Vector-valued image regularization with PDEs: a common framework for different applications

By David Tschumperlé, Rachid Deriche. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2005

722 citations recorded by the source corpus.

Subfields: Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/a898afec65255966b3c651d8875743312cc70b8a

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In Computer Vision and Pattern Recognition

Citations in the corpus

Fast Anisotropic Smoothing of Multi-Valued Images using Curvature-Preserving PDE's (2006, methodology): “Extensions of these techniques to color images and more generally multi-valued datasets have been also tackled in [38, 44, 48, 53].”
Image Compression With Edge-Based Inpainting (2007, methodology): “Then, results generated by the PDE-based diffusion [ 35 ], which is the traditional solution to structural regions, are shown in the second column.”
Clustering-Based Denoising With Locally Learned Dictionaries (2009, background): “Tschumperle et al. [ 20 ] also reported the equivalence between variational denoising methods and anisotropic diffusion.”
Image deblurring with blurred/noisy image pairs (2007, methodology): “Other approaches include anisotropic diffusion [Perona and Malik 1990], PDE-based methods [Rudin et al. 1992; Tschumperle and Deriche 2005], fields of experts [Roth and Black 2005], and nonlocal methods [Buades et al.”
Graph spectral image smoothing using the heat kernel (2008, background): “Extension of these regularization PDEs to multi-valued images also leads to a system of coupled equations for all the image channels [11,16,19].”
Single-Image Super-Resolution Using Sparse Regression and Natural Image Prior (2010, positive): “As a regularized solution, KRR leads to a better generalization than simply storing the examples as has been done in existing example-based algorithms and results in much less noisy images.”
Image Denoising Using the Higher Order Singular Value Decomposition (2013, neutral): “In these methods, an image is convolved with a pointwise-varying local geometry-driven mask [34].”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, neutral): “between vector components into account [53], [54].”
Non-local Regularization of Inverse Problems (2008, methodology): “The anisotropic diffusion of Tschumperle and Deriche [39] also progressively builds an adapted operator (parameterized by a tensor field) but they solve a PDE and not a regularization as we do.”
Inpainting and Zooming Using Sparse Representations (2009, methodology): “For comparative purposes, inpainting results of a PDEbased method [5] are also reported in each case.”