A Two-Stage Image Segmentation Method for Blurry Images with Poisson or Multiplicative Gamma Noise

In this paper, a two-stage method for segmenting blurry images in the presence of Poisson or multiplicative Gamma noise is proposed. The method is inspired by a previous work on two-stage segmentation and the usage of an I-divergence term to handle the noise. The first stage of our method is to find a smooth solution $u$ to a convex variant of the Mumford--Shah model where the $\ell_2$ data-fidelity term is replaced by an I-divergence term. A primal-dual algorithm is adopted to efficiently solve the minimization problem. We prove the convergence of the algorithm and the uniqueness of the solution $u$. Once $u$ is obtained, in the second stage, the segmentation is done by thresholding $u$ into different phases. The thresholds can be given by the users or can be obtained automatically by using any clustering method. In our method, we can obtain any $K$-phase segmentation ($K\geq 2$) by choosing $(K-1)$ thresholds after $u$ is found. Changing $K$ or the thresholds does not require $u$ to be recomputed. Exper...