Recognizing human from a distance by gait biometric has attracted researchers in recent years. It has many advantages like; noninvasive, less obscured, unobtrusive, without subject cooperation, ability to work from a distance and with low quality video. Comparatively, gait biometric is newer modality than face, iris and fingerprint. Recognizing someone from a certain distance, where no fine details are available is very difficult task. In such case, gait biometrics in which the person gets recognized by the manner of walking only is useful. Gait is a potential biometric trait where unconstrained person identification is demanded. It is a protocol free biometric technique which does not require willingness of person and hence found application in surveillance. However, commonly used biometric recognition systems usually operate in constrained acquisition scenarios and under rigid protocols. The finger print, iris and face recognition could not be the right choice in the unconstrained environment, where distant data capture is required. Comparatively, gait comprised of motion trajectories of various body parts, have a potential to get captured properly from relatively far distance. It does not need systematic data capture process, where subjects should necessarily be informed. This makes the identification process protocol free. The extended application of gait recognition can be suspect identification in a sensitive area where security is at the highest priority. These characteristics of gait biometrics lead it to be an attractive modality from the perspective of human recognition from a distance.
In spite of various advantages, covariate factors like; walking speed, carrying conditions, clothing, the surface of walking, fatigue, drunkenness, pregnancy, injury to feet and the psychosomatic condition affect the normal walking style. View angle also plays vital role while testing such system. It may be possible that certain view angle provides discriminant information of walking individual while another may not. Hence, an investigation is needed to find robust gait representation which can cope up with these challenges in multiview scenario.
The main contribution of this paper is the achievement of significant recognition rate in covariate conditions like carrying bag and cloth variation. There is no need to segment bag from subject to remove covariate. It does not need any complex model to extract static or dynamic features. This scheme is simple, as it does not need color and texture information of the sequences and innovative in the sense that, the application of cross wavelet transform and graph model is not proposed in fusion approach yet.
Rest of the paper is organized as follows. Section Ⅱ briefs existing methods of gait recognition. In Section Ⅲ, proposed method is discussed. Section Ⅳ explores feature extraction and feature fusion along with training and testing of the system in details. Experimental results are discussed in Section Ⅴ followed by conclusion in Section Ⅵ.
Ⅱ. LITERATURE OVERVIEWGait recognition and analysis have been studied heavily in recent past. In this section we will discuss it briefly. The approaches in the literature can be broadly classified into two types viz. model free [1][4] and modelbased [5][8]. In these approaches, various static and dynamic features of gait sequences were extracted by using shape analysis, image geometry transformations, wavelet analysis, so on and so forth. The model free approach extracts features directly from the image plane. Whereas, the model based approach models the human gait and then extracts model parameters as features. In [1], procrustes shape analysis is used to represent gait signature, which is obtained by extracting the mean shape of the unwrapped silhouette. Whereas, [2] is a 3D approach for gait recognition, which constructs 3D silhouette vector of 2D scene by using stereo vision method. In a recent work [4], complete canonical correlation analysis is used to compute correlation between two gait energy image (GEI) features. In another recent paper [3], authors extract different width vectors and combined them to construct gait signature. This feature is then approximated by radial basis function (RBF) network for recognition.
In an earlier model based approach [5], gait pattern was detected in XYT spatiotemporal volume. The bounding contour of walking person is found by the snake. Furthermore a 5stick human model is controlled by these contours. Various angle signals are then extracted by using this model for recognition. Whereas in [6], each silhouette is first labelled manually. Various features like; area, gravity center, orientation of each body part is then calculated. In [8], the gait cycle is modelled as chain of key poses first, then features like pose energy image and pose kinematic are extracted. View invariant approaches have also been proposed in the regard of gait recognition such as [7]. In this paper, authors estimate marker less joints followed by viewpoint verification.
Either static or dynamic feature alone can perform well for recognition but with some limitations. While dealing with static features, one can not analyze dynamic features and viceversa. Extracting both features simultaneously improves the recognition rate on the cost of increased computational complexity. Various approaches are proposed in this regard, which extract static and dynamic features simultaneously, either fusing model free and model based approaches [9][13] or fusing various features into a single augmented feature vector [14][17].
