Vision and Lie's approach to invariance

The application of invariance theory has gained a renewed interest in the computer vision community. Recent results show that it offers a strong, unifying framework that helps in tackling problems such as calibration-less vision, efficient matching, shape-from-motion, grouping, and several other problems considered crucial to intelligent vision. Nonetheless, a systematic approach to the problem of extracting invariants is far from trivial. This paper describes one such approach, the theory of Lie groups. After a concise and non-rigorous account on the method itself, typical problems that arise in vision are discussed. For each of these problems, one or more relevant examples are given.

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