Recognition System
of Japanese Characters
Introduction
The principal tasks of a Recognition System are:
To extract the principal movement characteristics.
To compare the results with a predifined set of movements.
To identify the most likely data sequence.
Hidden Markov Models (HMMs)
"An HMM is a doubly stochastic process with an underlying stochastic process which is not observable, but can only be observed through another set of stochastic process that produce the sequence of observed symbols"
[Rabiner & Joung, 1986]
HMM elements
The principal elements of an HMM are:
State q
Symbol sequence O
Number of States N
Observation Lenght T
Codebook size M
Initial State
Distribution
State-Transition probability A NxN
Observable Symbol probability B MxN
HMM parameter
set
Output
probability
HMM's Elements
Types of HMMs
There are two principal types of HMMs:
1. Ergodic Model: Every state can reach any other state of the model in a single step. The State-Transition matrix (A) is a full matrix.
Ergodic Model
1. Bakis Model: As shown in the figure, some states may need more than one step to reach another state of the model. The State-Transition matrix isn't a full matrix. It's properties depends of the model's order.
Bakis Model (Left-Right Model)
Advantages of HMMs
The main advantages of using an HMM in handwritting recognition are:
Partial (on-line) evaluation of sequences.
On-line training with movements.
HMMs can be programmed by examples.
Detection problem has a linear complexity.
HMM recognition produces the whole hit list analysis.
Basic problems of HMMs
Probability Evaluation: How can
we evaluate the probability function ?. Using the
Backward-Forward procedure.
Parameter Estimation: How can we estimate the parameter set to maximize its function ?. Using Baum-Welch procedure.
Optimal State Sequence: How can we find the optimal state sequence ?. Using the Viterbi algorithm.
Last update 01.15.2004
These pages are maintained by Jorge Solis