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Computational Symmetry
This lab is no longer active.
Head: Yanxi Liu
Contact: Yanxi Liu
Associated center(s) / consortia:
 Vision and Autonomous Systems Center (VASC)
Overview
A computational model for symmetry is especially pertinent to robotics, computer vision and machine intelligence, because in these fields we are studying how a man-made intelligent being can perceive and interact with the chaotic real world in the most effective way. Recognition of symmetries is the first step towards capturing the essential structure of a real world problem, and minimizing redundancy which can often lead to drastic reductions in computation. One fundamental limitation of computers is their finite representational power. One simple floating point error can destroy any perfect symmetry. One's ability to tolerate departure from perfect symmetry reflects one's level of sophistication in perception, which need to be built into the development of machine/artificial intelligence. Besides our poor understanding of human natural capability of symmetry perception, the mathematical theory for symmetry, group theory, has not been utilized effectively in practice. Group theory is usually introduced in classrooms in an abstract way (if it is introduced to computer science majors at all in the United States) that is hard to relate to everyday life. More importantly, the non-coherent topological nature of symmetry groups poses challenging computation problems on computers.