Multi-label Image Segmentation for Medical Applications Based on Graph-Theoretic Electrical Potentials

A novel method is proposed for performing multi-label, semi-automated image segmentation. Given a small number of pixels with user-defined labels, one can analytically (and quickly) determine the probability that a random walker starting at each unlabeled pixel will first reach one of the pre-labeled pixels. By assigning each pixel to the label for which the greatest probability is calculated, a high-quality image segmentation may be obtained. Theoretical properties of this algorithm are developed along with the corresponding connections to discrete potential theory and electrical circuits. This algorithm is formulated in discrete space (i.e., on a graph) using combinatorial analogues of standard operators and principles from continuous potential theory, allowing it to be applied in arbitrary dimension.