cycle is circularly shifted by a circular permutation matrix. Subsequently, an element-wise frame interpolation is correspondingly applied to produce length invariant gait signatures. The experiments on OU-ISIR gait database and CASIA gait database reveal promising recognition accuracy. The element-wise frame interpolation method is able to preserve temporal information even when the gait cycles change, and therefore offers a better robustness to slight variation in walking speed. Ó 2013 Elsevier B.V. All rights reserved.

Communicated by S. Sarkar Keywords: Gait recognition Fourier descriptor Shape interpolation

1. Introduction Walking is a bipedal type of locomotion that seems simple, but requires great neural control. The mastering of the erect bipedal type of locomotion appears to be a combination of instinct and learning (Rose and Gamble, 2006). If walking is a learned activity, it is not surprising that each of us displays certain personal peculiarities despite the basic pattern of bipedal locomotion. One can often recognize an acquaintance by his manner of walking even when seen at a distance. Much attention has been devoted to the use of human gait patterns as a biometric and to the analysis of human motion in general. Studying this motion, however, is a difficult task. The aim of computer vision-based analysis of human gait is to automatically discover and describe human gait accurately with minimal human intervention. Many approaches have been proposed for the description of the human gait. Sundaresan et al. (2003) deployed Hidden Markov Models (HMMs) for recognition of individuals from their gait. Wang et al. (2003a,b) obtained an eigenshape as gait signature using Procrustes shape analysis method. Bobick and Johnson (2001) introduced four static body parameters and then calculated the ratio between the volume of the individual variation density to the overall population by computing the Maximum Likelihood estimate Gaussian density. Zhang et al. (2004) constructed a 2D five-link biped locomotion model to represent human body in the image sequences when the person is walking in lateral view. ⇑ Corresponding author. Tel.: +60 6 2523172. E-mail addresses: [email protected] (A.W.C. Tan), [email protected] (S.C. Tan).

(C.P.

Lee),

[email protected]

0167-8655/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.patrec.2013.01.013

Some other studies proposed appearance-based gait features to describe human motion. Liu and Sarkar (2004) engaged an average silhouette method which represents human motion in a single image while preserving temporal information. Han and Bhanu (2006) developed a similar representation called the Gait Energy Image (GEI) by combining the real and synthetic templates for gait recognition. Wang et al. (2010) preserved the temporal information among gait frames via color mapping to generate a chrono-gait image (CGI). Zhang et al. (2010) proposed an active energy image (AEI) method by accumulating image difference between subsequent silhouette images. Lam et al. (2011) generated a gait flow image (GFI) by using the optical flow field from the gait image sequence. Many Fourier descriptor-based techniques have also been proposed in the literature. A major advantage of Fourier descriptors is that, when representing a shape in the Fourier domain, one can readily access its frequency components. This can be useful, as macroscopic features are found in the lower frequencies, whereas microscopic features are found in the higher frequencies (Mowbray and Nixon, 2003). Mowbray and Nixon (2003) adopted a Fourier series to represent the shape boundary, with the coefficients of the series being the Fourier descriptors of the shape. Tian et al. (2004) described global and local features of shape contour using Fourier descriptors. Dynamic time warping is then applied to align gait sequences of different lengths. This, however, introduces significant computational overhead and, as a result, the approach suffers from heavy computational cost. Lu et al. (2008) represented every gait cycle as four key frames, denoted as differential coefficient, closing up, heel and striding. These frames are then processed with the Fourier transform to obtain the Fourier

