Abstract
This paper describes a general mathematical formulation for the problem of constructing steerable functions. The formulation is based on Lie group theory and is thus applicable to transformations which are Lie groups, such as, rotation, translation, scaling, and affine transformation. For one-parameter and Abelian multi-parameter Lie transformation groups, a canonical decomposition of all possible steerable functions, derived using the Jordan decomposition of matrices, is developed. It is shown that any steerable function under Lie transformation groups can be described using this decomposition. Finally, a catalog of steerable functions for several common multi-parameter image transformation groups is also provided.
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Hel-Or, Y., Teo, P.C. Canonical Decomposition of Steerable Functions. Journal of Mathematical Imaging and Vision 9, 83–95 (1998). https://doi.org/10.1023/A:1008274211102
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DOI: https://doi.org/10.1023/A:1008274211102