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• W2775163108 abstract "We introduce numerical schemes for computing distances and shortest paths with respect to several planar paths models, featuring curvature penalization and data-driven velocity: the Dubins car, the Euler/Mumford elastica, and a two variants of the Reeds–Shepp car. For that purpose, we design monotone and causal discretizations of the associated Hamilton–Jacobi–Bellman PDEs, posed on the three-dimensional domain $${mathbb R}^2 times {mathbb S}^1$$ . Our discretizations involve sparse, adaptive and anisotropic stencils on a cartesian grid, built using techniques from lattice geometry. A convergence proof is provided, in the setting of discontinuous viscosity solutions. The discretized problems are solvable in a single pass using a variant of the fast-marching algorithm. Numerical experiments illustrate the applications of our schemes in motion planning and image segmentation." @default.
• W2775163108 created "2017-12-22" @default.
• W2775163108 creator A5029194666 @default.
• W2775163108 date "2017-12-13" @default.
• W2775163108 modified "2023-09-30" @default.
• W2775163108 title "Fast-Marching Methods for Curvature Penalized Shortest Paths" @default.
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• W2775163108 doi "https://doi.org/10.1007/s10851-017-0778-5" @default.
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