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The boundary-value problem is discretized o n several grids (or finite-element spaces) of widely different mesh sizes. Interactions between these levels enable us (i) to solve the possibly nonlinear system of n discrete equations in O(n) operations (40n additions and shifts for Poisson problems); (ii) to conveniently adapt the discretization (the local mesh(More)
Finding salient, coherent regions in images is the basis for many visual tasks, and is especially important for object recognition. Human observers perform this task with ease, relying on a system in which hierarchical processing seems to have a critical role. Despite many attempts, computerized algorithms have so far not demonstrated robust segmentation(More)
We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns, for every internal point of the silhouette, a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson's equation, with the silhouette(More)
Techniques are developed for accelerating multigrid convergence in general, and for advection-diffusion and incompressible flow problems with small viscosity in particular. It is shown by analysis that the slowing down of convergence is due mainly to poor coarse-grid correction to certain error components, and means for dealing with this problem are(More)
Texture segmentation is a difficult problem, as is apparent from camouflage pictures. A Textured region can contain texture elements of various sizes, each of which can itself be textured. We approach this problem using a bottom-up aggregation framework that combines structural characteristics of texture elements with filter responses. Our process(More)
We introduce a fast, multiscale algorithm for image segmentation. Our algorithm uses modern numeric techniques to nd an approximate solution to normalized cut measures in time that is linear in the size of the image with only a few dozen operations per pixel. In just one pass the algorithm provides a complete hierarchical decomposition of the image into(More)
Exact numerical convergence factors for any multigrid cycle can be predicted by local mode (Fourier) analysis. For general linear elliptic PDE systems with piecewise smooth coeecients in general domains discretized by uniform grids, it is proved that, in the limit of small meshsizes, these predicted factors are indeed obtained, provided the cycle is(More)
Multigrid methods are known for their high efficiency in the solution of definite elliptic problems. However, difficulties that appear in highly indefinite problems, such as standing wave equations, cause a total loss of efficiency in the standard multigrid solver. The aim of this paper is to isolate these difficulties, analyze them, suggest how to deal(More)
General purely algebraic approaches for repeated coarsening of deterministic or statistical field equations are presented, including a universal way to gauge and control the quality of the coarse-level set of variables, and generic procedures for deriving the coarse-level set of equations. They apply to the equations arising from variational as well as(More)