In [14], gait energy image and motion energy images are combined to form feature vector, whereas in [15], the static silhouette template (SST) and dynamic silhouette template (DST) are fused to construct dynamic static silhouette template (DSST). The position of the gravity center of human body may change because of various covariate factors as aforementioned. This problem is addressed by [16]. In this paper, authors divide the GEI transformed image into three body parts like; head, torso and leg. Furthermore, they compute shifted energy image (SEI) features which are horizontal centres of body parts. Next, gait structural profile (GSP) extracted to capture body geometry. For this, silhouette segmented into four body parts as per the anatomical measurements like; head, torso, left and right leg. The GSP, which is the difference of gravity center of these segmented body parts and entire body is computed. These two features are then used in combination for recognition. In [17], two distinct features namely frieze pattern and wavelet coefficients are extracted. The frieze pattern preserves spatial information and wavelet coefficients preserve low frequency information. Factorial hidden Morcow model (HMM) is used to combine these features and parallel HMM facilitates decision level fusion of two individual classifiers for recognition. All these approaches signify that, the fusion of multiple gait features improves the recognition system performance.
There are certain methods, which explore static and dynamic characteristics of the human body. They fuse static and dynamic features for improvement in performance of gait recognition system. In [13], features like; centroid, arm swing, stride length, mean height were extracted from the binary silhouette. Further, they fit ellipse on each region and compute it's aspect ratio and orientation. These features are then combined and transformed by discrete cosine transform (DCT) and applied to generalized regression neural network for recognition. Whereas in [9], mean shape is extracted by using Procrustes shape analysis as a static feature. The dynamic features are extracted by modelling human body parts by truncated cone, head by sphere and computing joint angles of this model. A human skeleton model is adopted in [10] to extract dynamic features and computing various angles of key body points. The static feature is denoted by wavelet descriptor, which is obtained by applying wavelet transform to the boundarycentroid distance.
In [18], HMMs are used to extract static and dynamic gait features, without using any human body model. The static features are extracted by conventional HMM and dynamic features by hierarchical HMM. After labelling, they extract three features namely; component area, component center and component orientation. First HMM represents general shape information while the second HMM extracts detailed subdynamic information. Whereas in [19], local binary pattern is used to denote the texture information of optical flow as the static feature. Dynamic feature is represented by HMM with Gaussian mixture model. In [11], the GEI is transformed by dual tree complex wavelet transform (DTCWT) with different scales and orientations. A two stage Gaussian mixture model denote the patch distribution of each DTCWT based gait image. Further, to model the correlation of multiview gait feature, a sparse local discriminant canonical correlation model is used. In a recent paper [12], the dynamic feature is extracted by LucasKanade based optical flow image. The mean shape of head and shoulder are then extracted by using Procrustes shape analysis, which is the static feature. The fusion is done on score level.
It can be noted that not all the aforementioned methods adopt human body model such as skeleton to extract dynamic features. Most often, authors prefer mathematical modelling, as it is efficient to extract different kinds of features and also facilitate lower computational complexity.
Ⅲ. PROPOSED GAIT RECOGNITION METHODThis paper aims to develop a method, which is the fusion of both approaches, viz., model free and model based, without using human body model such as skeleton. It facilitates to extract static and dynamic feature sets simultaneously. Dynamic feature set is obtained by computing cross wavelet transform among dynamic body parts like hand and leg from each gait sequence. Further, to extract static feature set, the bipartite graph is used to model gait silhouette, as the graph is a powerful tool to represent an image on the basis of pixel adjacency. We apply quadrature mirror filter (QMF)graph wavelet filter bank proposed by [20] to each gait sequence. Only analysis filter bank is used for this task. The feature vector (FV) represented by fusion of these two feature sets.
The static and dynamic feature sets extracted from all the sequences with 11 view angles and 10 covariate conditions. These features are combined on feature level. The centroid of clusters of these augmented feature vectors then obtained by using kmeans clustering. The Euclidean distance computed between each feature vector and centroid of clusters which is linearly classified in linear discriminant analysis (LDA) space. For identification, we use Bayesian framework. These steps are depicted in Fig. 1.
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Fig. 1 Proposed method. 
In this work, we use CASIA B multiview gait database [21], which consists of 124 persons. Each person is depicted in 10 sequences with various covariate (
The silhouettes which are available readily in CASIA B database have holes as shown in Fig. 2(a) and breaks in successive frames as shown in Figs. 2(b) and 2(c). In order to extract meaningful features, we do morphological operations like; dilation, erosion, opening and closing. Further, it is required to divide silhouette which contains body parts like hands and legs. A bounding box technique is applied after cropping the divided silhouette from complete silhouette to get horizontal width of cropped silhouette. This width varies in each frame as hands/legs displaces. We divide entire silhouette into three equal parts, viz., the portions containing head and shoulder, hands, legs. We processed only the portions containing hand and legs by first cropping and then applying bounding box on both the portions separately. The width of the bounding box is saved as 1D width vector. Here, in this work we consider the movement of hand and leg only for the computation of dynamic feature using cross wavelet transform.
