Some Riemannian methods for image processing

Résumé

In image processing, intensities generally live in non-Euclidean spaces; however, the classical methods used to process images do not take this fact into account: they proceed as if the intensity spaces were vectorial. This is why, over the past decade, methods issued from differential geometry have appeared to address this shortcoming. This thesis is a contribution showing that Riemannian geometry in non-positively curved spaces is the "natural" mathematical ecosystem in which to perform low-level image processing. We generalize many methods from the Euclidean setting to the Riemannian one. Experiments show that this formalism is relevant and yields consistent, high-quality results. We apply our Riemannian formalism to several areas of image processing, such as anisotropic denoising, segmentation, compression and quality assessment. We also propose a new formalism for defining stable arithmetic operations, such as addition and scalar multiplication, in the space of intensities. This formalism opens broad perspectives for applications in many fields, such as medical or remote-sensing imaging. The methods we propose are applied to different image modalities, including DT-MRI, grayscale and color images.

Citer ce document

Accès au document

Ce document est hébergé sur son dépôt institutionnel d'origine.

Auteur(s)

Statistiques

Consultations : 3

Téléchargements : 0