Conformal Image Viewpoint Invariant

Abstract

In this paper, we introduce an invariant by image viewpoint changes by applying an important theorem in conformal geometry stating that every surface of the Minkowski space R3,1 leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ∐αHα of R3,1 by means of the powerful tools of the conformal Clifford algebras. We explain that every viewpoint change is given by a planar similarity and a perspective distortion encoded by the latitude angle of the camera. We model the perspective distortion by the point at infinity of the conformal model of the Euclidean plane described by D. Hestenesand we clarify the spinor representations of the similarities of the Euclidean plane. This leads us to represent the viewpoint changes by conformal transformations of ∐αHα for the Minkowski metric of the ambient space.