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Abstract: In this talk, it will be shown how the convolution product and fourier transform of functions on the group of rigid-body motions can be used in robotics and image understanding. In particular, these tools are used to determine the positions and orientations that a robot arm can reach, and can be used to generate the boundaries of configuration space obstacles for mobile robots. In image understanding, noncommutative harmonic analysis forms the basis for invariant pattern matching. Numerical approximations of the convolution product are discussed, as well as inverse problems which are naturally addressed using techniques from nonabelian harmonic analysis.