Bregman Iteration for Optical Flow

Sample Optical Flow

Abstract

Osher and his colleagues introduced Bregman iterations in image processing in 2005. This technique is known to yield excellent results for denoising/deblurring and compressed sensing tasks but it has so far been rarely used for other image processing problems. Some of the assets of the Bregman framework are the high flexibility and the existence of a thorough convergence theory. In this thesis we adapt the split Bregman iteration, originally developed by Goldstein and Osher, to the optical flow problem. The versatility of the Bregman framework allows us to present a general approach to solve variational formulations with modern data terms incorporating higher order constancy assumptions as well as discontinuity preserving smoothness terms such as the popular total variation regulariser. Several models will be analysed, and for each one a detailed algorithm based on the split Bregman iteration will be presented. Finally, we will analyse the theoretical properties of the Bregman iteration. The most interesting questions such as convergence and error estimation will be treated in detail, thus providing a solid mathematical basis for further research.

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