Showing papers by "Irad Yavneh published in 2002"

An Algebraic Multigrid Approach for Image Analysis

Abstract: We apply a new algebraic multigrid method for solving computer vision problems with constraints. As particular examples we solve the "shape from photometric stereo" and "image binarization" problems. A variational formulation is applied to the problem of shape reconstruction from three or more images of an object with the same viewing direction and different lighting conditions, supplemented by some pointwise height constraints. In order to obtain a smooth reconstruction, we use a weight-function that is singular at the constrained points, resulting in an elliptic equation with singular coefficients, which is solved efficiently by the algebraic multigrid algorithm. As a second example a similar technique is applied to construct a threshold surface which interpolates between values at centers of edges. This surface is then used for image binarization.

Automated Transformations for PDE Systems with Application to Multigrid Solvers

Abstract: An approach for transforming systems of partial differential equations in order to obtain new formulations which are more accessible to numerical solution is studied. An algorithm is developed for generating such transformations automatically, using symbolic computations employing Grobner bases. The algorithm is implemented using freely available software. This approach, along with planned developments, will potentially provide a powerful set of tools for handling large systems of partial differential equations.