Random Walks for Image Segmentation

TLDR

The study proposes a novel multilabel, interactive image‑segmentation method. The method models image pixels as nodes on a graph and analytically computes, for each unlabeled pixel, the probability that a random walker first reaches a user‑labeled pixel, deriving theoretical links to discrete potential theory and electrical circuits. Assigning each pixel to the label with the highest computed probability yields high‑quality segmentations.

Abstract

A novel method is proposed for performing multilabel, interactive image segmentation. Given a small number of pixels with user-defined (or predefined) labels, one can analytically and quickly determine the probability that a random walker starting at each unlabeled pixel will first reach one of the prelabeled 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 on arbitrary graphs.