Projective Invariants for Vision

Patrick Gros 1, 2 Long Quan 1, 2
1 MOVI - Modeling, localization, recognition and interpretation in computer vision
GRAVIR - IMAG - Graphisme, Vision et Robotique, Inria Grenoble - Rhône-Alpes, CNRS - Centre National de la Recherche Scientifique : FR71
Abstract : This paper studies the invariant theory for its applications to computer vision. In the first part of the paper, three methods of invariant calculation are presented: 1. the infinitesimal method which gives a precise enumeration of the maximal number of independent invariants existing in a given problem; 2. the generalization and constraint method; 3. the use of canonical invariants associated with some transformations, which is, in our opinion, the method to be used primarily, for all problems where only simple elements (points, straight lines, conics) are involved. In the last part, invariants are applied to 3D vision problems: 3D invariant computation from multiple images in investigated in detail in the case of uncalibrated cameras. Experimental results are given on artificial data: this allows to study the robustness of invariants to increasing levels of noise. Some results are also given on real data to show that 3D invariants are usable in practice.
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Patrick Gros, Long Quan. Projective Invariants for Vision. [Technical Report] RT 90 IMAG - 15 LIFIA, 1992, pp.47. ⟨inria-00590013⟩

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