Geometric Partial Differential Equations and Image Analysis: Introduction

By Guillermo Sapiro. 2001

635 citations recorded by the source corpus.

Subfields: History, Political Science and International Relations

View Paper: https://www.semanticscholar.org/paper/a666868ce70e932f33e943ba023ab01111561ef6

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Citations in the corpus

Structural shape and topology optimization in a level-set-based framework of region representation (2004, background): “The mean curvature flow is also interpreted in the literature as an anisotropic diffusion ( Sapiro 2001 ), and it diffuses only in the tangential direction of the surface.”
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation (2002, background): “…Kimmel and Bruckstein, 1995; Tek and Kimia, 1995; Deriche and Faugeras, 1996; Zhao et al., 1996; Bertalmio et al., 1998; Faugeras and Keriven, 1998; Kornprobst et al., 1998; Malladi and Sethian, 1998; Lorigo et al., 2000; Jehan-Besson et al., 2001; Sapiro, 2001; Sifakis et al., 2001; VLSM, 2001).”
LOCAL SOLVABILITY OF A CONSTRAINED GRADIENT SYSTEM OF TOTAL VARIATION (2003, background): “See [25] for background of our problem (1.”
Anisotropic diffusion of surfaces and functions on surfaces (2003, background): “Hence the equation describes the mean curvature motion, whose regularization effect could be seen, for κ = 3, from the following equations (see Clarenz [2000] and Sapiro [2001]).”
Stability of Persistence Diagrams (2005, background): “Due to its practical importance, it has been studied extensively in a number of areas including morphology [2] and image processing [20].”
Integrable equations arising from motions of plane curves (2002, background): “The recent book by Sapiro [24] contains a full discussion on this subject.”
A level set method for structural topology optimization and its applications (2004, background): “It is well known the level set evolving in its normal direction with the mean curvature velocity will converge to the minimal manifold [20,21], and this is also interpreted in the literatures as the anisotropic diffusion, which diffuse only in the tangential space of the level set and has been wildl”
Does median filtering truly preserve edges better than linear filtering (2006, methodology): “In particular, inspired by seminal work of Mumford and Shah [26] and Perona and Malik [27], a whole community in applied mathematics has arisen around the use of nonlinear partialdifferential equations (PDEs) for image processing—including noise suppression [25, 31, 34].”
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).”
Structure topology optimization: fully coupled level set method via FEMLAB (2005, methodology): “The basic idea behind the level set method is to express a curve or surface in an implicit form, as the zero level set or isophote of a high-dimensional function, and then trace the deformation of the curve or surface by means of the deformation of this embedding function ( Sapiro 2001; Osher and F”
Nonlinear diffusions in topology optimization (2004, methodology): “This approach is also called the gradient-descent flow (Aubert and Kornprobst 2000; Sapiro 2001 ).”