A Class of generalized Laplacians on vector bundles devoted to multi-channels image processing
type: Dataset
description: In the context of fiber bundles theory, there exist some differential operators of order 2 , called generalized Laplacians, acting on sections of vector bundles over Riemannian manifolds, and generalizing the Laplace-Beltrami operator. Such operators are determined by the choice of a covariant derivative on the vector bundle. In this paper, we construct a class of generalized Laplacians, devoted to multi-channels image processing, from the construction of particular covariant derivatives. The construction requires to deal with the notion of associated bundle, that relates principal and vector bundles by the choice of a group representation. In particular, covariant derivatives are determined by connection 1-forms on principal bundles. We consider a minimization problem to construct particular connection 1-forms. Then, from the heat equation of the corresponding Laplacian, we obtain a class of diffusions whose behaviours depend of the choice of the group representation. We provide experiments on grey-level and color images.
issued: 2026-05-14T16:06:34.711469
language: en
modified: 2026-05-14T16:06:34.711475
contact point: Organization
  fn: CCSD
keyword: differential-geometry
keyword: generalized-laplacian
keyword: heat-equation
keyword: infoeu-reposemanticspreprint
keyword: infoinfo-tscomputer-science-cssignal-and-image-processing
keyword: mathmath-dgmathematics-mathdifferential-geometry-mathdg
keyword: multi-channel-image-processing
keyword: preprints-working-papers-
keyword: spisignalengineering-sciences-physicssignal-and-image-processing
keyword: variational-methods
landing page: https://hal.science/hal-00683953

A Class of generalized Laplacians on vector bundles devoted to multi-channels image processing
type: Distribution
format: HTML
issued: 2026-05-14T16:06:34.758658
modified: 2026-05-14T16:06:34.692077
access URL: https://hal.science/hal-00683953

test_moissonnage_selune
type: Agent