Conformal Image Viewpoint Invariant

Ghina El Mir (), Karim Youssef and Chady El Mir
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Ghina El Mir: College of Business Administration, American University of the Middle East, Egaila 54200, Kuwait
Karim Youssef: College of Engineering and Technology, American University of the Middle East, Egaila 54200, Kuwait
Chady El Mir: LaMA-Liban Laboratory, Faculty of Science, Lebanese University, Tripoli P.O. Box 37, Lebanon

Mathematics, 2024, vol. 12, issue 16, 1-20

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 R 3 , 1 leads to an invariant by conformal transformations. For this, we identify the domain of an image to the disjoint union of horospheres ∐ α H α of R 3 , 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 ∐ α H α for the Minkowski metric of the ambient space.

Keywords: computer vision; Clifford algebras; conformal transformations; invariant; viewpoint change; horosphere; latitude angle; Minkowski metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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