Fast Schemes for Computing Similarities between Gaussian HMMs and Their Applications in Texture Image Classification

Abstract

An appropriate definition and efficient computation of similarity (or distance) measures between two stochastic models are of theoretical and practical interest. In this work, a similarity measure, that is, a modified "generalized probability product kernel," of Gaussian hidden Markov models is introduced. Two efficient schemes for computing this similarity measure are presented. The first scheme adopts a forward procedure analogous to the approach commonly used in probability evaluation of observation sequences on HMMs. The second scheme is based on the specially defined similarity transition matrix of two Gaussian hidden Markov models. Two scaling procedures are also proposed to solve the out-of-precision problem in the implementation. The effectiveness of the proposed methods has been evaluated on simulated observations with predefined model parameters, and on natural texture images. Promising experimental results have been observed.

Keywords

• similarity measure
• hidden Markov model
• kernel method
• Bhattacharyya affinity
• texture classification