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Fig. 2 Inferior silhouette. (a) Hole in silhouette 
Let
$ {X_n} = \{x_1, x_2, x_3, \ldots, x_t \} $  (1) 
$ Y_n= \{y_1, y_2, y_3, \ldots, y_t \} $  (2) 
where
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Fig. 3 1D signals extraction. 
After preprocessing, the width vectors extracted from each silhouette which represents the dynamic movements of hands and legs throughout the entire gait sequence. Cross wavelet transform then applied to these 1D signals. Morlet wavelet (with
$ \psi_0(\eta)=\pi^{\frac{1}{4}}e^{i\omega_0\eta}e^{\frac{\eta^2}{2}} $  (3) 
where
1) Cross Wavelet Transform: The cross wavelet transform is defined over two time series, which reveal an area of common higher power and relative phase in the timefrequency domain. Cross wavelet transform of two time signals
$ W(X_n, Y_n)=W(X_n)\cdot W(Y_n)^* $  (4) 
where
$ W_p=W(X_n, Y_n). $  (5) 
The local relative phase between
$ \Phi_n={\rm arg}\left(W(X_n, Y_n)\right). $  (6) 
The complete representation of wavelet cross spectrum is
$ W(X_n, Y_n)=W(X_n, Y_n)e^{i\phi_n} $  (7) 
where
2) Wavelet Coherence: More significant coherence between two continuous wavelet transformed signals is found even when common power is low. This relationship is expressed as wavelet coherence (WCOH). Wavelet coherence denotes the relationship between two independent time series signals expressed in terms of area of the common frequency band at a certain time interval, across which these two signals vary simultaneously. Following [22], [23], wavelet coherence between two signals
$ WC(X_n, Y_n)= \frac{ \varsigma \left[W(X_n, Y_n)\right]}{\sqrt{\varsigma\left[W(X_n)\right]\times \varsigma \left[W(Y_n)\right]}} $  (8) 
where
For demonstration purpose, we show 1D signals extracted at angle
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Fig. 4 
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Fig. 5 Wavelet cross spectrum at view angle 
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Fig. 6 Wavelet coherence at view angle 
The dynamic feature set includes the mean value of cross wavelet spectrum along with wavelet coherence and phase across the entire gait sequence. The length of dynamic features varies with the number of frames present in that particular sequence, hence zero padding is done to individual feature to make the feature set of fixed length.
C. Static Feature ExtractionVarious static features like; mean height, centroid, mean shape, wavelet descriptor have been presented earlier, which are already discussed in literature overview. We do not extract such features. Instead, first we represent gait silhouette by a bipartite graph and further use QMFgraph filter bank to compress the entire gait sequence. A brief about graph and QMFgraph filter bank is discussed next.
1) Graph Model: A graph
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Fig. 7 Bipartite graph. 
Here, we apply only analysis filter of perfect reconstruction two channel critically sampled QMFgraph wavelet filter bank as shown in Fig. 8 to compress the graphstructured data. As suggested in [20], the colouring of the vertices is done by using BSC algorithm [25], followed by decomposition of the graph into the set of bipartite graphs using Harary's algorithm [26]. Each subgraph is down sampled by
$ H_0= h_0\left(\mathcal{L}\right)= \sum\limits_{\lambda \in \sigma\left(G\right)} h_0\left(\lambda\right)P_{\lambda} $  (9) 
$ H_1= h_1\left(\mathcal{L}\right)= \sum\limits_{\lambda \in \sigma\left(G\right)} h_1\left(\lambda\right)P_{\lambda} $  (10) 
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Fig. 8 Graph wavelet filter bank (analysis). 
where,
As discussed in previous subsections, static and dynamic features are extracted, which have different discriminating power. We concatenated these two features to construct a single augmented feature vector. Since, these features are not directly comparable, we first normalize them using minmax normalization method [27]. The length of dynamic features varies with the number of frames present in that particular sequence, hence zero padding is done to individual feature to make the dynamic feature set of fixed length. The static feature set is of fixed length, hence zero padding is not required. Further, weights for normalized feature vectors are computed using the meanvariance method.