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descriptors. The method, however, tends to lose the temporal deformation information of gait sequences since substantial gait information may be contained in the discarded frames. Appearance-based approaches are basically region-based in nature while Fourier descriptors are boundary-based approaches. Region-based approaches rely on information in the region of interest, such as texture, or intensity homogeneity. Boundarybased techniques, on the other hand, rely on information provided by the object boundaries or the shape properties (Zhang et al., 2012). In most of the appearance-based methods, transient information is not preserved because all frames in a gait cycle are usually accumulated into a composite frame from which the gait descriptor is determined. In contrast, the boundary-based approach is able to preserve the transient information of a gait cycle where each frame is extracted and coded in a vector. Besides that, boundary-based approaches focus on the shape contour that contains more discriminating features between subjects. To this end, instead of analyzing the whole region of human body, only its boundary is considered. In this paper, we propose a Fourier descriptor-based gait recognition algorithm. In the proposed approach, we adopt Fourier descriptors to represent deforming human contours in gait cycles. The boundary coordinates are vectorized into one-dimensional complex coordinate system. To further ease processing, every video is divided into segments, each consisting of boundary vectors in half gait cycles. Fourier transform is then applied to the complex boundary vectors in each segment to obtain the Fourier descriptors. We define a new measure of similarity for closed curves inspired by the maximization of the product of Fourier coefficients. This measure of similarity is then applied in shape alignment to minimize the difference across the sequence of deformable contours. We also propose a frame interpolation method to normalize the segments of optimally aligned contours into some desired number of frames. The main contributions of the proposed algorithm are the circular alignment of consecutive contours, and frame interpolation that lends a certain property of invariance to gait cycle length and, in doing so, reduces the overall computational complexity in actual implementation. 2. Definition: gait recognition To bring into proper perspective the key issues considered in this paper, it is useful to digress for a moment to the following definition of the gait recognition problem. Let X denotes the gait signature space that contains all gait signatures and C be the set of class labels of the known classes. The central task of gait recognition is the assignment of gait signatures to classes with common characteristics, or equivalently, the mapping X ! C. The gait signature space, however, is usually overly redundant and as a preliminary step to the actual classification task, a feature extractor F : X ! Y is deployed to reduce the dimensionality of the gait signature space. The feature space Y should essentially contain the underlying motion elements of the gait under consideration. The mapping G : Y ! C completes the recognition process. 3. Gait signature extraction This section outlines the feature extraction phase for gait recognition in this paper. 3.1. Boundary representation

point of the nth pixel on the boundary, and N be the total number of boundary pixels. These coordinate points are organized into a vector of complex numbers v 2 CN where ½v n ¼ xn þ jyn .1 Without the loss of generality, we assume that these points are centered around the centroid, i.e., 1T v ¼ 0, and the shape boundary vector v is normalized to unity, i.e., kv k2 ¼ 1. Selecting an appropriate N is important in characterizing the boundary edge. The larger N is, the more detail of the shape is preserved. However, this also increases computational complexity and introduces noise around the shape boundary. On the other hand, choosing a smaller N compromises on the amount of detail, and possibly leading to poor performance in shape analysis. In practice, N is usually determined empirically; in our experiments, we chose N ¼ 100. 3.2. Measure of similarity Recall that v 2 CN is a complex-valued shape boundary vector. For notational simplicity, we assume that ½v nkN ¼ ½v n ; 8k 2 Z. This assumption is intuitively sound as shape boundaries are essentially closed curves. We define the measure of dissimilarity2 dðv ; uÞ of v and another shape boundary vector u as

dðv ; uÞ ¼ minkPm v  uk2 m

where P m is a circular permutation matrix, and P m v has the effect of circularly shifting the elements of v by amount m, i.e., ½Pm v n ¼ ½v nþm . The assumption kv k ¼ kuk ¼ 1 in the preceding section enables us to rewrite (1) as

dðv ; uÞ ¼ maxRðr m Þ

ð2Þ

m

where

rm ¼

N1 X ½v nþm ½un n¼0

is the cross-correlation of v and u. A corresponding measure of similarity sðv ; uÞ may readily be established simply by changing the sign of (2), or

sðv ; uÞ ¼ dðv ; uÞ ¼ maxRðrm Þ m

ð3Þ

By the properties of the discrete Fourier transform, we recognize the cross-correlation as being equivalent to F 1 ðF ðv Þ  F  ðuÞÞ,3 where F ðÞ denotes the Fourier transform. In this case, Fourier transform of the shape boundary vector v is given by

