Arbitrary shape Hough transform by invariant geometric features

The Hough transform (HT) is an established technique which evidences a shape by mapping image edge points into a parameter space. Previously, the formulation of the HT has been extended to extract analytic arbitrary shapes which change their appearance according to similarity transformations. In this paper, we discuss a more general formulation which incorporates the extraction of arbitrary shapes under more general transformations than similarity mappings. The main contributions of this paper are: we show that, in general, the complexity of the HT mapping does not depend on the complexity or irregularity of the shape to be located; and we demonstrate that the concept of invariance can provide a general principle to avoid increase in computational complexity when the HT is extended to arbitrary shapes and general transformations.