Path-Gradient - A Theory of Computing Full Intensity-Transition Between Two Points

A major challenge for path-based segmentation methods is to select the optimum scale capturing the total intensity variation across object interfaces without losing small-scale structures. Minimum barrier distance (MBD) attempts to alleviate this issue using a unique path-cost function that computes the maximum intensity variation on the path. Two major concerns of MBD are related to high computational complexity and convoluted trajectory of the optimum path between two points on either side of an object interface limiting benefits of MBD. Here, we introduce the 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 path cost, which improves segmentation still at considerably reduced computation cost than regular MBD. Efficient algorithms for computing PG and regularized PG are presented and their segmentation performances are compared with that of MBD.