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A Lie group approach to steerable filters

Recently Freeman and Adelson (1991) published an approach to steer filters in their orientation by Fourier decompositions with respect to the angular coordinate of a polar representation. Simoncelli et al. (1992) generalized this method to steer other parameters than the orientation. In this paper we formulate the problem of steerability using the Lie group that performs the deformation of the filters. Within the presented theoretical framework we especially discuss the following points: (1) The possible scope and (2) the optimality of steerability by Fourier decompositions, (3) approximate steerability using a limited number of basis functions, (4) the nature of the singularity that occurs when steering the scale.

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