Bag of lines models for non-central linear cameras

Xavier Goaoc

Loria, France

Abstract

In computer vision, reconstruction techniques such as stereography follow easily from modelling central cameras as a "pinhole camera", that is the set of rays passing through a point: two image points are in epipolar correspondance (that is, may be the projection of the same 3D point) if and only if the two associated rays intersect.

This invites to consider a camera from a line geometry perspective, as a "bags of lines". In this work, we develop this viewpoint and show that it leads to a unified treatment of stereography between any two central, pushbroom, X-slit, pencil and linear oblique cameras. These results are obtained through a new description of the "linear line congruences" (that is, 2D sections of the Plucker quadric by a projective space) that underlie each of these cameras; this description is encapsulated in an affine map, in 3-space, that globally preserves