In this paper we formulate steerable filters as the representations of transformation groups. The transformation groups on the image plane considered thus far concentrate on rotation, scaling, and translation. So we construct the steerable filter for the projective rotation group based on the representation of the projective rotation group. We further discuss the steerability for the 3D Euclidean motion group from the standpoint of the representation of the Euclidean motion group. We also show a given image can be expanded with steerable functions, which is a special case of Fourier transform on Lie groups.
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