Damian Kaliroff, Guy Gilboa, arXiv

We propose a new and completely data-driven approach for generating an unconstrained illumination invariant representation of images. Our method trains a
neural network with a specialized triplet loss designed to emphasize actual scene
changes while downplaying changes in illumination. For this purpose we use the
BigTime image dataset, which contains static scenes acquired at different times.
We analyze the attributes of our representation, and show that it improves patch
matching and rigid registration over state-of-the-art illumination invariant representations.
We point out that the utility of our method is not restricted to handling
illumination invariance, and that it may be applied for generating representations
which are invariant to general types of nuisance, undesired, image variants.

Ido Cohen, Guy Gilboa, “Energy dissipating flows for solving nonlinear eigenpair problems”, Journal of Computational Physics 375 (2018), 1138-1158.

This work is concerned with computing nonlinear eigenpairs, which model solitary waves and various other physical phenomena. We aim at solving nonlinear eigenvalue problems of the general form
$T(u)=\lambda Q(u)$. In our setting $T$ is
a variational derivative of a convex functional (such as the Laplacian operator with respect to the Dirichlet energy),
$Q$ is an arbitrary bounded nonlinear operator and $\lambda$ is an unknown (real) eigenvalue.
We introduce a flow that numerically generates an eigenpair solution by its steady state.

Analysis for the general case is performed, showing a monotone decrease in the convex functional throughout the flow.
When $T$ is the Laplacian operator, a complete discretized version is presented and analyzed. We implement our algorithm on \ac{KdV} and \ac{NLS} equations in one and two dimensions.
The proposed approach is very general and can be applied to a large variety of models. Moreover, it is highly robust to noise and to perturbations in the initial conditions, compared to classical Petiashvili-based methods.

Tags: eigenpairs , nonlinear eigenfunction analysis , normalized reaction diffusion , solitons