General Deformations of Point Configurations Viewed By a Pinhole Model Camera

This paper is a theoretical study of the non-rigid structure from motion problem: what can be computed from a monocular view of a parametrically deforming set of points? We treat various variations of this problem for 3D affine and general smooth deformations (under some mild technical restrictions) with either a calibrated or an uncalibrated camera. We show that in general at least three images related by quasi-identical deformations are needed to have a finite set of solutions to the points’ structure.