Level Set Methods and Fast Marching Methods

By M. Subasic. 2003

2,023 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/c20e00a00d5b06388fb94205ae49f13aedadf8b6

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In Computational Mechanics

In Computer Graphics and Computer-Aided Design

Citations in the corpus

Integrating spatial fuzzy clustering with level set methods for automated medical image segmentation (2011, methodology): “The fuzzy level set method presented in this paper is derived from the classical Hamilton-Jacobi functional [16,17], where the level set evolution is subject to various internal and external forces.”
Non‐planar 3D crack growth by the extended finite element and level sets—Part II: Level set update (2002, methodology): “INTRODUCTION Level set methods have been applied e ectively to many problems of moving fronts (see References [1; 2]).”
Segmentation and tracking of migrating cells in videomicroscopy with parametric active contours: a tool for cell-based drug testing (2002, methodology): “methods [17] has become increasingly popular (e.”
Topology optimization approaches (2013, background): “…some form of dissipation in the streamline direction, i.e. upwinding, and include essentially nonoscillatory (ENO) and weighted essentially non-oscillatory (WENO) schemes, stream-line diffusion and streamline upwinding Petrov-Galerkin finite element methods (Sethian 1999; Burger and Osher 2005).”
Optimal Transport for Applied Mathematicians: Calculus of Variations, PDEs, and Modeling (2015, methodology): “One of the most efficient ways is the so-called Fast Marching Algorithm (see [283]): at every step of the algorithm, the values ui;j of a bunch of points of the grid have already been computed and the corresponding points are colored in red, and all the other values are set to C1; then, a tentative ”
An Eulerian approach to fluid–structure interaction and goal‐oriented mesh adaptation (2006, methodology): “Examples for the use of a phase variable are the volume of fluid method (VOF) [10] and the level set method [8, 20, 22].”
Anatomically motivated modeling of cortical laminae (2014, methodology): “Implementation details follow the classical narrow band algorithm with first order differences (Sethian, 1999).”
User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability (2006, methodology): “One class of semiautomatic methods formulates the problem of segmentation in terms of active contour evolution (Zhu and Yuille, 1996; Caselles et al., 1997; Sethian, 1999), where the human expert must specify the initial contour, balance the various forces which act upon it, as well as monitor the e”
Towards realism in drawing areas of interest on architecture diagrams (2009, methodology): “(4) using the fast marching method as described by Sethian in [40], on the same pixel grid as the one on which the scanned contour C is stored, and obtain the distance map D at a pixel-level spatial resolution.”
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].”
Random Walks for Image Segmentation (2006, background): “Although the family of active contours and level sets is large [16], a user is generally asked to place a contour near the desired boundary and the algorithm evolves the boundary to a local energy minimum.”
Practical animation of liquids (2001, methodology): “This signed distance function can be created quickly using the Fast Marching Method [24] starting from the initial guess of φ(x) defined by the particles as outlined above.”
Using a signed distance function for the simulation of metal forming processes: Formulation of the contact condition and mesh adaptation. From a Lagrangian approach to an Eulerian approach (2009, methodology): “The reader can refer to Sethian [1] and Osher et al.”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, background): “As understood by many practitioners of level set methods (see [19, 22]), reinitialization every time step (or close to every time step) is a poor strategy, since each reinialization causes error in the position of the front.”
A hybrid particle level set method for improved interface capturing (2002, methodology): “The application of level set methods to a wide variety of problems including fluid mechanics, combustion, computer vision, and materials science is discussed in the recent review articles by Osher and Fedkiw [20] and Sethian [34] as well as the recent books of Osher and Fedkiw [21] and Sethian [33].”
Automated Cell Lineage Construction: A Rapid Method to Analyze Clonal Development Established with Murine Neural Progenitor Cells (2006, methodology): “23 Level set methods 24,25 are able to handle topology changes due to cell division; however, deciding which cell is the parent of each child would still be an issue with such methods.”
ITK-SNAP: an interactive tool for semi-automatic segmentation of multi-modality biomedical images (2016, background): “numerical stability and computational efficiency, C is represented implicitly as the zero level set of a function φ defined on the image volume, and the evolution equation (1) is approximated as an evolution of φ in the narrow region around the zero level set [5], [6].”