Segmentation of noisy colour images using Cauchy distribution in the complex wavelet domain

This study proposes a novel image segmentation technique for noisy colour images, in which the heavy-tailed characteristics of the image are modelled by Cauchy distributions. First, the RGB colour bands of the noisy image are decomposed into multiresolution representations using the dual-tree complex wavelet transform. For each wavelet subband, a model is built assuming that the input coefficients are contaminated with signal-independent additive white Gaussian noise. Hence, the authors derive an estimation rule in the wavelet domain to obtain the noise-free coefficients based on the bivariate Cauchy distribution. The bivariate model makes it possible to exploit the inter-scale dependencies of wavelet coefficients. Subsequently, the image is roughly segmented into textured and non-textured regions using the bivariate model parameters corresponding to the denoised coefficients. A multiscale segmentation is then applied to the resulting regions. Finally, a novel statistical region merging algorithm is introduced by measuring the Kullback-Leibler distance between the estimated Cauchy models for the neighbouring segments. The experiments demonstrate that the authors algorithm yields robust segmentation results for noisy images containing artificial or natural noise.