An efficient bi-convex fuzzy variational image segmentation method

Abstract Image segmentation is an important and well-known ill-posed inverse problem in computer vision. It is a process of assigning a label to each pixel in a digital image so that pixels with the same label have similar characteristics. Chan–Vese model which belongs to partial differential equation approaches has been widely used in image segmentation tasks. Chan–Vese model has to optimize a non-convex problem. It usually converges to local minima. Furthermore, the length penalty item which is critical to the final results of Chan–Vese model makes the model be sensitive to parameter settings and costly in computation. In order to overcome these drawbacks, a novel bi-convex fuzzy variational image segmentation method is proposed. It is unique in two aspects: (1) introducing fuzzy logic to construct a bi-convex object function in order to simplify the procedure of finding global optima and (2) efficiently combining the length penalty item and the numerical remedy method to get better results and to bring robustness to parameter settings and greatly reduce computation costs. Experiments on synthetic, natural, medical and radar images have visually or quantitatively validated the superiorities of the proposed method compared with five state-of-the-art algorithms.