Convolution-thresholding methods for interface motion

Convolution-thresholding is a new approach to describing interface motion t hat unifies and generalizes Huygens' principle, threshold growth cellular a utomata, and reaction-diffusion equations. Convolution methods have many de sirable properties, including automatic capture of topological change, prod uction of curvature motion without explicit computation of curvature, natur al extension to the motion of triple-point junctions, and fast, accurate im plementation. In this paper, we summarize the relation of convolution-thres holding schemes to previous methods, and we review the theoretical and algo rithmic development of this approach. We also review recent applications to computer vision, developmental biology, excitable media, and material scie nce. (C) 2001 Academic Press.