Pyramid implementation of optimal-step conjugate-search algorithms for some low-level vision problems

The authors present a parallel pyramid implementation of the line search conjugate gradient algorithm for minimizing the cost function in low-level vision problems. By viewing the global cost function as a Gibbs energy function, it is possible to compute the gradients, inner products, and optimal-step size efficiently using the pyramid. Implementation of this algorithm for shape-from-shading results in a multiresolution conjugate gradient algorithm. The robustness and efficiency of the algorithm are demonstrated for edge detection using the graduated nonconvexity (GNC) algorithm. This formulation is also applied to image estimation based on Markov models. A compound model for the original image is defined that consists of a 2D noncausal Gauss-Markov random field to represent the homogeneous regions and a line process to represent the discontinuities. A deterministic algorithm based on the GNC formulation is derived to obtain a near-optimal maximum a posteriori probability estimate of images corrupted by additive Gaussian noise