Issue No. 11 - November (2006 vol. 28)

ISSN: 0162-8828

pp: 1768-1783

L. Grady , Dept. of Imaging & Visualization, Siemens Corp. Res., Princeton, NJ

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

INDEX TERMS

Image segmentation, Iterative algorithms, Probability, Pixel, Electric potential, Circuits, Graph theory, Laplace equations, Sparse matrices, Symmetric matrices,boundary completion., Image segmentation, interactive segmentation, graph theory, random walks, combinatorial Dirichlet problem, harmonic functions, Laplace equation, graph cuts

CITATION

L. Grady, "Random Walks for Image Segmentation",

*IEEE Transactions on Pattern Analysis & Machine Intelligence*, vol. 28, no. , pp. 1768-1783, November 2006, doi:10.1109/TPAMI.2006.233