Jean-Francois Aujol, Guy Gilboa, Nicolas Papadakis, “Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals”, accepted to SIAM J. on Imaging Sciences.
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 ows for nding such eigenfunctions, generalizing a method recently suggested by Nossek and Gilboa. We analyze the ows on grids and graphs in the time-continuous and timediscrete settings. For a specic type of ow 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 ows can be used on images and graphs.