Algebraic cameras in Computer Vision

An important task in computer vision is the reconstruction of a 3D scene from multiple pictures. The core of this problem requires solving a system of polynomial equations, which leads to interesting problems in projective and algebraic geometry.

In this talk, I will present a new general framework for 3D vision, in which a camera is modeled geometrically as a mapping from $P^3$ to a line congruence. This viewpoint applies to traditional pinhole cameras, but also to many other practical devices, such as two-slit cameras, pushbroom cameras, catadioptric cameras, and many more. The multi-view geometry of all these systems can be studied using the "concurrent lines variety", which consists of n-tuples of lines in $P^3$ that intersect at a point. Moreover, several classical features of pinhole cameras, such as intrinsic and extrinsic parameters, can be defined in a very general setting.