Scale-Space Theory in Computer Vision
Scale-Space Theory in Computer Vision
Vector-Valued Image Regularization with PDEs: A Common Framework for Different Applications
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's
International Journal of Computer Vision
Geometric Partial Differential Equations and Image Analysis
Geometric Partial Differential Equations and Image Analysis
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Image Processing And Analysis: Variational, Pde, Wavelet, And Stochastic Methods
Mathematical Problems in Image Processing: Partial Differential Equations and the Calculus of Variations (Applied Mathematical Sciences)
Regularizing Flows over Lie Groups
Journal of Mathematical Imaging and Vision
A Geometric Framework and a New Criterion in Optical Flow Modeling
Journal of Mathematical Imaging and Vision
Fast GL(n)-Invariant Framework for Tensors Regularization
International Journal of Computer Vision
International Journal of Computer Vision
International Journal of Computer Vision
SIAM Journal on Imaging Sciences
International Journal of Computer Vision
Heat Equations on Vector Bundles--Application to Color Image Regularization
Journal of Mathematical Imaging and Vision
Polyakov action on (ρ,g)-equivariant functions application to color image regularization
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Group-Valued regularization framework for motion segmentation of dynamic non-rigid shapes
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
A general framework for low level vision
IEEE Transactions on Image Processing
A Short- Time Beltrami Kernel for Smoothing Images and Manifolds
IEEE Transactions on Image Processing
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In the context of fibre 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 covariant derivatives on vector bundles. In this paper, we construct a class of generalized Laplacians, devoted to multi-channel image processing, from the construction of optimal covariant derivatives. The key idea is to consider an image as a section of an associate bundle, that is a vector bundle related to a principal bundle through a group representation. In this context, covariant derivatives are determined by connection 1-forms on principal bundles. We construct optimal connection 1-forms by the minimization of a variational problem on principal bundles. From the heat equations of the generalized Laplacians induced by the corresponding optimal covariant derivatives, we obtain diffusions whose behaviors depend of the choice of the group representation. We provide experiments on color images.