Nonmonotonic Front Propagation on Weighted Graphs With Applications in Image Processing and High-Dimensional Data Classification

In this paper, we propose an adaptation of partial difference equations (PDEs) level set method for nonmonotonic front propagation on weighted graphs. This adaptation leads to a PDE, whose coefficients are data geometry dependent. Our motivation is to extend their applications to any discrete data that can be represented by a weighted graph. This paper follows several preliminaries of our works, and introduces several significant improvements: A simplified and explicit representation of a front on a weighted graph, a new formulation of the level set equation on weighted graphs considering both time-dependent and stationary versions of this equation in the case of signed velocities, and an efficient algorithm that generalized the fast marching to graphs with signed velocities. We propose to use this method for image processing and for high-dimensional data classification.