Critical configurations for three projective views

TL;DR

This paper investigates the specific conditions under which 3D structure from motion becomes impossible with three projective cameras, identifying critical configurations as intersections of quadric surfaces.

Contribution

It provides a complete algebraic classification of critical configurations for three projective cameras, detailing the geometric conditions for non-uniqueness.

Findings

Critical configurations lie on intersections of quadric surfaces.

Complete classification of critical configurations for three cameras.

Algebraic characterization of non-uniqueness cases.

Abstract

The problem of structure from motion is concerned with recovering the 3-dimensional structure of an object from a set of 2-dimensional images taken by unknown cameras. Generally, all information can be uniquely recovered if enough images and point correspondences are provided, yet there are certain cases where unique recovery is impossible; these are called critical configurations. We use an algebraic approach to study the critical configurations for three projective cameras. We show that all critical configurations lie on the intersection of quadric surfaces, and classify exactly which intersections constitute a critical configuration.