Abstract
The paper gives a short overview over some basic facts from the representation theory of groups and algebras. Then we describe iterative algorithms to normalize coefficient vectors computed by expanding functions on the unit sphere into a series of spherical harmonics. Typical applications of the normalization procedure are the matching of different three-dimensional images, orientation estimations in low-level image processing or robotics. The algorithm illustrates general methods from the representation theory of Lie-groups and Lie-algebras which can be used to linearize highly-non-linear problems. It can therefore also be adapted to applications involving groups different from the group of three-dimensional rotations. The performance of the algorithm is illustrated with a few experiments involving random coefficient vectors.
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© 1997 Springer-Verlag Berlin Heidelberg
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Lenz, R. (1997). Some applications of representations of lie algebras and lie groups. In: Sommer, G., Koenderink, J.J. (eds) Algebraic Frames for the Perception-Action Cycle. AFPAC 1997. Lecture Notes in Computer Science, vol 1315. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017863
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DOI: https://doi.org/10.1007/BFb0017863
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