Multi-Dimensional Dependency-Tree Hidden Markov Models

In this paper, we propose a new type of multi-dimensional hidden Markov model based on the idea of dependency tree between positions. This simplification leads to an efficient implementation of the re-estimation algorithms, while keeping a mix of horizontal and vertical dependencies between positions. We explain DT-HMM and we present the formulas for the maximum likelihood re-estimation. We illustrate the algorithm by training a 2-dimensional model on a set of coherent images

[1]  Paul D. Gader,et al.  Generalized hidden Markov models. I. Theoretical frameworks , 2000, IEEE Trans. Fuzzy Syst..

[2]  Gerhard Rigoll,et al.  A comparison of discrete and continuous output modeling techniques for a pseudo-2D hidden Markov model face recognition system , 2001, Proceedings 2001 International Conference on Image Processing (Cat. No.01CH37205).

[3]  Robert M. Gray,et al.  Image classification by a two dimensional hidden Markov model , 1999, 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings. ICASSP99 (Cat. No.99CH36258).

[4]  J. Baker.  Trainable grammars for speech recognition , 1979 .

[5]  L. Baum,et al.  Statistical Inference for Probabilistic Functions of Finite State Markov Chains , 1966 .

[6]  P. Gader,et al.  Generalized Hidden Markov Models — Part I : Theoretical Frameworks , 2008 .

[7]  Roberto Pieraccini,et al.  Dynamic planar warping for optical character recognition , 1992, [Proceedings] ICASSP-92: 1992 IEEE International Conference on Acoustics, Speech, and Signal Processing.

[8]  Kenneth Rose,et al.  Deformable face mapping for person identification , 2003, Proceedings 2003 International Conference on Image Processing (Cat. No.03CH37429).

[9]  Lawrence R. Rabiner,et al.  A tutorial on hidden Markov models and selected applications in speech recognition , 1989, Proc. IEEE.

[10]  Yoram Singer,et al.  The Hierarchical Hidden Markov Model: Analysis and Applications , 1998, Machine Learning.

[11]  Stéphane Marchand-Maillet,et al.  Approximate Viterbi decoding for 2D-hidden Markov models , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[12]  Frederick Jelinek,et al.  Statistical methods for speech recognition , 1997 .

[13]  Hisham Othman,et al.  A simplified second-order HMM with application to face recognition , 2001, ISCAS 2001. The 2001 IEEE International Symposium on Circuits and Systems (Cat. No.01CH37196).