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 ℓ₂ datafidelity 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 ≥ 2) by choosing (K - 1) thresholds after u is found. Changing K or the thresholds does not require u to be recomputed. Experimental results show that our two-stage method performs better than many standard two-phase or multiphase segmentation methods for very general images, including antimass, tubular, magnetic resonance imaging, and low-light images.