Physically-based adaptive preconditioners for early vision

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. The adaptation of the preconditioner to an early vision problem is achieved via the explicit use of the spectral characteristics of the regularization filter 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 preconditioning technique is demonstrated for the surface reconstruction, shape from shading and optical flow computation problems. We experimentally establish the superiority of our preconditioning method over previously presented preconditioning techniques for these problems