MRF-based texture segmentation using wavelet decomposed images

Abstract

In recent textured image segmentation, Bayesian approaches capitalizing on computational efficiency of multiresolution representations have received much attention. Most of the previous researches have been based on multiresolution stochastic models which use the Gaussian pyramid image decomposition. In this paper, motivated by nonredundant directional selectivity and highly discriminative nature of the wavelet representation, we present an unsupervised textured image segmentation algorithm based on a multiscale stochastic modeling over the wavelet decomposition of image. The model, using doubly stochastic Markov random fields, captures intrascale statistical dependencies over the wavelet decomposed image and intrascale and interscale dependencies over the corresponding multiresolution region image.

Introduction

An important problem in image processing is segmentation of an image into disjoint regions which may possess the same average gray level but differ in the spatial distribution of gray levels (texture). Segmentation of images based on textural features is a critical preliminary operation in various image processing applications ranging from computer vision to remote sensing. In the last decade, there has been considerable interest in Bayesian estimation techniques in conjunction with Markov random fields (MRFs) for segmenting textured images. These methods use distinct stochastic processes to model textures covering each region and typically an MRF with smooth spatial behavior to model a region image. Segmentation of an image is then achieved by finding an approximate Maximum a posteriori (MAP) estimate of the unknown region image given the observed image.

Recently, motivated by the importance of utilizing information at various scales, a number of authors proposed multiresolution approaches to textured image segmentation, mainly to capitalize on computational efficiency of multiresolution models. Multiresolution approaches make it possible to capture and utilize correlations over a set of neighborhoods of increasing size by making use of multiresolution representations for the region image and single [1], [2] or multiresolution representations [3], [4] for the observed image. Bouman et al. [1] used a Gaussian autoregressive model for the observed image. The MAP estimate of the region image at the coarsest resolution is approximated first, using iterated conditional modes (ICM) [5], and the result is then used as an initial condition for segmentation at the next finer level of resolution, and the process is continued until individual pixels are classified at the finest resolution. Krishnamachari et al. [3] used a Gauss Markov random field (GMRF) to model the observed image at each resolution with the assumption that the random variables at a given resolution are independent of the random variables at other levels. It was assumed that the GMRF parameters at the finest resolution are known. The MAP estimate is approximated at each resolution using ICM first at the coarsest level and then progressively at finer levels. Comer et al. [4] proposed a multiresolution Gaussian autoregressive model for the observed image which takes into account the correlation between adjacent levels of resolutions. It was assumed that the parameters of the Gibbs distribution of the region process are known. Segmentation is achieved there as the maximum posterior marginals (MPM) estimate rather than the MAP estimate.

Most of the previous multiresolution approaches, however, have been based on modeling of the region and/or observed image over the lattice structure which corresponds to the Gaussian pyramid decomposition [6] of the observed image. In this paper, we propose a multiresolution Bayesian approach based on modeling over the lattice structure which corresponds to the wavelet decomposition [7] of the observed image. The wavelet decomposition of an image, as opposed to the Gaussian pyramid decomposition, results in nonredundant and direction (horizontal, vertical, diagonal) sensitive features at different scales and hence allows more selective feature extraction in space-frequency domain. It might also be easier to model the nonredundant and direction sensitive subbands of a wavelet decomposed image than to model each subband of a Gaussian pyramid decomposed image where the image at a resolution contains all the information in the lower resolutions.

The proposed modeling scheme captures, over the wavelet pyramidal lattice, significant intrascale and interscale statistical dependencies in the region image and intrascale statistical dependencies in the observed image, using doubly stochastic MRFs. To estimate model parameters, a version of the expectation-maximization (EM) algorithm [8] is used where the Baum function is approximated using the mean-field-based decomposition of a posteriori probability of the region process [9]. The mean-field-based decomposition is also used in finding the MAP estimate of the region process.

The paper is organized as follows. In Section 2, a doubly stochastic MRF model, usually used to model textured images, is described. The proposed multiscale stochastic model of textured images in wavelet domain is presented in Section 3. The corresponding EM-based parameter estimation and MAP-based image segmentation algorithms are given in Section 4. Simulation results are given in Section 5, followed by concluding results in Section 6.