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
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
SIAM Journal on Imaging Sciences
Heat Equations on Vector Bundles--Application to Color Image Regularization
Journal of Mathematical Imaging and Vision
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In this paper, we explore the theory of vector bundles over Riemannian manifolds in order to smooth multivalued images. In this framework, we consider standard PDE's used in image processing as generalized heat equations, related to the geometries of the base manifold, given by its metric and the subsequent Levi-Cevita connection and of the vector bundle, given by a connection. As a consequence, the smoothing is made through a convolution with a 2D kernel, generalizing Gaussian, Beltrami and oriented kernel. In particular, we construct an extension of the oriented kernel, and illustrate it with an application to color image smoothing.