Shape modeling is an important constituent of computer vision as well graphics research. models aid the tasks object representation and recognition. This paper presents a new approach to shape which retains some attractive features existing methods overcomes their limitations. The authors' techniques can be applied model arbitrarily complex shapes, include shapes with significant protrusions, situations where no priori assumption about object's topology made. A single instance model, when...

A fast marching level set method is presented for monotonically advancing fronts, which leads to an extremely scheme solving the Eikonal equation. Level methods are numerical techniques computing position of propagating fronts. They rely on initial value partial differential equation a function and use borrowed from hyperbolic conservation laws. Topological changes, corner cusp development, accurate determination geometric properties such as curvature normal direction naturally obtained in...

Fast Marching Methods are numerical schemes for computing solutions to the nonlinear Eikonal equation and related static Hamilton--Jacobi equations. Based on entropy-satisfying upwind fast sorting techniques, they yield consistent, accurate, highly efficient algorithms. They optimal in sense that computational complexity of algorithms is O(N log N), where N total number points domain. The use a variety applications, including problems shape offsetting, distances from complex curves surfaces,...

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

▪ Abstract We provide an overview of level set methods, introduced by Osher and Sethian, for computing the solution to fluid-interface problems. These are computational techniques that rely on implicit formulation interface, represented through a time-dependent initial-value partial-differential equation. discuss essential ideas behind techniques, coupling these finite-difference methods incompressible compressible flow, collection applications including two-phase ship hydrodynamics,...

We present a fast algorithm for solving the eikonal equation in three dimensions, based on marching method. The is of order O(N log N), where N total number grid points computational domain. can be used any orthogonal coordinate system and globally constructs solution to each point method unconditionally stable solutions consistent with exact arbitrarily large gradient jumps velocity. In addition, resolves overturning propagation wavefronts. begin mathematical foundation using follow...

We introduce a new limiting system of equations to describe combustion processes at low Mach number in either confined unbounded regions ~d numerically solve these for the case fiame propagating closed vessel.This allows large heat release, substantial temperature and density variations, interaction with hydrodynamic ftow field, including effects turbulence.However, this is much simpler than complete equation~ compressible reacting gas fiow since detailed acoustic waves have been...

We develop a family of fast methods for approximating the solutions to wide class static Hamilton--Jacobi PDEs; these include both semi-Lagrangian and fully Eulerian versions. Numerical problems are typically obtained by solving large systems coupled nonlinear discretized equations. Our techniques, which we refer as "Ordered Upwind Methods" (OUMs), use partial information about characteristic directions decouple systems, greatly reducing computational labor. techniques considered in context...

Deep convolutional neural networks have been successfully applied to many image-processing problems in recent works. Popular network architectures often add additional operations and connections the standard architecture enable training deeper networks. To achieve accurate results practice, a large number of trainable parameters are required. Here, we introduce based on using dilated convolutions capture features at different image scales densely connecting all feature maps with each other....

The Fast Marching Method is a numerical algorithm for solving the Eikonal equation on rectangular orthogonal mesh in O(M log M) steps, where M total number of grid points. scheme relies an upwind finite difference approximation to gradient and resulting causality relationship that lends itself Dijkstra-like programming approach. In this paper, we discuss several extensions technique, including higher order versions unstructured meshes Rn manifolds connections more general static...

In many physical problems, interfaces move with a speed that depends on the local curvature.Some common examples are flame propagation, crystal growth, and oil-water boundaries.We idealize front as closed, nonintersecting, initial hypersurface flowing along its gradient field curvature.Because explicit solutions seldom exist, numerical approximations often used.In this paper, we review some recent work algorithms for attacking these problems.We show based direct parametrizations of moving...

We review recent work on level set methods for following the evolution of complex interfaces. These techniques are based solving initial value partial differential equations functions, using borrowed from hyperbolic conservation laws. Topological changes, corner and cusp development, accurate determination geometric properties such as curvature normal direction naturally obtained in this setting. The methodology results robust, accurate, efficient numerical algorithms propagating interfaces...