Trinocular Geometry Revisited

Matthew Trager (1, 2) , Jean Ponce (1, 3, 2) , Martial Hebert (4)

1 LIENS - Laboratoire d'informatique de l'école normale supérieure
2 WILLOW - Models of visual object recognition and scene understanding
3 PSL - Université Paris sciences et lettres
4 The Robotics Institute

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

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

Matthew Trager, Jean Ponce, Martial Hebert. Trinocular Geometry Revisited. International Journal of Computer Vision, 2016. ⟨hal-01152348v3⟩