Convolution–Thresholding Methods for Interface Motion

Convolution–thresholding is a new approach to describing interface motion that unifies and generalizes Huygensʹ principle, threshold growth cellular automata, and reaction–diffusion equations. Convolution methods have many desirable properties, including automatic capture of topological change, production of curvature motion without explicit computation of curvature, natural extension to the motion of triple-point junctions, and fast, accurate implementation. In this paper, we summarize the relation of convolution–thresholding schemes to previous methods, and we review the theoretical and algorithmic development of this approach. We also review recent applications to computer vision, developmental biology, excitable media, and material science.