Face Recognition

Face Recognition

Daijin Kim (Pohang University of Science & Technology, Korea) and Jaewon Sung (LG Electronics, Korea)
Copyright: © 2009 |Pages: 92
DOI: 10.4018/978-1-60566-216-9.ch005

Abstract

In the modern life, the need for personal security and access control is becoming an important issue. Biometrics is the technology which is expected to replace traditional authentication methods that are easily stolen, forgotten and duplicated. Fingerprints, face, iris, and voiceprints are commonly used biometric features. Among these features, face provides a more direct, friendly and convenient identification method and is more acceptable compared with the individual identification methods of other biometrics features. Thus, face recognition is one of the most important parts in biometrics.
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5.2 Embedded Hidden Markov Model

An embedded hidden Markov model (EHMM) is an extension of the previous 1-D HMM in order to deal with two-dimensional data such as images and videos. The EHMM was previously used for character recognition by Kuo and Agazzi (Kuo and Agazzi, 1994). In fact, a fully connected 2-D HMM would be desirable for modelling a 2-D face image. However, the computational complexity for a fully connected 2-D HMM increases explosively as the number of states grows. In this work, we adopt the Samaria's Pseudo 2-D HMM (P2D-HMM) obtained by linking 1-D left-right HMMs to form super states. The structure includes one internal 1-D HMM in each state in the outer 1-D HMM. While transitions in a vertical direction are allowed between two adjacent super states which include the super state itself, transitions in a horizontal direction are only allowed between two adjacent states in a super state including the state itself. From this structure, we know that the sequence of super states are used to model a horizontal slice of face image along the vertical direction and that the sequence of states in a super state are used to model a block image along the horizontal direction. We call this model an embedded HMM. It differs from a 2-D HMM since a transition between the states in different states are allowed. Figure 1 illustrates a 5-super states EHMM for face modelling, where each super state represents vertical facial features, such as forehead, eyes, nose, mouth, and chin in the face and each state in the super state represents horizontal local block features in the corresponding facial feature.

Figure 1.

An illustration of 2-D EHMM with 5 super states for face modeling

978-1-60566-216-9.ch005.f01

The EHMM is defined by specifying the following parameters (Samaria and Young, 1994):

  • N0 is the number of super states in the vertical direction of EHMM.

  • 978-1-60566-216-9.ch005.m20 is the initial super state distribution, where π0,i is the probability of observation sequence 978-1-60566-216-9.ch005.m21 being in the ith super state.

  • 978-1-60566-216-9.ch005.m22 is the super state transition probability matrix, where 978-1-60566-216-9.ch005.m23 is the probability of transition from the ith to the jth super state.

  • 978-1-60566-216-9.ch005.m24 is the set of left-right 1-D HMMs in each super state. Each 978-1-60566-216-9.ch005.m25 is specified by the standard 1-D HMM parameters as follows.

    • -

      978-1-60566-216-9.ch005.m26 is the number of states in the kth super state.

    • -

      978-1-60566-216-9.ch005.m27 is the initial state distribution, where 978-1-60566-216-9.ch005.m28 is the probability of observation 978-1-60566-216-9.ch005.m29 being in the jth state of the kth super state.

    • -

      978-1-60566-216-9.ch005.m30 is the state transition probability matrix, where 978-1-60566-216-9.ch005.m31 is the probability of transition from the ith to the jth state of the kth super state.

    • -

      978-1-60566-216-9.ch005.m32 is the output probability function, where

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