Variational Problems and Partial Differential Equations on Implicit Surfaces: The Framework and Exam

By Marcelo Bertalmío, Li-Tien Cheng, Stanley J. Osher. 2000

320 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Graphics and Computer-Aided Design

View Paper: https://www.semanticscholar.org/paper/91dcacff9ec1530cb249694993ed64f084fde410

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

1. Gerhard Dziuk
2. Charles M. Elliott
3. Martin Burger
4. Stanley J. Osher
5. Daniel Cremers
6. Stefano Soatto
7. Chandrajit L. Bajaj
8. Guoliang Xu

In Computer Graphics and Computer-Aided Design

1. Martin Burger
2. Daniel Cremers
3. Stefano Soatto
4. Chandrajit L. Bajaj
5. Guoliang Xu
6. Charles M. Elliott
7. Gerhard Dziuk
8. Anthony J. Yezzi Jr.

Citations in the corpus

• Finite element approximation of elliptic partial differential equations on implicit surfaces (2009, methodology): “The numerical methods in [4] and subsequent work (cf.”
• A survey on level set methods for inverse problems and optimal design (2005, methodology): “A more genuine level set approach consists in using the actual level set function φ for the formulation of the differential equation on each level set, and using subsequent averaging to obtain an equation on the whole domain [17, 18].”
• Shedding light on stereoscopic segmentation (2004, methodology): “For more details, we refer the reader to [2, 12].”
• Modelling dynamic scenes by registering multi-view image sequences (2005, background): “As regards the regularization term, in this case it is typically the harmonic energy of the flow over the surface, and the corresponding minimizing flow is an intrinsic heat equation [2].”
• Finite elements on evolving surfaces (2007, methodology): “An alternative approach to our method based on the use of (1.2) is to embed the surface in a family of level set surfaces (Bertalmio et al., 2001; Adalsteinsson & Sethian, 2003; Xu & Zhao, 2003; Greer et al., 2006).”
• Eulerian finite element method for parabolic PDEs on implicit surfaces (2008, background): “A general framework for formulating partial differential equations on implicit surfaces was proposed by the authors of [3].”
• Anisotropic diffusion of surfaces and functions on surfaces (2003, methodology): “Recently, level-set methods were also used in surface fairing and surface reconstruction (see Bertalmio et al. [2000a,b], Chopp and Sethian [1999], Osher and Fedkiw [2000], Whitaker and Breen [1998], and Zhao et al. [2001, 2000]).”