Trinocular Geometry Revisited

Jean Ponce (1, 2) , Martial Hebert (3) , Matthew Trager (1, 2)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure
2 WILLOW - Models of visual object recognition and scene understanding
3 CMU - Carnegie Mellon University [Pittsburgh]

When do the visual rays associated with triplets of point correspondences converge, that is, intersect in a common point? Classical models of trinocular geometry based on the fundamental matrices and trifocal tensor associated with the corresponding cameras only provide partial answers to this fundamental question, in large part because of underlying, but seldom explicit, general configuration assumptions. This paper uses elementary tools from projective line geometry to provide necessary and sufficient geometric and analytical conditions for convergence in terms of transversals to triplets of visual rays, without any such assumptions. In turn, this yields a novel and simple minimal parameteriza-tion of trinocular geometry for cameras with non-collinear or collinear pinholes, which can be used to construct a practical and efficient method for trinocular geometry parameter estimation. We present numerical experiments using synthetic and real data.

Mots clés: Trinocular geometry; Trilinearities; Minimal parameterizations of camera geometry; Camera parameter estimation.

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

Jean Ponce, Martial Hebert, Matthew Trager. Trinocular Geometry Revisited. 2015. ⟨hal-01152348v2⟩