Affine Shape Representation from Motion Through Reference Points

Long Quan (1, 2) , Roger Mohr (1, 2)

1 MOVI - Modeling, localization, recognition and interpretation in computer vision
2 LIFIA - Laboratoire d'Informatique Fondamentale et d'Intelligence Artificielle

This paper shows how an affine representation of spatial configuration is obtained from a pair of projection views. Calibration of cameras and knowledge of the camera's motion are not necessary; however, some preselected reference points and their correspondences are needed. Projective and affine geometry invariants are trickily manipulated to do the affine reconstruction. The method is thus geometrically constructive. When it is compared with the solution proposed in 1989 by J.J. Koenderink and A.J. Van Doorn (ldquoAffine Structure from Motion,rdquo Technical Report, Utrect University), the method provides a viewpoint-independent affine representation under parallel projections. Further, we investigate the central-projection case in which, with three additional special reference points, the same affine reconstruction can be done. We also discuss some important applications of this viewpoint independence of shape representation.

Mots clés: affine geometry; projective geometry; computer vision; shape representation

Domaines: Vision par ordinateur et reconnaissance de formes [cs.CV]

Long Quan, Roger Mohr. Affine Shape Representation from Motion Through Reference Points. Journal of Mathematical Imaging and Vision, 1992, 1 (2), pp.145--151. ⟨10.1007/BF00122209⟩. ⟨inria-00548443⟩