We present a fast marching level set method for monotonically advancing fronts, which leads to an extremely fast scheme for solving the Eikonal equation. Level set methods are numerical techniques for computing the position of propagating fronts. They rely on an initial value partial differential

A wide range of computer vision applications such as distance field computation, shape from shading, and shape representation require an accurate solution of a particular Hamilton-Jacobi (HJ) equation, known as the Eikonal equation. Although the fast marching method (FMM) is the most stable and consistent method among existing techniques for solving such equation, it suffers from large numerical error along diagonal directions as well as its computational complexity is not optimal. In this paper, we propose an improved version of the FMM that is both highly accurate and computationally efficient for Cartesian domains. The new method is called the multi-stencils fast marching (MSFM), which computes the solution at each grid point by solving the Eikonal equation along several stencils and then picks the solution that satisfies the fast marching causality relationship. The stencils are centered at each grid point x and cover its entire nearest neighbors. In 2D space, 2 stencils cover the 8-neighbors of x, while in 3D space, 6 stencils cover its 26-neighbors. For those stencils that are not aligned with the natural coordinate system, the Eikonal equation is derived using directional derivatives and then solved using a higher order finite difference scheme. 1.

We are quickly passing through the historical moment when people work in front of a single computer, dominated by a small CRT and focused on tasks involving only local information. Networked computers are becoming ubiquitous and are playing increasingly significant roles in our lives

that the distributions of packet features (IP addresses and ports) observed in flow traces reveals both the presence and the structure of a wide range of anomalies. Using entropy as a summarization tool, we show that the analysis of feature distributions leads to significant advances on two fronts: (1) it enables highly

modeling monotonically advancing fronts, including Hamilton-Jacobi-Bellman and Hamilton-Jacobi-Isaacs equations which arise in the framework of optimal control problems and differential games. We also show the convergence of the algorithm to the viscosity solution. Finally we present several numerical

in a computer animation environment. In order to better obtain photorealism in the behavior of the simulated water surface, we introduce a new "thickened" front tracking technique to accurately represent the water surface and a new velocity extrapolation method to move the surface in a smooth

A new real-time obstacle avoidance approach for mobile robots has been developed and implemented. This approach permits the detection of unknown obstacles simultaneously with the steering of the mobile robot to avoid collisions and advancing toward the target. The novelty of this approach, entitled

Compiler infrastructures that support experimental research are crucial to the advancement of high-performance computing. New compiler technology must be implemented and evaluated in the context of a complete compiler, but developing such an infrastructure requires a huge investment in time

-visual automatic speech recognition and present novel contributions in two main areas: First, the visual front end design, based on a cascade of linear image transforms of an appropriate video region-of-interest, and subsequently, audio-visual speech integration. On the later topic, we discuss new work on feature

. The notion of pulsating travelling fronts generalizes that of travelling fronts for planar or shear flows. Various existence, uniqueness and monotonicity results are proved for two classes of reaction terms. Firstly, for a combustion-type nonlinearity, it is proved that the pulsating travelling front exists