A new Hilbert invariant for pattern of points under affine transformation

Abstract

This paper presents a new Hilbert Invariant for a pattern of points in an image. The Hilbert invariant is invariant under any affine transformation (translation, scaling, rotation and shearing). It is constructed based on the Hilbert transform. Hilbert transform is originally used for generating the imaginary part from the real part of a continuous or discrete complex signal to recover the original one in signal processing. In this paper, the real part is a discrete signal formed by a sequence of coordinates of image points. The Hilbert transformed signal is then used to construct a relative and an absolute affine invariant.