½F ðv Þk ¼

N1 X ½v n ej2pkn=N

ð4Þ

n¼0

In the literature of image processing, the Fourier transform of the complex-valued boundary edge is referred to as the Fourier descriptor (Fig. 1). 3.3. Frame interpolation Frame interpolation is concerned with normalizing the number of frame in the gait cycle when comparing gait cycles of different lengths. We use the ratio of human body height to width when analyzing the period of gait cycle. By identifying two consecutive local minima, we can approximately identify the start frame and end frame of half cycle. 1

The notation ½v n (n ¼ 0; 1; . . . ; N  1) denotes the nth element of the vector

v 2 CN . 2

The silhouette boundary edge is obtained using a boundary tracing algorithm. Let ðxn ; yn Þ; n ¼ 0; 1; . . . ; N  1, be the coordinate

ð1Þ

The greater dðv ; uÞ is, the less similar (or more dissimilar) the vectors v and u are. The operation v  u denotes the element-wise product of vectors v and u, i.e., ½v  un ¼ ½v n ½un . 3

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Fig. 2. Comparison of original frames and interpolated frames, (a) x over time, (b) y over time, and (c) x and y over time. 0

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Fig. 1. Transforming complex boundary points into Fourier descriptors: (a) human contour, (b) boundary points in complex coordinate system, and (c) Fourier descriptors.

Let all the L shape boundary vectors in a half cycle be collected into the set V ¼ fv k ; k ¼ 1; 2; . . . ; Lg. Contour alignment begins with the determination of the index

m ¼ arg minkPm v kþ1  v k k2 m

ð5Þ

where v k and v kþ1 represent the shape boundary vectors of the current and next frame, respectively. The optimally aligned

v0kþ1 ¼ Pm v kþ1 is obtained via circularly shifting the latter by the same amount. This process is repeated, in turn, throughout all frames of interest, and in doing so, optimal circular alignment for each pair of successive vectors in V is accomplished. Suppose all shape boundary vectors in V have been optimally aligned. Frame interpolation, as proposed here, comprises N independent linear interpolation of the coordinate points of V element-wise. More specifically, for the nth coordinate point, the linear interpolation procedure is applied to the sequence ½v k n ; k ¼ 1; 2; . . . ; L, to generate a linearly interpolated sequence ½v 0k n ; k ¼ 1; 2; . . . ; L0 , of some desired length L0 (Fig. 2). The optimally interpolated gait signature is given by V 0 ¼ fv 0k ; k ¼ 1; 2; . . . ; L0 g.

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Table 1 Summary of the proposed optimal interpolation algorithm.

Table 2 Recognition accuracy using different approaches.

Feature extraction

Dataset

Given v 2 CN as a complex-valued shape boundary vector. Let all the L shape boundary vectors in a half-cycle be collected into the set V ¼ fv k ; k ¼ 1; 2; . . . ; Lg, do: 1. Circular alignment for each pair of successive vectors to maximize the measure of similarity (Eq. 3) between successive vectors, based on Eq. 5. 2. For all N coordinate points, do element-wise frame interpolation to generate a linearly interpolated gait signature of desired length, L0 . Classification Let fV i ; i ¼ 1; 2; . . . ; Mg denote the probe set of M unlabeled gait signatures, each associated to a particular half cycle in a gait video. Let ðjÞ

fU i ; i ¼ 1; 2; . . . ; Mj ; j ¼ 1; 2; . . . ; Q } denote the gallery set of labeled gait

Recognition accuracy (%) Proposed method

OU-ISIR dataset D 92 (DBhigh ) OU-ISIR dataset D 91 (DBlow ) CASIA dataset B 62.03 Execution time (s)

Zhang Lu Frame Mowbray Tian and Nixon et al. et al. et al. drop (2004) (2008) (2010) method (2003) 57

44

94

46

79

62

40

88

58

79

35.44

44.30

63.29

56.96 84.80

0.21

0.48

25.84

0.23

1.41

0.15

ðjÞ

signatures, where U i corresponds to the gait signature of the ith halfcycle of subject j. 1. For i ¼ 1 to M, assign sublabel based on Eq. 7. 2. Considering all M half cycles in the probe set, determine the final class label given by Eq. 8.

