Color texture analysis using the wavelet-based hidden Markov model

The wavelet-domain hidden Markov model (WD HMM), in particular the hidden Markov tree (HMT), has recently been proposed and applied to gray texture analysis with encouraging results. For color texture analysis, the previous WD HMM can only be used to model the different color planes individually, assuming they are independent of each other. However, this assumption in general is unrealistic. We show in this paper that the wavelet coefficients have certain inter-dependences between color planes. This paper presents a novel approach to modeling the dependences between color planes as well as the interactions across scales. In our approach, the wavelet coefficients at the same location, scale and sub-band, but different color planes are grouped into one vector. We then propose a multivariate Gaussian mixture model (MGMM) for approximating the marginal distribution of the wavelet coefficient vectors in one scale and capturing the interactions of different color planes. In addition, the statistical dependence between different scales is captured by the transition matrix of the hidden Markov tree. Using this approach, we can improve the performance of the WD HMM on the color texture classification. The experiments show that our WD HMM approach provides 85% of correct classifications (PCC) on 68 color textures from Oulu texture database and outperforms the other wavelet-based methods we study. In this paper, we also investigated the classification performance of the WD HMM methods on different color spaces.