Mathematical problems in image processing

By G. Aubert. 2001

807 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/4af90e511b8a581f4cd7975b3c672f8b6428f53c

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Citations in the corpus

A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model (2002, methodology): “Also, for recent expositions of geometric PDE’s, variational problems and image processing (including snakes, active contours, curve evolution problems), we refer the reader to Sapiro (2001), Aubert and Kornprobst (2001), and Guichard and Morel (to appear).”
Imaging and image processing in porous media research (2008, methodology): “An introduction to these methods is given in [33] and an overview, with more recent results and applications, is provided by Osher and Paragios [63].”
3-D Active Meshes: Fast Discrete Deformable Models for Cell Tracking in 3-D Time-Lapse Microscopy (2011, unknown): “cell division) and cell appearance/disappearance [ 4 ].”
A Variational Approach to Removing Multiplicative Noise (2008, background): “To recover y from x, the classical assumption is E(z) = 0: this is the basic assumption in all the classical additive image restoration methods [11, 4] (total variation minimization, nonlinear diffusion, wavelet shrinkage, nonlocal means, heat equation, etc.”
From Information Scaling of Natural Images to Regimes of Statistical Models (2007, background): “W (x, y)g((x − x)/s, (y − y)/s) = W ∗ gs, (2) Is(i, j) = us(x0 + is, y0 + js), (3) where gs is a smoothing kernel with bandwidth s, and it corresponds to κij in equation (1).”
Analysis of Half-Quadratic Minimization Methods for Signal and Image Recovery (2005, background): “In some image processing applications, the regularization term Φ in (1.2) reads [ 2 ]”
Nonlocal Linear Image Regularization and Supervised Segmentation (2007, background): “For some recent theory and applications see [3, 47, 46, 19] and the references therein.”
Regularizing Flows for Constrained Matrix-Valued Images (2004, unknown): “nonlinear diffusion equations in image processing can be found in [3, 36, 44]).”
Topological design of structures and composite materials with multiobjectives (2007, methodology): “This technique was originally used in image processing for domain identification (Weickert, 1997; Aubert and Kornprobst, 2000; Charbonnier et al., 1997) and later was successfully introduced to structural topology optimization in Bourdin (2001) and Wang et al.”
Nonlinear diffusions in topology optimization (2004, methodology): “In the literature of digital image processing, a number of more efficient numerical methods are developed for nonlinear diffusions, including semi-implicit scheme and multi-grid techniques (cf. Aubert and Kornprobst 2000 ).”
Image enhancement and denoising by complex diffusion processes (2004, methodology): “The second approach is based on variational calculus, whereby the diffusion-like PDE is derived by a functional minimization process (see [3] and references therein).”