Physically-based Adaptive Preconditioning for Early Vision 1

Several problems in early vision have been formulated in the past in a regularization framework. These problems when discretized lead to large sparse linear systems. In this paper, we present a novel physically-based adaptive preconditioning technique which can be used in conjunction with a conjugate gradient algorithm to drastically improve the speed of convergence for solving the aforementioned linear systems. A preconditioner based on the membrane spline or the thin plate spline or a convex combination of the two is termed as a physically-based precon-ditioner for obvious reasons. The adaptation of the preconditioner to an early vision problem is achieved via the explicit use of the spectral characteristics of the regularization lter in conjunction with the data. This spectral function is used to modulate the frequency characteristics of a chosen wavelet basis leading to the construction of our preconditioner. The precondition-ing technique is demonstrated for the surface reconstruction, shape from shading and optical ow computation problems. We experimentally establish the superiority of our preconditioning method over previously presented preconditioning techniques for the surface reconstruction and shape from shading problems. Performance of the preconditioning technique is demonstrated via experimental results on real and synthetic data.