Fundamental relationship between bilateral filtering, adaptive smoothing, and the nonlinear diffusion equation

By Danny Barash. 2002

585 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

View Paper: https://www.semanticscholar.org/paper/0f58d792e30233b8d9871689452c16672cc0624b

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In Computational Mechanics

In Computer Vision and Pattern Recognition

Citations in the corpus

From Local Kernel to Nonlocal Multiple-Model Image Denoising (2009, background): “Further development and interpretation of this sort of local estimator can be seen in Elad (2002) and Barash (2002). In the works by Yaroslavsky (1985) the localization of the weights is enabled by taking observations from a ball centered at x0. The accuracy analysis of these algorithms can be seen ”
Real-time edge-aware image processing with the bilateral grid (2007, background): “Other edge-preserving techniques include anisotropic diffusion [Perona and Malik 1990; Tumblin and Turk 1999] which is related to the bilateral filter [Durand and Dorsey 2002; Barash 2002].”
Joint bilateral upsampling (2007, background): “It is related to broader class of non-linear filters such as anisotropic diffusion and robust estimation [Barash 2002; Durand and Dorsey 2002; Elad 2002].”
A Fast Approximation of the Bilateral Filter Using a Signal Processing Approach (2006, methodology): “In a similar spirit, Barash [2002] uses points in the S×R domain to interpret the bilateral filter.”
Bilateral filtering for structural topology optimization (2005, methodology): “Bilateral filtering has recently been accepted as a noniterative alternative to anisotropic diffusion [34] due to their similar nature of edge-preserving smoothing [41].”
Multiresolution Bilateral Filtering for Image Denoising (2008, unknown): “[21] and [22] relate the bilateral filter with the anisotropic diffusion.”
Nonlocal Operators with Applications to Image Processing (2008, methodology): “Deeper understanding of these ﬁlters and their relation to PDE’s were given by Barash and Elad [5, 6, 26].”
An Optimized Blockwise Nonlocal Means Denoising Filter for 3-D Magnetic Resonance Images (2008, background): “Strong theoretical links exist between most of these techniques, as recently shown for local mode ltering [18], bilateral ltering, anisotropic diffusion and robust estimation [17], [22] and adaptive smoothing [ 23 ], anisotropic diffusion and total variation minimization scheme [24].”
Video enhancement using per-pixel virtual exposures (2005, background): “Bilateral filtering [Tomasi and Manduchi 98] provides a single-step noise removal process that shares many visual and mathematical qualities with anisotropic diffusion [Barash 02].”
Nonlocal Discrete Regularization on Weighted Graphs: A Framework for Image and Manifold Processing (2008, background): “In particular, one iteration of the diffusion process (25), associated with the weight function and the scalar feature , is equivalent to the bilateral filter introduced in the context of image denoising [47], [48].”
Optimal Spatial Adaptation for Patch-Based Image Denoising (2006, methodology): “Finally, if we substitute a Gaussian window to the hard disk-shaped window around the current position , we get variants of the bilateral filtering [ 2 ], [55] (e.g., Lee’s [32], Susan’s [51], and Saint-Marc’s [49] filters) of the form”
Clustering-Based Denoising With Locally Learned Dictionaries (2009, background): “Barash [ 19 ] studied the relationship between thebilateralfilteringprocessandanisotropic diffusion.”