A Multiple Resolution Approach To Regularization

Charles Bouman; Bede Liu

doi:10.1117/12.968993

25 October 1988 A Multiple Resolution Approach To Regularization

Charles Bouman, Bede Liu

Proceedings Volume 1001, Visual Communications and Image Processing '88: Third in a Series; (1988) https://doi.org/10.1117/12.968993
Event: Visual Communications and Image Processing III, 1988, Cambridge, MA, United States

Abstract

Regularization of optical flow estimates and the restoration of noisy images are examples of problems which may be solved by modeling the unknown field as a Markov random field (MRF) and calculating the maximum a posteriori (MAP) estimate. This paper presents a multiple resolution algorithm for maximizing the a posteriori probability associated with a class of MRF's. These MRF's combine the smooth regions found in Gaussian random fields with the abrupt boundaries characteristic of discrete valued MRF's. This makes them well suited for modeling image properties which vary smoothly over large regions but change abruptly at object boundaries. The multiple resolution algorithm first performs the maximization at coarse resolution and then proceeds to finer resolutions until the pixel level is reached. Since coarser resolution solutions are used to guide maximization at finer resolutions, the algorithm is resistant to local maxima and has performance equivalent to simulated annealing, but with dramatically reduced computation. In fact, the multiple resolution algorithm has been found to require less computation than local greedy algorithms because constraints propagate more rapidly at coarse resolutions. Regularization of optical flow problems and the restoration of fields corrupted with additive white Gaussian noise are explicitly treated and simulation results are presented.

Citation Download Citation

Charles Bouman and Bede Liu "A Multiple Resolution Approach To Regularization", Proc. SPIE 1001, Visual Communications and Image Processing '88: Third in a Series, (25 October 1988); https://doi.org/10.1117/12.968993

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