Timothy and RahulE6886 Project1 Statistically Recognize Faces Based on Hidden Markov Models Presented by Timothy Hsiao-Yi Chin Rahul Mody

Timothy and RahulE6886 Project2 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.

Timothy and RahulE6886 Project3 Mathematical Notation of HMM Suppose that there are T states {S 1, …, S T } and the probability between state i and j is P ij. Observation of system can be defined as o t at time t. Let b S i (o i ) be the probability function of o t 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

Timothy and RahulE6886 Project4 Which probability function of o t ? In HMM framework, observation o is assumed to be governed by the density of a Gaussian mixture distribution. Where k is the dimension of o t, and where o i and are the mean vector and covariance matrix, respectively

Timothy and RahulE6886 Project5 Re-estimation of mean, covariances, and the transition probabilities

Timothy and RahulE6886 Project6 Example: A Markov Model* Sunny Rainy Snowy 70% 25% 5% 60% 12% 28% 20% 70%10%

Timothy and RahulE6886 Project7 Represent it as a Markov Model* States: State transition probabilities: Initial state distribution:

Timothy and RahulE6886 Project8 What is sequence o in this example?* Sequence o: The probability could be computed by the conditional probability:

Timothy and RahulE6886 Project9 Example: A HMM* Sunny Rainy Snowy 80% 15% 5% 60% 2% 38% 20% 75% 5% 70% 10% 20% 75% 5% 20% 50% 5% 45%

Timothy and RahulE6886 Project10 What other parameters will be needed? If we can not see what is inside blue circle, what can we actually see? Observations: Observation probabilities:

Timothy and RahulE6886 Project11 Forward-Backward Algorithm: Forward If Observation probability is then

Timothy and RahulE6886 Project12 Forward-Backward Algorithm: Backward If there is a Then The Forward-Backward Algorithm tells us that for any time t

Timothy and RahulE6886 Project13 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.

Timothy and RahulE6886 Project14 Face identification using HMM In practice, we only need one S sequence which maximizes This is a dynamic programming optimization procedure.

Timothy and RahulE6886 Project15 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.

Timothy and RahulE6886 Project16 Algorithm itself Initialization where denotes the collection of that sequence which is based on max Recursion:

Timothy and RahulE6886 Project17 Algorithm itself (2) Termination Sequence constructing from T to t

Timothy and RahulE6886 Project18 So far we have this block diagram

Timothy and RahulE6886 Project19 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.

Timothy and RahulE6886 Project20 Acknowledgement The authors of this presentation slides would like to give thanks to Dr. Doan, UIUC.

Timothy and RahulE6886 Project21 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