Globally convergent variable time-step level set method for fast and ribust image segmentation

Abstract

Segmentation is an image processing technique that separates foreground object from the background of image. It transforms low-level image data to high-level knowledge and makes many advanced image analysis and understanding tasks to be possible. Image segmentation is a persistent hot research field for a long time and different mechanisms have been proposed to optimize the segmentation process. Among them, active contour method (ACM) is one of the most advanced and widely used methods. Level set is an implicit application of ACM which represents the evolving contours as the zero level set of a higher dimensional function, thus make it possible to handle the numerical estimation with curves and surfaces without using parametric representation. In this way, the level set method is able to represent complex topology and their changes in an efficient manner. Edge-based and region-base approaches are two major ways of realizing level set method in image segmentation. A critical factor that controls the speed of convergence of both edge and region based methods is the time-step parameter. The selection of a larger time-step speeds up the convergence rate but endanger the numerical stability of the algorithm. A smaller time step slows the convergence rate and increases the computational time. In this work, we propose a globally convergent level set method using multiple optimization criteria, such as, edge, region, and neighborhood and formulate a variable time-step parameter for the level set method that maximizes the between-class variance among the foreground and background region in each iteration and thereby ensures numerical stability as well as fast convergence speed. Consequently the computational complexity of the level set method is reduced. The performance of the proposed segmentation technique is tested on synthetic, natural and medical images and is compared to existing state-of-the-art methods. The segmentation results of different techniques is numerically evaluated using Dice criterion, PSNR, Hausdorff distance, and mean sum of square distance (MSSD) with a reference.