Section: New Results

3D visibility, theory and applications

Calibration for linear cameras

The linear camera is a fairly general geometric model of imaging devices proposed by Jean Ponce and based on linear line congruences, two-dimensional sections of the Klein quadric (a classical model for the space of lines). In a previous work, in collaboration with Jean Ponce, we explored properties of this model. We established in particular the equivalence of linear camera with another model proposed by Tomas Pajdla (which we generalized along the way). The complementarity of these models allowed to extend standard computer vision techniques, such as stereo-reconstruction, to any imaging system modeled by a linear camera. We went one step further and explored how the notion of “calibration” extends to linear cameras. We enriched the usual “intrinsic” parameters used for central cameras by additional parameters that encode the geometry of linear line congruences. This required to investigate the Euclidean aspects of linear line congruences, objects that are usually studied in a projective setting.

This work is part of Guillaume Batog's PhD thesis (defended in December 2011) [12] and a journal version is in preparation.