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Anisotropic geometric diffusion in surface processing
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Discrete regularization on weighted graphs for image and mesh filtering
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Bayesian non-local means filter, image redundancy and adaptive dictionaries for noise removal
SSVM'07 Proceedings of the 1st international conference on Scale space and variational methods in computer vision
Regularization on discrete spaces
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Generalised Nonlocal Image Smoothing
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A Framework for Moving Least Squares Method with Total Variation Minimizing Regularization
Journal of Mathematical Imaging and Vision
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We propose a discrete regularization framework on weighted graphs of arbitrary topology, which unifies local and nonlocal processing of images, meshes, and more generally discrete data. The approach considers the problem as a variational one, which consists in minimizing a weighted sum of two energy terms: a regularization one that uses the discrete p-Dirichlet form, and an approximation one. The proposed model is parametrized by the degree p of regularity, by the graph structure and by the weight function. The minimization solution leads to a family of simple linear and nonlinear processing methods. In particular, this family includes the exact expression or the discrete version of several neighborhood filters, such as the bilateral and the nonlocal means filter. In the context of images, local and nonlocal regularizations, based on the total variation models, are the continuous analog of the proposed model. Indirectly and naturally, it provides a discrete extension of these regularization methods for any discrete data or functions.