Reconciling distance functions and level sets

By José Gomes, Olivier D. Faugeras. 2000

364 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computer Vision and Pattern Recognition

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Citations in the corpus

Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, background): “It has been observed that in its conventional formulation the level set function often develop complications related to ill-conditioning during the evolution process, [13].”
Manufacturing Constraints and Multi-Phase Shape and Topology Optimization via a Level-Set Method (2014, methodology): “The present work, inspired by a similar choice in thermodynamic modeling presented by the ideal Gibbs interface and the Guggenheim model (Guggenheim 1959) (see Figure 1), seeks to take advantage of new design possibilities enabled by the interfacial transition zone. In particular, we investigate the”
CURVES: Curve evolution for vessel segmentation (2001, methodology): “For this reason, we minima in traditional methods; they thus become increas- developed the «-Level Set Method which defines a thin ingly close together so the manifold is no longer a distance tube of radius « around the initial curve, then evolves that function ( Gomes and Faugeras, 2000 ).”
Distance Regularized Level Set Evolution and Its Application to Image Segmentation (2010, methodology): “From a practical viewpoint, the use of reinitialization introduces some fundamental problems yet to be solved, such as when and how to apply the reinitialization [25].”
Image Segmentation Using Active Contours: Calculus of Variations or Shape Gradients? (2003, methodology): “To implement the level set method, solutions must be found to circumvent problems coming from the fact that the signed distance function U is not a solution of the PDE (26); see [20] for details.”
An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics (2007, methodology): “Our strategy to deal with the spreading problem borrows some aspects from recent improvements of Level Set methods (Adalsteinsson and Sethian, 1999; Gomes and Faugeras, 2000) in which the authors tackled the issue of maintaining the gradient of the Level Set function unity by modifying locally the v”
Implicit Surface Representations As Layers in Neural Networks (2019, background): “It has been observed that in its conventional formulation the level set function often develop complications related to illconditioning during the evolution process, [13].”
Geodesic Active Regions and Level Set Methods for Supervised Texture Segmentation (2002, methodology): “The re-initialization requirement can be avoided by modifying the level set embedding function as proposed in Gomes and Faugeras (2000).”
A quasi-dense approach to surface reconstruction from uncalibrated images (2005, background): “It seems that the complication by this dependency on the surface normal is rather unnecessary in practice [16].”
3D distance fields: a survey of techniques and applications (2006, background): “Alternatively, Gomes and Faugeras [ 42 ] propose a reformulation of the LSM which preserves the distance field property apparently without need for reinitialization.”
MULTI-PHASE STRUCTURAL OPTIMIZATION VIA A LEVEL SET METHOD ∗, ∗∗ (2014, background): “For example, in [25] it is shown that the transported level set function remains the signed distance function (at least for a small time) if the advection velocity remains constant along the normal, namely (θ · n)(x) = (θ · n)(pΓ(x)).”
Level set evolution without re-initialization: a new variational formulation (2005, methodology): “However, as pointed out by Gomes and Faugeras [12], re-initializing the level set function is obviously a disagreement between the theory of the level set method and its implementation.”
Fast Global Minimization of the Active Contour/Snake Model (2007, background): “See [39] for more details and another approach to solve the re-distancing problem.”
An efficient local Chan-Vese model for image segmentation (2010, background): “Moreover, it is quite complicated and time-consuming, and when and how to apply it is still a serious problem [40].”
View-based 3-D object recognition using shock graphs (2002, background): “Several of these new approaches rely on a threshold to determine whether a given point is singular or not [40, 1, 38, 23].”