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)
A Metric Approach to nD Images Edge Detection with Clifford Algebras
Journal of Mathematical Imaging and Vision
Heat kernels of generalized Laplacians-application to color image smoothing
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
SIAM Journal on Imaging Sciences
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
A Class of Generalized Laplacians on Vector Bundles Devoted to Multi-Channel Image Processing
Journal of Mathematical Imaging and Vision
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We use the framework of heat equations associated to generalized Laplacians on vector bundles over Riemannian manifolds in order to regularize color images. We show that most methods devoted to image regularization may be considered in this framework. From a geometric viewpoint, they differ by the metric of the base manifold and the connection of the vector bundle involved. By the regularization operator we propose in this paper, the diffusion process is completely determined by the geometry of the vector bundle. More precisely, the metric of the base manifold determines the anisotropy of the diffusion through the computation of geodesic distances whereas the connection determines the data regularized by the diffusion process through the computation of the parallel transport maps. This regularization operator generalizes the ones based on short-time Beltrami kernel and oriented Gaussian kernels. Then we construct particular connections and metrics involving color information such as luminance and chrominance in order to perform new kinds of regularization.