The normalized static and dynamic feature vectors are
$ \overline{FV}_{\rm static}= \frac{FV_{\rm static} \min \left(FV_{\rm static}\right)}{\max \left(FV_{\rm static}\right)\min \left(FV_{\rm static}\right)} $  (11) 
$ \overline{FV}_{\rm dynamic}= \frac{FV_{\rm dynamic} \min \left(FV_{\rm dynamic}\right)}{\max \left(FV_{\rm dynamic}\right)\min \left(FV_{\rm dynamic}\right)}. $  (12) 
The weights for normalized features vectors are
$ w_{\rm static}=\frac{m_{\rm static}}{\sigma_{\rm static}} $  (13) 
$ w_{\rm dynamic}=\frac{m_{\rm dynamic}}{\sigma_{\rm dynamic}} $  (14) 
where,
Finally, these two features are concatenated as shown in (15) to form a single augmented vector for representation and further processing,
$ FV= \left[\left(w_{\rm static}\cdot\overline{FV}_{\rm static}\right), \left( w_{\rm dynamic}\cdot\overline{FV}_{\rm dynamic}\right)\right]. $  (15) 
For demonstration of the proposed fusion approach, we computed dynamic and static features of a person walking normally with view angle of
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Fig. 9 Normalized WCS feature. 
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Fig. 10 Normalized WCOH feature. 
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Fig. 11 Normalized phase feature. 
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Fig. 12 Normalized filter bank coefficients. 
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Fig. 13 Augmented feature vector. 
For each gait sequence we extract feature vector
$ \sum\limits_{q=1}^{Q} \sum\limits_{i=1}^{P_N} \alpha_{iq} \Vert FV^{(P_N, V_A, C_V)}  p_q \Vert ^2 $  (16) 
where
The
$ d_{Ed}=\Vert FV^{(P_N, V_A, C_V)}  p_q \Vert. $  (17) 
Other distances can also be used but Euclidean distance exhibit simple representation hence preferred. Each distance vector is then finally represented as
$ R_{FV}=\frac{d_{Ed}}{\Vert d_{Ed}\Vert}. $  (18) 
To make this membership vector duration invariant, as we use multiperiod gait sequences, the mean of
$ v_i= \frac{1}{t_j} \sum\limits_{k=1}^{t_j}R_{FV}^{ik}. $  (19) 
Further, linear discriminant analysis is applied to
$ W_{\rm opt}= {\rm arg\, min} \frac{\left( W^T S_w W\right)}{\left( W^T S_b W\right)} $  (20) 
where
$ S_w= \sum\limits_{n=1}^{C} S_i $  (21) 
$ S_i= \sum\limits_{x \epsilon \omega_i} \left(x\mu_i \right)\left(x\mu_i\right)^T $  (22) 
$ S_b= \sum\limits_{i=1}^{C} n_i \left(\mu_i  \mu \right)\left(\mu_i  \mu \right)^T $  (23) 
where
$ \mu= \frac{1}{n} \sum\limits_{\forall x} x $  (24) 
The test feature vector is obtained using similar steps as used to obtain the training feature vector. For identification, we use probabilistic model such as Bayesian framework. The Bayesian probabilistic decision theory is a fundamental approach in pattern classification. Assuming equiprobable classes and all probabilities are known, let
$ \tiny{P(jP_1, V_1, C_1, \ldots, P_N, V_N, C_N)}\\ ~~~~~=\frac{P(P_1, V_1, C_1, \ldots, P_N, V_N, C_Nj)\cdot P(j)} {\sum\limits_{n=1}^{N_P}P(P_1, V_1, C_1, \ldots, P_N, V_N, C_Nn)\cdot P(n)}. \\ $  (25) 
Experiments are performed on CASIA B multiview gait database, considering all view angles and covariate conditions in MATLAB environment. All the training classes are equiprobable as Bayesian framework is used for identification. Training includes all view angles and covariate factors considering only hand and leg movement. The mean value of wavelet cross spectrum (WCS) along with wavelet coherence and phase (
We compare our work with [16], [11] and [28], even though it is not straight forward. The rank
Whereas in [28], authors extract static and dynamic features. The histogram distribution of optical flow vector is used as dynamic feature and Fourier descriptor is used as static feature. This work is similar to ours in this sense but they consider only three view angles, viz.,
The proposed method outperforms the above methods as the features we extracted are robust and found invariant to covariate conditions especially carrying bag and cloth variations.
Ⅵ. CONCLUSIONIn this work, we use cross wavelet transform and bipartite graph model for gait based human recognition in multiview scenario. The experimental results show that, the fusion of different kinds of features represent gait pattern of an individual significantly.
Table Ⅱ shows that our method outperforms others in covariate conditions also. The average recognition rate considering all viewangles and covariate conditions in Bayesian framework is
Portions of the research in this paper use the CASIA gait database collected by Institute of Automation, Chinese Academy of Sciences. Authors are grateful to Prof. Yogesh Ratnakar Vispute, for proof reading of the paper.
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