Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations

By Stanley J. Osher, James A. Sethian. 1988

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Citations in the corpus

Occupancy Networks: Learning 3D Reconstruction in Function Space (2018, background): “This idea is related to classical level set [10, 14, 50] approaches to multi-view 3D reconstruction [18,24,32,40,53,78].”
Deep Level Sets: Implicit Surface Representations for 3D Shape Inference (2019, methodology): “The level set method introduced in [8, 26], and successfully applied in segmentation and medical image analysis [18, 32], is a mathematically elegant way of implicitly representing shape of an object and its boundary evolution in time, which can be represented as a zero level set of an embedding…”
Image inpainting (2000, background): “The subindexesb andf denote backward and forward differences respectively, while the subindexes m andM denote the minimum or maximum, respectively, between the derivative and zero (we have omitted the space coordinates (i; j) for simplicity); see [16] for details.”
Geometric constraints for shape and topology optimization in architectural design (2017, methodology): “The level set method was pioneered in [50], then introduced in the context of shape optimization in [7, 8, 49, 57, 64]; see the monographs [48, 56] for extensive discussions around the features of this method.”
Double-detonation supernovae of sub-Chandrasekhar mass white dwarfs (2007, methodology): “The propagation of the detonation flame is modeled with the “level set technique” (Osher & Sethian 1988) in the implementation of Golombek & Niemeyer (2005), which in turn is based on the deflagration flame model of Reinecke et al. (1999b).”
Modelling dynamic scenes by registering multi-view image sequences (2005, methodology): “We have implemented our method in the level set framework [9], motivated by its numerical stability and its ability to handle topological changes automatically.”
Hamilton–Jacobi Formulation for Reach–Avoid Differential Games (2009, methodology): “Numerical algorithms based on level set methods have been developed by [19] and [20], have been coded in efficient computational tools by [18] and [21], and can be directly applied to reachability computations.”
Experimental and computational investigation of vertical downflow condensation (2015, methodology): “Level-Set Method (LSM) [31] and Volume-of-Fluid (VOF) method [32] are two representative examples based on the Eulerian perspective.”
Three-dimensional delayed-detonation models with nucleosynthesis for Type Ia supernovae (2012, background): “1999; Osher & Sethian 1988; Smiljanovski et al. 1997).”
An efficient and parallel level set reinitialization method - Application to micromechanics and microstructural evolutions (2015, methodology): “Among existing approaches, the Level Set (LS) method introduced in 1988 [1] receives a growing attention.”
Medical image processing on the GPU - Past, present and future (2013, background): “thresholding (global or spatially varying), clustering, level sets (Osher and Sethian, 1988), active contours (snakes) (Kass et al.”
Deep learning in nano-photonics: inverse design and beyond (2020, methodology): “A more systematic alternative was the combination of numerical simulation methods with gradient-based or heuristic optimization algorithms, such as stimulated annealing, topology optimization, and genetic algorithms [32,41 – 44].”
An interface-capturing method for incompressible two-phase flows. Validation and application to bubble dynamics (2007, methodology): “This is especially the case of the Level Set method (Osher and Sethian, 1988; Sussman et al., 1994; Sethian, 1999) which is based on a smooth distance function whose zero value corresponds to the location of the interface.”