A variational approach to simultaneous image segmentation and bias correction

Abstract—This paper presents a novel variational approach for simultaneous estimation of bias field and segmentation of images with intensity inhomogeneity. We model intensity of inhomoge-neous objects to be Gaussian distributed with different means and variances, and then introduce a sliding window to map the orig-inal image intensity onto another domain, where the intensity distribution of each object is still Gaussian but can be bet-ter 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 slid-ing window. A maximum likelihood energy functional is then defined on each local region, 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. An efficient iterative algorithm is proposed for energy minimization, via which the image seg-mentation and bias field correction are simultaneously achieved. Furthermore, the smoothness of the obtained optimal bias field is ensured by the normalized convolutions without extra cost. Experiments on real images demonstrated the superiority of the proposed algorithm to other state-of-the-art representative methods. Index Terms—Bias field, computer vision, energy minimization, image segmentation, variational approach. I