11 research outputs found
Unsupervised Learning of the Total Variation Flow
The total variation (TV) flow generates a scale-space representation of an image based on the TV functional. This gradient flow observes desirable features for images such as sharp edges and enables spectral, scale, and texture analysis. The standard numerical approach for TV flow requires solving multiple non-smooth optimisation problems. Even with state-of-the-art convex optimisation techniques, this is often prohibitively expensive and strongly motivates the use of alternative, faster approaches. Inspired by and extending the framework of physics-informed neural networks (PINNs), we propose the TVflowNET, a neural network approach to compute the solution of the TV flow given an initial image and a time instance. We significantly speed up the computation time by more than one order of magnitude and show that the TVflowNET approximates the TV flow solution with high fidelity. This is a preliminary report, more details are to follow
The Infinity Laplacian eigenvalue problem: reformulation and a numerical scheme
In this work we present an alternative formulation of the higher eigenvalue
problem associated to the infinity Laplacian, which opens the door for
numerical approximation of eigenfunctions. A rigorous analysis is performed to
show the equivalence of the new formulation to the traditional one. We define
consistent numerical schemes for approximating infinity ground states and
higher eigenfunctions and perform numerical experiments which also shed light
on some open conjectures in the field.Comment: 20 pages, 8 figure