Table 3 Rank 1 to rank 5 results on (a) OU-ISIR dataset D (DBhigh ), (b) OU-ISIR dataset D (DBlow ), and (c) CASIA dataset B. Method

4. Gait signature classification Let V ¼ fv k ; k ¼ 1; 2; . . . ; L0 g4 and U ¼ fuk ; k ¼ 1; 2; . . . ; L0 g be two optimally interpolated gait signature obtained according to the procedure in the preceding section. To measure the difference between the two, we make use of the dissimilarity measure defined previously. Specifically, the sum of dissimilarity measures (referred simply to as the gait distance hereafter) for each pair of shape boundary vectors of the same instance is calculated, i.e.,

DðV; UÞ ¼ min m

L X kP m v k  uk k2

ð6Þ

k¼1

Let fV i ; i ¼ 1; 2; . . . ; Mg denote the probe set of M unlabeled gait signatures, each associated to a particular half cycle in a gait video. ðjÞ Let fU i ; i ¼ 1; 2; . . . ; M j ; j ¼ 1; 2; . . . ; Q } denote the gallery set of laðjÞ beled gait signatures, where U i corresponds to the gait signature of the ith half-cycle of subject j. Define ðjÞ

li0 ¼ arg minDðV i0 ; U i Þ

ð7Þ

i;j

(a) Proposed method Frame drop method Mowbray and Nixon (2003) Tian et al. (2004) Lu et al. (2008) Zhang et al. (2010) (b) Proposed method Frame drop method Mowbray and Nixon (2003) Tian et al. (2004) Lu et al. (2008) Zhang et al. (2010) (c) Proposed method Frame drop method Mowbray and Nixon (2003) Tian et al. (2004) Lu et al. (2008) Zhang et al. (2010)

Recognition accuracy (%) Rank 1

Rank 2

Rank 3

Rank 4

Rank 5

92 57 44 94 46 79

94 67 50 96 48 79

97 72 51 97 49 80

98 75 51 97 50 81

98 77 52 97 50 81

91 62 40 88 58 79

96 73 53 90 63 82

98 81 54 92 63 83

99 84 55 92 64 83

99 89 56 92 66 84

62.03 35.44 44.30 63.29 56.96 84.80

77.22 41.77 55.70 75.95 64.56 86.08

84.81 46.84 56.96 77.22 65.82 86.08

87.34 51.90 59.49 78.48 67.09 88.61

88.61 51.90 59.49 86.08 68.35 89.87

0

as the assigned sublabel of the i th unlabeled gait signature, corresponding to the subject with the minimum gait distance. The final class label, considering all the M half cycles in the probe set, is given by the mode of the sublabels, i.e.,

l0 ¼ modeðl1 ; l2 ; . . . ; lM Þ

ð8Þ

The proposed algorithm is summarized in Table 1. 5. Experiments and discussions This section studies the performance of the proposed algorithm, tested on OU-ISIR gait dataset A, OU-ISIR gait dataset D (Makihara et al., 2012), and CASIA dataset B (Zheng et al., 2011; Yu et al., 2006). 5.1. Datasets OU-ISIR gait dataset D contains 370 gait sequences of 185 subjects observed from the lateral view. The dataset focuses on the gait fluctuations over a number of periods. The gait fluctuations were measured by Normalized AutoCorrelation (NAC) of size-normalized silhouettes for the temporal axis. The dataset is divided into two subsets: DBhigh comprising 100 subjects with the highest 4 If there is no ambiguity, the subscript is dropped from the equation hereafter to improve readability.

