Hybrid Hidden Markov Model for Face Recognition

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  • Topic: Probability density function, Facial recognition system, Normal distribution
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  • Published : January 3, 2013
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Hybrid Hidden Markov Model for Face Recognition

Hisham Othman and Tyseer Aboulnasr School of Information Technology and Engineering, University of Ottawa Ottawa, Ontario, Canada, K1N 6N5. hisham@site.uottawa.ca aboulnas@eng.uottawa.ca Abstract In this paper, we introduce a Hybrid Hidden Markov Model (HMM) face recognition system. The proposed system contains a low-complexity 2-D HMM-based face recognition (LC 2D-HMM FR) module that carries out a complete search in the compressed-domain followed by a 1-D HMM-based face recognition (1D-HMM FR) module which refines the search based on a candidate list provided by the first module. We also examine a remote database search methodology that may be helpful for accessing remote resources, where no prior information is assumed regarding the contents of the remote database. The performance of the Hybrid HMM face recognition system is reported for both, local and remote database search modes. complexity. The effect of the training data size on the model robustness is addressed in Section 4 and the results are given in Section 5.

1.1

Hidden Markov Model bases

Consider a random sequence, O={ot}, that consists of successive outcomes of a finite-state stochastic process. A HHM will efficiently represent such environment if: 1- The probability of the current state given all past states is only dependant on the past r states, hence, the process is called rth–order Markovian process. P[ q t | q t −1 , q t − 2 , ..., q t − r ,..., q 0 ] = P[q t | q t −1 , q t − 2 , ..., q t − r ] (1) where t is the time index. 2- The state transition itself is a stationary process, i.e.: (2) P[ q t | q t −1 , q t − 2, ..., q t − r ] = P[q t ’ | q t ’−1 , q t ’−2, ..., q t ’− r ] ∀t & t ’

1

Introduction

for all possible values of t and t’. 3- The outcomes are statistically independent, i.e.:

Face recognition (FR) technology provides an automated way to search, identify or match a human face versus the contents of a pre-stored facial database. Automatic face recognition is needed in criminal mug shot examinations and personal record retrieval. It is also integrated in surveillance and security systems that restrict access to certain service or location. The baseline feature of the face recognition system is identifying a person by his frontal facial view allowing face expressions, some tilt, and common changes like removing glasses or closing eyes. Many variations of the HMM have been introduced to the FR problem, including luminance-based 1D-HMM FR [1], DCT-based 1D-HMM FR [2], 2-D Pseudo HMM (2D-PHMM) FR [1], and the Low-Complexity 2D HMM (LC 2D-HMM) FR [3]. In the rest of this Section, the fundamentals of HMM are briefly described, then both the 1D-HMM and LC 2D-HMM face recognition systems are reviewed. The description of the proposed Hybrid HMM face recognition system is found in Section 2, while Section 3 contains a detailed discussion of the system

P[O | Q] = ∏ P[ot | q t ]
t =0

T −1

(3)

Implicitly, each state is assumed to be stationary. Note that, the term time is used to annotate the progressive dimension of the sequence, without loss of generality. HMM is usually used to approximate quasi-stationary random processes by a source that has two stationary layers. The behavior of that source is only observable through the process outcomes, i.e. the observation layer, while the state layer is hidden, hence called Hidden Markov Model. The Model main parameters are: 1- The transition probability matrix, A, that defines the probability of possible state transitions. 2- The observation probability matrix, B, that contains either discrete probability distributions or continuous probability density functions of the observations given the state. 3- The initial state probabilities, Π. Hence, the classic HMM is uniquely defined by these parameters and written as λ=[A, B, Π].

1.2

1D-HMM Face Recognition

The first-order 1D-HMM was applied to FR in [1] where the image of...
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