Massively parallel computation of globally optimal shortest paths with curvature penalization

Abstract

We address the computation of paths globally minimizing an energy involving their curvature, with given endpoints and tangents at these endpoints, according to models known as the Reeds-Shepp car (reversible and forward variants), the Euler-Mumford elasticae, and the Dubins car. For that purpose, we numerically solve degenerate variants of the eikonal equation, on a three-dimensional domain, in a massively parallel manner on a graphical processing unit. Due to the high anisotropy and nonlinearity of the addressed Partial Differential Equation, the discretization stencil is rather wide, has numerous elements, and is costly to generate, which leads to subtle compromises between computational cost, memory usage, and cache coherency. Accelerations by a factor 30 to 120 are obtained w.r.t a sequential implementation. The efficiency and the robustness of the method is illustrated in various contexts, ranging from motion planning to vessel segmentation and radar configuration.

Computing geodesic paths encoding a curvature prior for curvilinear structure tracking

“…Furthermore, the computation time of the HFM method can be deeply speeded up by exploiting a GPU-implemented scheme for estimating the geodesic distances, as proposed in ref. 58 . The codes for the HFM method associated with the variant of the Euler–Mumford elastica model equipped with a curvature prior, involving the construction for the stencils, the computation for the geodesic distance map and the numerical solution to the geodesic backtracking ODE, can be downloaded from https://github.com/Mirebeau/HamiltonFastMarching .…”