NAC (stable gait), and DBlow comprising 100 subjects with the lowest NAC (fluctuated gait). There are 15 subjects overlapped in DBhigh and DBlow . CASIA gait dataset B is a large multiview gait database. There are 124 subjects, and the gait data was captured from 11 views. Three variations, namely viewing angle, clothing and carrying condition changes, are separately considered. In order to have fair comparisons across different datasets, we only consider lateral view (90o ) and normal clothing. Besides that, as silhouette preprocessing is not within the scope of this work, only 79 subjects with almost complete silhouettes are chosen to be included in the experiments. The OU-ISIR gait dataset A is composed of gait silhouette sequences of 34 subjects from side view with speed variation ranging from 2 km/h to 7 km/h at 1 km/h interval. For each walking speed, it comprises 68 videos with two videos per subject. 5.2. Results In our experiments, each video is divided into a number of half cycles, where the key frames bounding each half cycle are decided based on the local maxima of height–width ratios of body contour. Every half cycle is normalized to L0 ¼ 20 frames. For purposes of comparison, the experiments also include a typical frame drop method, three other approaches based on Fourier descriptors

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(a)100

(b) 100

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Fig. 3. Rank 1 to rank 5 results on (a) OU-ISIR dataset D (DBhigh ), (b) OU-ISIR dataset D (DBlow ), and (c) CASIA dataset B.

(Mowbray and Nixon, 2003; Tian et al., 2004; Lu et al., 2008), and an appearance-based AEI method (Zhang et al., 2010) discussed in Section 1. The frame drop method selects a desired number of frames (20 frames in the experiments) at specific interval. Mowbray and Nixon (2003) represented the deformation of the shape boundary in one gait cycle by a two-dimensional discrete Fourier series. Classification is performed on these spatio-temporal Fourier descriptors using the k-nearest neighbor classifier. Their method used simple regular sampling to normalize the number of frames in a gait cycle while we applied linear frame interpolation to normalize the gait length. The work of Tian et al. (2004) adopted Fourier descriptors to describe global and local features of shape contour. In the classification stage which featured the k-nearest neighbor classifier, dynamic time warping is applied to align gait sequences of different lengths. The method proposed by Lu et al. (2008) extracted four key frames from every gait cycle. These frames are then processed with the Fourier transform to obtain the Fourier descriptors. In the testing phase, each key frame is matched with the template of the corresponding key frame in the gallery set. The classification criterion is based on the nearest neighbor with optimal matching for all four key frames. The method, however, is different from our proposed method in that it only considers four frames from each gait cycle. The loss of temporal deformation information will lead, as

the experiments will later show, to a drop in accuracy since substantial gait information may be contained in the discarded frames. In Zhang et al. (2010), the active regions are first extracted by calculating the difference of two adjacent silhouette images, and an AEI is constructed by accumulating these active regions. Next, the Euclidean distance is calculated as a measure of similarity, and recognition is accomplished by using the nearest neighbor rule. The recognition rates and computational time for the feature extraction phase and classification phase are listed in Table 2. Besides that, the Rank 1 to Rank 5 results on OU-ISIR Dataset D and CASIA dataset B (Table 3) are also presented in Fig. 3. For OU-ISIR dataset D, it is apparent from these results, that the proposed optimal interpolation method outperforms the frame drop method, the two-dimensional Fourier descriptor-based approach (Mowbray and Nixon, 2003), and the method of Lu et al. (2008). The proposed approach performs comparably with dynamic time warping based method (Tian et al., 2004). Our method performs slightly better than the appearance-based method of Zhang et al. (2010), mainly because of the absence of transient information in the composite energy image. As gait is a continuous motion, it is reasonable to assume that the loss of transient information will lead to a general loss of accuracy. This is especially true considering that such detectors will fail to distinguish the same ac-

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Table 4 Comparison of recognition accuracy in different walking speeds. Probe speed

