Distributed Source Coding for Gait Recognition in .NET

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22.5 Distributed Source Coding for Gait Recognition
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reduces the security of the system. Thus, the design of an effective biometric system based on the channel codes involves the careful selection of the channel code rate to achieve the optimal trade-off between performance and security. Besides the channel code rate, the error-correcting capabilities of the channel decoder also depend on the information of the noise channel and the relationship between the noise induced by the channel and the side information y. Accurate modeling of the distribution of the noise channel may improve the knowledge of the channel decoder, as will be analyzed in Section 22.5.3. It must be noted that the proposed biometric authentication framework can be used with any biometric trait, provided that a robust feature extraction method exists. As a case study, a gait recognition system is developed based on the proposed framework in this chapter. The feature extraction process of the gait sequences is brie y presented in the following section.
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Gait recognition has emerged as a very tempting approach for unobtrusive real-time authentication method during the last years. Many methods have been proposed in the literature for the ef cient representation of the human walking. These methods can be categorized into feature-based and model-based techniques. The former do not use any speci c model of the human body for gait analysis [12 17], while the latter study static and dynamic body parameters [18 21] of the human locomotion. In this chapter, three novel feature-based techniques are used for feature extraction. Two of them are based on the generalized Radon Transform, namely the Radial Integration Transform (RIT) and the Circular Integration Transform (CIT), which have been proven to provide a full analytical representation of the human silhouette using a few coef cients. The third technique is based on the Krawtchouk moments that are well known for their compactness and discrimination capability. It should be noted that the use of moments for shape identi cation has received increased attention [22, 23] recently. Shutler and Nixon [23] proposed the use of Zernike velocity moments to describe and analyze the motion throughout a gait sequence. Motivated by the successful use of these continuous orthogonal moments, a set of discrete orthogonal moments based on Krawtchouk moments are presented, which have been proven to offer reliable reconstruction of the original image using relatively low-order moments [24]. Since the exact description of the gait recognition system is out of the scope of this chapter, only a brief discussion is provided for sake of self-completeness in the Appendix. The interested readers are referred to reference 13 for additional details on the features for gait representation.
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When the features for the representation of gait are extracted, the distributed source coding framework of Section 22.3 can be applied. The biometric system is divided in
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Distributed Source Coding for Biometrics
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two stages: (a) the enrollment stage and (b) the authentication stage, which are further analyzed below.
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Enrollment Stage
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At the enrollment stage, the signature of the gait sequence is extracted, as described in Section 22.4. The extracted features are concatenated and form the vector x = [x1 , . . . , xk ]T , thus x Rk . The feature vector x must be transformed from the continuous to the discrete domain so that it can be further processed by the channel encoder. This mapping can be represented by a uniform quantizer with 2L levels. Each component of x is then mapped to an index in the set Q, through the function Q : Rk Qk , where Q = {0, 1, . . . , L 1}. The resulting vector q = Q(x) is fed to the Slepian Wolf encoder, which performs the mapping e : Qk Cn , where C = {0, 1} and outputs the codeword c = e(q), c Cn . In this work, the Slepian Wolf encoder is implemented by a systematic LDPC encoder [25]. LDPC codes were selected due to their excellent error detecting and correcting capabilities. They also provide near-capacity performance over a large range of channels while simultaneously admitting implementable decoders. An LDPC code (n, k) is a linear block code of codeword length n and information block length k which is de ned by a sparse (n k) n parity matrix H, where n k denotes the parity bits produced by the encoder. The code rate is de ned as r = k/n. A code is a systematic code if every codeword consists of the original k-bit information vector followed by n k parity bits. In the proposed system, the joint bit-plane encoding scheme of reference 26 was employed to avoid encoding and storing the L bit-planes of the vector q separately. Alternatively, LDPC codes in a high-order Galois eld could be employed, but binary LDPC codes (GF(2)) were selected due to ease of implementation. Subsequently, the k systematic bits of the codeword c are discarded and only the parity bits s that is, the n k parity bits of the codeword c are stored to the biometric database. Thus, the biometric template of an enrolled user consists of the parity bits s, s C(n k) and its size is n k.
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