Statistically recognize faces based on hidden markov models
Download
1 / 21

Statistically Recognize Faces Based on Hidden Markov Models - PowerPoint PPT Presentation


  • 116 Views
  • Uploaded on

Statistically Recognize Faces Based on Hidden Markov Models. Presented by Timothy Hsiao-Yi Chin Rahul Mody. What is Hidden Markov Model?. Its underlying is a Markov Chain.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Statistically Recognize Faces Based on Hidden Markov Models' - osman


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
Statistically recognize faces based on hidden markov models

Statistically Recognize Faces Based on Hidden Markov Models

Presented by

Timothy Hsiao-Yi Chin

Rahul Mody

E6886 Project


What is hidden markov model

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.

E6886 Project


Mathematical notation of hmm
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

E6886 Project


Which probability function of o t
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 oiand

    are the mean vector and covariance matrix, respectively

E6886 Project


Re estimation of mean covariances and the transition probabilities
Re-estimation of mean, covariances, and the transition probabilities

E6886 Project


Example a markov model

70%

60%

25%

28%

5%

12%

70%

10%

20%

Example: A Markov Model*

Sunny

Rainy

Snowy

E6886 Project


Represent it as a markov model
Represent it as a Markov Model*

  • States:

  • State transition probabilities:

  • Initial state distribution:

E6886 Project


What is sequence o in this example
What is sequence o in this example?*

  • Sequence o:

  • The probability could be computed by the conditional probability:

E6886 Project


Example a hmm
Example: A HMM*

5%

70%

80%

20%

20%

Sunny

60%

Rainy

15%

38%

2%

5%

5%

75%

10%

75%

Snowy

20%

45%

5%

50%

E6886 Project


What other parameters will be needed
What other parameters will be needed?

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

  • Observations:

  • Observation probabilities:

E6886 Project


Forward backward algorithm forward
Forward-Backward Algorithm: Forward

  • If Observation probability is

  • then

E6886 Project


Forward backward algorithm backward
Forward-Backward Algorithm: Backward

  • If there is a

  • Then

  • The Forward-Backward Algorithm tells us that

  • for any time t

E6886 Project


Face identification using hmm
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.

E6886 Project


Face identification using hmm1
Face identification using HMM

  • In practice, we only need one S sequence

    which maximizes

  • This is a dynamic programming optimization procedure.

E6886 Project


Viterbi algorithm
Viterbi Algorithm

  • Given a S sequence, a dynamic programming approach to solve this problem

  • where

  • By induction, the max Probability in state i+1 at time t+1 is based on the max probability in state I at time t.

E6886 Project


Algorithm itself
Algorithm itself

  • Initialization

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

  • Recursion:

E6886 Project


Algorithm itself 2
Algorithm itself (2)

  • Termination

  • Sequence constructing from T to t

E6886 Project



Face detection
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.

E6886 Project


Acknowledgement
Acknowledgement

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

E6886 Project


Reference
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

E6886 Project