We describe a fast solver for the inhomogeneous heat equation in free space, following the time evolution of the solution in the Fourier domain. It relies on a recently developed spectral approximation of the free-space heat kernel coupled with the non-uniform fast Fourier transform. Unlike finite difference and finite element techniques, there is no need for artificial boundary conditions on a...

An adaptive method for polygonization of implicit surfaces is presented. The method insists on the shape of triangles and the accuracy of resulting approximation as well. The presented algorithm is based on the surface tracking scheme and it is compared with the other algorithms based on the similar principle, such as the Marching cubes and the Marching triangles methods. The main advantages of...

In this paper we introduce an extension of the Fast Marching Method introduced by Sethian [6] for the eikonal equation modelling front evolutions in normal direction. The new scheme can deal with a time-dependent velocity without any restriction on its sign. This scheme is then used for solving dislocation dynamics problems in which the velocity of the front depends on the position of the front...

In this paper we present a novel method for solving optimization problems governed by partial di erential equations. Existing methods use gradient information in marching toward the minimum, where the constrained PDE is solved once (sometimes only approximately) per each optimization step. Such methods can be viewed as a marching techniques on the intersection of the state and costate hypersurf...

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on a rectangular orthogonal mesh in O(M log M) steps, where M is the total number of grid points. In this paper we extend the Fast Marching Method to triangulated domains with the same computational complexity. As an application, we provide an optimal time algorithm for computing the geodesic distances and thereb...

In these notes, we present an introduction to the classical Fast Marching Method (FMM). The FMM has been first introduced to find numerical approximations of the solutions to the stationary eikonal equation. More generally we show that this method allows to find exactly the solutions of numerical schemes that satisfy a certain causality assumption. In order to motivate this method, we present t...

The fast marching algorithm computes an approximate solution to the eikonal equation in O(N logN) time, where the factor logN is due to the administration of a priority queue. Recently, [YBS06] have suggested to use an untidy priority queue, reducing the overall complexity to O(N) at the price of a small error in the computed solution. In this paper, we give an explicit estimate of the error in...

We propose a novel method, slice marching 1, for segmenting opacified vessels tree in 3D images (volume data), from multislice computed tomography (MSCT) scans. The method uses fast marching with freezing of boundaries to advance inside the vessel, slice per slice. Large scale features, such as vessel section and curvature, are evaluated for each slice. These features can then be used to influe...

Localization and quantification of the light sources generated by the expression of bioluminescent reporter genes is an important task in bioluminescent imaging of small animals, especially the generically engineered mice. To employ the Monte Carlo method for the light-source identification, the surfaces that define the anatomic structures of the small experimental animal is required; to perfor...