Statistically Recognize Faces Based on Hidden Markov Models

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Statistically Recognize Faces Based on Hidden
Markov Models

• Presented by
• Timothy Hsiao-Yi Chin
• Rahul Mody

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What is Hidden Markov Model?

• Its underlying is a Markov Chain.
• An HMM, at each unit of time, a single
  observation is generated from the current state
  according to the probability distribution, which
  is dependent on this state.

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Mathematical Notation of HMM

• Suppose that there are T states S1, , ST and
  the probability between state i and j is Pij.
  Observation of system can be defined as ot at
  time t. Let bSi(oi) be the probability function
  of ot at time t. Lastly, we have the initial
  probability , i 1, , n of Markov chain.
  Then the likelihood of the observing the sequence
  o is

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Which probability function of ot?

• In HMM framework, observation o is assumed to be
  governed by the density of a Gaussian mixture
  distribution.
• Where k is the dimension of ot , and where oi and
• are the mean vector and covariance
  matrix, respectively

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Re-estimation of mean, covariances, and the
transition probabilities
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Example A Markov Model
Sunny
Rainy
Snowy
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Represent it as a Markov Model

• States
• State transition probabilities
• Initial state distribution

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What is sequence o in this example?

• Sequence o
• The probability could be computed by the
  conditional probability

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Example A HMM
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What other parameters will be needed?

• If we can not see what is inside blue circle,
  what can we actually see?
• Observations
• Observation probabilities

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Forward-Backward Algorithm Forward

• If Observation probability is
• then

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Forward-Backward Algorithm Backward

• If there is a
• Then
• The Forward-Backward Algorithm tells us that
• for any time t

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Face identification using HMM

• An Observation sequence is extracted from the
  unknown face, the likelihood of each HMM
  generating this face could be computed.
• In theory, the likelihood is
• The maximum P(O) can identifies the unknown
  faces.
• However, it takes too much time to compute.

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Face identification using HMM

• In practice, we only need one S sequence
• which maximizes
• This is a dynamic programming optimization
  procedure.

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Viterbi Algorithm

• Given a S sequence, a dynamic programming
  approach to solve this problem
• where
• By induction, the max Probability in state i1 at
  time t1 is based on the max probability in state
  I at time t.

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Algorithm itself

• Initialization
• where denotes the collection of that
  sequence which is based on max
• Recursion

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Algorithm itself (2)

• Termination
• Sequence constructing from T to t

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So far we have this block diagram
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Face Detection

• In simple face recognition framework, the picture
  is assumed to be a frontal view of a single
  person and the background is monochrome.
• This project assumes that with the techniques of
  face detection, the performance of face
  recognition may be better than the approach
  presented above.

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Acknowledgement

• The authors of this presentation slides would
  like to give thanks to Dr. Doan, UIUC.

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Reference

• 1 Ferdinando Samaria, and Steve Young,
  HMM-based architecture for face identification.
• 2 Jia, Li, Amir Najmi, and Robert M. Gray,
  Image Classification by a Two-Dimensional Hidden
  Markov Model
• 3 Ming-Hsuan Yang, David J. Kriegman, Narendra
  Ahuja, Detecting Faces In Images A survey
• 4 T.K. Leung, M. C. Burl, and P. Perona,
  Finding Faces in Cluttered Scenes using Random
  Labeled Graph Matching
• 5 James Wayman, Anil Jain, Davide Maltoni, and
  Dario Maio, Biometric Systems, Springer, 2005