# video-based face recognition using Adaptive HMM

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# Introduction

## Human face recognition

Human face recognition is a subarea of object recognition aims to identify persons face given a scene or still images. Face recognition benefits many fields such as computer security and video compression. Two approaches are commonly used in face recognition are video-based and still images. Since 80’s, image-based recognition approach is more dominant in face recognition in comparison with the video-based approach. Few recent studies took advantages of the features of video scenes as it provides more dynamic characteristic of the human face that help the recognition process. Also, video scene provides more features of 3D representation and high resolution images. Besides, in video-based recognition the prediction accuracy can be improved using the farm sequence. Motivated by speaker adaptation, this paper presents an Adaptive Hidden Markov model to recognise human face from frames sequence. The proposed model train HMM on the training data and then improve the recognition constantly using the test data.

## Hidden Markov Model (HMM)

Hidden Markov Model is graphical model that suitable to represent sequential data. HMM consists of hidden variables, initial state and Marov chain unobserved states. HMM characterized by [math]\lambda=(A,B,\pi)[/math] :

Given N of states [math]S ={S_1 ,S_2 , ,S_N }[/math] and [math]q_t[/math] state of time T

A a transition matrix where [math]a_ij[/math] is the (i,j) entry in A:

[math]a_ij=P(q_t=S_j|q_{t-1}=S_i)[/math] where [math]1\leq i,j \leq N[/math]

B the observation pdf [math]B={b_i(O)}[/math]

[math]b_i(O)=\sum_{k=1}^M c_{ik} N(O,\mu_{ik},U_{ik})[/math] where [math]1\leq i \leq N [/math]

where [math]c_{ik}[/math] is the mixture coefficient for [math]k_th[/math] mixure component of [math]S_i[/math]

M number of component in Gaussian mixture model .

[math]\mu_{ik}[/math] is the mean vector and [math]U_ik[/math] is the covariance matrix .

the intial state [math]\pi_i=p(q_t=S_i)[/math] wherer [math]1\leq i \leq N[/math]