Novel Theory and Algorithms of Path-Gradient and Their Application to Image Segmentation

Abstract

Image segmentation is a major challenge in many real-life applications. Path-based segmentation methods are popularly used, which expectedly grow a region from initial seeds along the target object while arresting between-object leakages. An ever-existing challenge with such methods is to select the optimum scale capturing the total intensity variation across object interfaces without smearing small-scale structures. The recent method of minimum barrier distance (MBD) addresses this issue using a path-cost function computing the maximum intensity variation along the path. Major concerns of MBD emerge from its high computational complexity and convoluted trajectory of the optimum path between two points located at two different sides of an object interface, which limit the benefits of MBD. Here, we introduce a new notion of path-gradient (PG) that exhibits similar behavior as MBD for object segmentation with significantly reduced computation. The formulation of PG allows the addition of a regularization term in the path cost function formulating regularized path-gradient (RPG), which improves segmentation still at considerably reduced computation cost than regular MBD. Efficient algorithms for computing PG and RPG are presented and their properties are qualitatively demonstrated, and segmentation performances are compared with that of MBD.