Discrete infinity harmonic functions: towards a unified interpolation framework on graphs

Mahmoud Ghoniem (1) , Abderrahim Elmoataz (1) , Olivier Lezoray (1)

1 Equipe Image - Laboratoire GREYC - UMR6072

In this paper, we introduce fast and robust digital algorithms for solving the Dirichlet problem with infinity-harmonic functions on graphs. Several PDEs and variational techniques have been proposed for a number of interpolation problems. Our motivation for this work is to extend some of these PDEs on graphs to deal with interpolation problems with a new approach in a discrete framework using the infinity-Laplacian on weighted graphs arbitrary topology. We show the experimental results for some applications of image interpolation that demonstrate the efficiency of our method and point out the interest of the novel algorithm with p = 1 for interpolation problems.

Mots clés: infinity-harmonic functions; interpolation; inpainting; semi-supervised segmentation; infinity-Laplacian

Domaines: Traitement des images [eess.IV]

Mahmoud Ghoniem, Abderrahim Elmoataz, Olivier Lezoray. Discrete infinity harmonic functions: towards a unified interpolation framework on graphs. International Conference on Image Processing (IEEE), Sep 2011, Bruxelles, Belgium. pp.1361-1364, ⟨10.1109/ICIP.2011.6115690⟩. ⟨hal-00813251⟩