Non-Abelian invariant feature detection

Abstract

We present a novel formulation of non-Abelian invariant feature detection. By choosing suitable measuring functions, we show that the measuring space and the corresponding feature space are equivariant with respect to the SL(2, Ropf) Lie transformation group. This group is non-Abelian and may be decomposed via the Iwasawa decomposition into meaningful transformations on images. We calculate the induced representations of this group on the measuring space. Then, via these representations we construct a set of three PDEs determining an invariant function of the features. We show that this set of equations is solved by the discriminant of a binary form of order n. Hence, the discriminant plays the role of an invariant feature detector with respect to this transformation group.