5 km/h 6 km/h 7 km/h

Gallery speed (6 km/h) Proposed approach

Frame drop method

Mowbray and Nixon (2003)

Tian et al. (2004)

Lu et al. (2008)

Zhang et al. (2010)

88.24 91.18 91.18

35.29 58.82 47.06

2.94 64.71 61.76

64.71 91.18 61.76

35.29 52.94 20.59

55.88 67.65 58.82

(a) 80 70 60 50 40 30 20 10 0

6

7

8

9

10

11

12

13

14

15

(b) 100

6. Conclusion

90 80 70 60 50 40 30 20 10 0

We have also conducted experiments on OU-ISIR dataset A to investigate the performance change due to speed change. In our experiments, we use 6 km/h as the gallery sequence while 5 km/ h and 7 km/h are used as the probe sequences. From the results shown in Table 4, the proposed frame interpolation approach, method (Mowbray and Nixon, 2003), and method (Zhang et al., 2010) are able to maintain the performance rate for small change of walking speed. The same cannot be said of the methods of Tian et al. (2004) and Lu et al. (2008). The results, thus, demonstrate that the proposed method is able to preserve temporal information even when the gait cycles change, and therefore offers a better robustness to slight variation in walking speed. We have also further analyzed the accuracy of the proposed approach on gait cycles of different frame lengths. The samples are taken from video sequences with 5 km/h speed in OU-ISIR dataset A. The results (Fig. 4) show the accuracy rates for gait cycles of varying lengths from the normalized gait length. From the results, we may conclude that the proposed approach is insensitive to variations in the gait cycle.

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Fig. 4. Recognition accuracy on different frame lengths, (a) Number of sample, and (b) Percentage of correct recognition.

tion performed backwards. Besides that, our method requires significantly less computation time (combining feature extraction and classification time) without compromising on the performance. It is noteworthy to mention that the proposed approach reduces almost 90% of the time spent by the dynamic time warping based method. As for CASIA dataset B, a slight drop in recognition accuracy is observed in all methods except (Zhang et al., 2010) mainly due to the slightly inferior quality of the binary silhouette in the dataset. Despite that, the proposed approach still outperforms method (Mowbray and Nixon, 2003; Lu et al., 2008) and performs comparably with Tian et al. (2004).

We propose a Fourier descriptor-based method that model the periodic deformation of human gait. A new measure of dissimilarity using product of Fourier descriptor is proposed to measure the distance among deformable contours. To minimize the distance of closed curves across gait cycle, each contour is circularly aligned corresponding to its preceding contour. An element-wise linear interpolation is proposed to normalize the gait signatures into some desired length. The classification of each subset of gait signature is accomplished by summing the measure of dissimilarity, producing sublabel for each subset. The ultimate class label is determined by a simple majority voting of all sublabels in a video. Experiments results on OU-ISIR gait dataset A and D, and CASIA gait dataset B reveal that our proposed approach achieves promising recognition accuracy. The element-wise frame interpolation method has also proven to be able to preserve temporal information for small change of walking speed and to reduce the execution time to almost one tenth of dynamic time warping. Acknowledgments Portions of the research in this paper use the CASIA Gait Database collected by Institute of Automation, Chinese Academy of Sciences. References Bobick, A.F., Johnson, A.Y., 2001. Gait recognition using static activity-specific parameters. In: Proc. IEEE Computer Vision and Pattern Recognition, pp. 423– 430. Han, J., Bhanu, B., 2006. Individual recognition using gait energy image. Tras. Pattern Anal. Machine Intell. 28 (2), 316–322. Lam, T., Cheung, K., Liu, J., 2011. Gait flow image: a silhouette-based gait representation for human identification. Pattern Recognit. 44 (4), 973–987. Liu, Z., Sarkar, S., 2004. Simplest representation yet for gait recognition: averaged silhouette. In: Proc. 17th Internat. Conf. on Pattern Recognition, pp. 211–214.

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