The goal of this paper is to study some numerical approximations of particular HamiltonJacobi-Bellman equations in dimension 1 and with possibly discontinuous initial data. We investigate two anti-diffusive numerical schemes, the first one is based on the Ultra-Bee scheme and the second one is based on the Fast Marching Method. We prove the convergence and derive L-error estimates for both sche...

In this paper, we present a shape recovery technique in 2D and 3D with speciic applications in visualizing and measuring anatomical shapes from medical images. This algorithm models extremely corrugated structures like the brain, is topologically adaptable , is robust, and runs in O(N log N) time where N is the total number of points in the domain. Our two-stage technique is based on the level ...

Common techniques for curve alignment find a solution in the form of a shortest network path by means of dynamic programming. In this paper we present an approach that employs Sethian’s Fast Marching Method to find the solution with sub-resolution accuracy and in consistence with the underlying continuous problem. We demonstrate how the method may be applied to compare closed curves, morph one ...

Knee osteoarthritis (OA) is prevalent among military servicemembers and has been linked to occupational load carriage. Lower extremity injury risk two times higher in female recruits. Effects of ambulation strategy (walk vs. run) on knee kinematics are known, however effects arthrokinematics during high-velocity walking (force march) unknown. Analyzing biomechanics a loaded march essential unde...

A fully Sinc-Galerkin method for solving advection-di usion equations subject to arbitrary radiation boundary conditions is presented. This procedure gives rise to a discretization which has it's most natural representation in the form of a Sylvester system where the coe cient matrix for the temporal discretization is full. The word \full" often implies a computationally more complex method com...

An accurate detection of the radiation field is crucial to 3D conformal radiotherapy (3D-CRT). Automated techniques to detect the field edges on double exposure portal images have previously focused on thresholding techniques. In this paper, we present a new approach based on a curve propagation technique (the Fast Marching method) which proves to be more effective at detecting the radiation fi...

Marching triangles is a method for producing a polygon mesh surface approximation composed of triangular facets which are approximately equilateral. This paper improves the Marching Triangles algorithm where the inputs are multiple range images of scenes. C discontinuities (fold edges) are detected and used to constrain the final triangulation, thus increasing the accuracy of the mesh at sharp ...

Dynamically adaptive numerical methods have been developed to efficiently solve differential equations whose solutions are intermittent in both space and time. These methods combine an adjustable time step with a spatial grid that adapts to spatial intermittency at a fixed time. The same time step is used for all spatial locations and all scales: this approach clearly does not fully exploit spa...

We consider two different non-autonomous anisotropic time-optimal control problems. For the min-time-from-boundary problem, we show that the value function is recovered as a viscosity solution of a static Hamilton–Jacobi–Bellman partial differential equation H(∇u(x), u(x),x) = 1. We demonstrate that the space-marching Ordered Upwind Methods (introduced in [29] for the autonomous control) can be...