Theoretical analysis of flows estimating eigenfunctions of one-homogeneous functionals

Nonlinear eigenfunctions, induced by subgradients of one-homogeneous functionals (such as the 1- Laplacian), have shown to be instrumental in segmentation, clustering, and image decomposition. We present a class of flows for finding such eigenfunctions, generalizing a method recently suggested by Nossek and Gilboa. We analyze the flows on grids and graphs in the time-continuous and timediscrete settings. For a specific type of flow within this class, we prove convergence of the numerical iterations procedure and prove existence and uniqueness of the time-continuous case. Several toy examples are provided for illustrating the theoretical results, showing how such flows can be used on images and graphs.