Image Segmentation and Bias Correction by Using Maximum Likelihood Algorithm

Abstract

This paper presents a novel optimization approach for de-noising and bias correction of MR image with intensity in-homogeneity. Intensity of inhomogeneous objects to be Gaussian distributed with different means and variances are modeled, and then a sliding window is introduced to map the original image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be better separated. The means of the Gaussian distributions in the transformed domain can be adaptively estimated by multiplying the bias field with a piecewise constant signal within the sliding window. A maximum likelihood energy functional is then defined on each of the local regional, which combines the bias field, the membership function of the object region, and the constant approximating the true signal from its corresponding object. The energy functional is then extended to the whole image domain by the Bayesian learning approach. Furthermore, the smoothness of the obtained optimal bias field is ensured by normalized convolutions without extra cost. Experiments on the real image demonstrate the superiority of the proposed algorithm to other state-of-the-art representative methods.