Nonlinear total variation based noise removal algorithms
Proceedings of the eleventh annual international conference of the Center for Nonlinear Studies on Experimental mathematics : computational issues in nonlinear science: computational issues in nonlinear science
Oscillating Patterns in Image Processing and Nonlinear Evolution Equations: The Fifteenth Dean Jacqueline B. Lewis Memorial Lectures
A Multi-scale Approach to 3D Scattered Data Interpolation with Compactly Supported Basis Functions
SMI '03 Proceedings of the Shape Modeling International 2003
Graph regularization for color image processing
Computer Vision and Image Understanding
Nonlocal Image and Movie Denoising
International Journal of Computer Vision
The digital TV filter and nonlinear denoising
IEEE Transactions on Image Processing
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing
IEEE Transactions on Image Processing
Hierarchical representation of discrete data on graphs
CAIP'11 Proceedings of the 14th international conference on Computer analysis of images and patterns - Volume Part I
Nonlinear Multilayered Representation of Graph-Signals
Journal of Mathematical Imaging and Vision
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The decomposition of images into their meaningful components is one of the major tasks in computer vision. Tadmor, Nezzar and Vese [1] have proposed a general approach for multiscale hierarchical decomposition of images. On the basis of this work, we propose a multiscale hierarchical decomposition of functions on graphs. The decomposition is based on a discrete variational framework that makes it possible to process arbitrary discrete data sets with the natural introduction of nonlocal interactions. This leads to an approach that can be used for the decomposition of images, meshes, or arbitrary data sets by taking advantage of the graph structure. To have a fully automatic decomposition, the issue of parameter selection is fully addressed. We illustrate our approach with numerous decomposition results on images, meshes, and point clouds and show the benefits.