Lipschitz Regularization of Images supported on Surfaces using Riemannian Morphological Operators

Jesus Angulo (1)

1 CMM - Centre de Morphologie Mathématique

Dierent imaging modalities produce nowadays images on smooth surfaces, represented by images painted on meshes or point clouds. These Riemannian images are often nonsmooth and their regularization can be needed in many applications. This paper deals with the approximation of a bounded nonsmooth image painted on a surface by a sequence of more regular functions, having in particular Lipschitz gradient, and without any hypothesis of dierentiability. We adopt here a geometric framework known as Lasry-Lions regularization. The aim of the present contribution is to consider the extension of Lasry-Lions regularization to Riemannian manifolds. We show that the key ingredients for such regularization are Riemannian morphological operators.

Domaines: Traitement des images [eess.IV]

Jesus Angulo. Lipschitz Regularization of Images supported on Surfaces using Riemannian Morphological Operators. 2014. ⟨hal-01108130v2⟩