A Variational Level Set Approach to Multiphase Motion

By Hongkai Zhao, Tony F. Chan, Barry Merriman, Stanley J. Osher. 1996

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Citations in the corpus

Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, methodology): “It is then also necessary to introduce continuous approximations of the Dirac delta function and Heaviside function, Following the work of [35] we use the following C 1 and C 2 approximations of δ and H respectively, and note that here H (cid:48) (cid:15) ( x ) = δ (cid:15) ( x ) .”
Structure topology optimization: fully coupled level set method via FEMLAB (2005, methodology): “Here, we use the gradient projection method that was proposed in Zhao et al. (1996) .”
Approaches to Modeling of Recrystallization (2011, unknown): “The model was also elaborated to consider interfaces with multiple junctions in [133,136].”
Motion Competition: A Variational Approach to Piecewise Parametric Motion Segmentation (2005, background): “One approach, investigated e.g. in Zhao et al. (1996) and Samson et al. (2000), is to represent each phase by a different level set function φ i : i = {x ∈ | φ i (x) ≥ 0}.”
A level set approach for shape-driven segmentation and tracking of the left ventricle (2003, background): “The Heaviside function can be considered to define such partition E R (8) = H (8)r O (I) d endocardium + (1 0 H(8))rB(I)d background (5) according to some region descriptors functions rO : R + !”
A multiple level set method for modeling grain boundary evolution of polycrystalline materials (2008, methodology): “In [39], a variational approach with Lagrange multiplier method is employed to couple the multiple level set functions at triple junction through local and/or global constraints.”
Review of brain MRI image segmentation methods (2010, methodology): “The dams are called watersheds and the segmented regions are called catchments basins ( Adalsteinsson and Sethian 1995; Li et al. 2007).”
Implicit Surface Representations As Layers in Neural Networks (2019, methodology): “It is then also necessary to introduce continuous approximations of the Dirac delta function and Heaviside function, Following the work of [36] we use the following C(1) and C(2) approximations of δ and H respectively,”
Deep Level Sets for Salient Object Detection (2017, methodology): “When applying level set methods [38, 61] for binary segmentation in 2D space Ω, the interface C ⊂ Ω is defined as the boundary of an open subset ω ⊂ Ω, and thus C = ∂ω.”
An 88-line MATLAB code for the parameterized level set method based topology optimization using radial basis functions (2018, unknown): “This scheme is firstly proposed by Zhao et al. (1996).”
Shape Priors for Level Set Representations (2002, background): “Let us also define the approximations of Dirac and Heaviside [26] distributions as: δ a (φ) = 0 , |φ| > α 1 2α 1 + cos πφ a , |φ| < α H α (φ) =    1 , φ > α 0 , φ −α 1 2 1 + φ α + 1 π sin πφ a , |φ| α Then it can be shown easily that Now, given an interface and (consequently) its level set re”
Transport and diffusion of material quantities on propagating interfaces via level set methods (2003, background): “It is straightforward to show that this choice of extension velocity maintains the signed distance function for the level sets of φ for all time (see, for example, [26]).”
A Review of Statistical Approaches to Level Set Segmentation: Integrating Color, Texture, Motion and Shape (2007, background): “Alternatively to the above derivation, one can obtain a level set equation from a variational formulation (cf. Zhao et al., 1996; Chan and Vese, 2001) Rather than deriving an appropriate partial differential equation for φ which implements the contour evolution Eq.”
Evolution, implementation, and application of level set and fast marching methods for advancing fronts (2001, background): “These extension velocities have been expl ìcit y constructed for a variety of specific problems; see, for example, [4, 19, 20, 51, 63, 86, 91, 103].”
Spatially adaptive techniques for level set methods and incompressible flow (2006, background): “[105] demonstrated that a signed distance function tends to remain a signed distance function if the velocity at each point is defined to be equal to the velocity at the closest interface point, and a number of authors have proposed oneway and two-way extrapolation techniques for accomplishing this,”
Shape recovery algorithms using level sets in 2-D/3-D medical imagery: a state-of-the-art review (2002, unknown): “[121] and Evans et al.”