Convex Relaxation Techniques for Computer Vision

Daniel Cremers
Technische Universtitat München

Numerous computer vision problems can be cast as labeling problems where each point of a domain is assigned one of several labels. The case of two labels includes problems like binary segmentation and multi-view reconstruction. The case of multiple labels includes problems such as stereo depth reconstruction, image denoising, optic
flow estimation and multi-region segmentation (in particular the piecewise-constant and piecewise smooth Mumford-Shah functional). In my presentation, I will introduce methods of convex relaxation and functional lifting which allow to solve such labeling problems in a spatially continuous setting. Solutions are either globally optimal or within a known bound of the optimum. For minimization, we introduce efficient and provably convergent primal dual algorithms. In contrast to corresponding graph cut algorithms, the proposed convex relaxation methods do not exhibit grid bias and are easily parallelized on graphics hardware leading to acceptable computation times even for larger problems.

This is joint work with Kalin Kolev, Thomas Pock, Antonin Chambolle and Bastian Goldluecke.

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