An Algebraic Multigrid Approach for Image Analysis

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.