3D COLORED MESH STRUCTURE-PRESERVING FILTERING WITH ADAPTIVE P-LAPLACIAN ON DIRECTED GRAPHS

International audienceEditing of 3D colored meshes represents a fundamental component of nowadays computer vision and computer graphics applications. In this paper, we propose a framework based on the p-laplacian on directed graphs for structure-preserving filtering. This relies on a novel objective function composed of a fitting term, a smoothness term with a spatially-variant pTV norm, and a structure-preserving term. The last two terms can be related to formulations of the p-Laplacian on directed graphs. This enables to impose different forms of processing onto different graph areas for better smoothing quality

Filtrage p-Laplacien adaptatif et guidé pour le traitement de la couleur associée à des nuages de points 3D

International audienceDe plus en plus d'applications nécessitent d'éditer la couleur associée aux sommets d'un maillage ou aux points d'un nuage 3D. Dans ce contexte, nous proposons un filtre régularisant sur graphes dirigés qui repose sur la minimisation d'une fonction composée d'un terme d'attache aux données, d'un terme de lissage basé sur une norme pTV spatialement variable, et d'un terme de préservation des structures basé sur l'amplitude du gradient. Les deux derniers termes peuventêtre liés aux formulations du p-Laplacien sur graphes dirigés. Cela permet d'imposer différentes formes de traitement sur différentes parties du graphe pour une meilleure qualité de lissage

p-Laplacian regularization of signals on directed graphs

International audienceThe graph Laplacian plays an important role in describing the structure of a graph signal from weights that measure the similarity between the vertices of the graph. In the literature, three definitions of the graph Laplacian have been considered for undirected graphs: the combinatorial, the normalized and the random-walk Laplacians. Moreover , a nonlinear extension of the Laplacian, called the p-Laplacian, has also been put forward for undirected graphs. In this paper, we propose several formulations for p-Laplacians on directed graphs directly inspired from the Laplacians on undirected graphs. Then, we consider the problem of p-Laplacian regularization of signals on directed graphs. Finally, we provide experimental results to illustrate the effect of the proposed p-laplacians on different types of graph signals