Finding point correspondence and determining motion of a rigid object from two weak perspective views

Abstract

Given two images of an n-point configuration which undergoes 3D rotation, translation, and scaling, our problems are (i) How can we match the corresponding points in the two images? Can all the possible mapping be found? (ii) What underlying motions and associated depth components of these points could account for the two images? (iii) Can the object be recovered uniquely? This formulation of the n-point problem is in the most general setting and does not assume attributes or features. A natural question to ask is whether an n-point problem is equivalent to a set of fewer-point problems. This paper presents a method which reduces an n-point problem to a set of 4-point problems. The effort of reduction takes O(n) steps and it also takes O(n) steps to construct all possible mappings of an n-point set from the solution to a 4-point problem. Other results include (1) coplanarity condition of four points in two views, (2) recovering the tilt direction of the rotational axis using four points in two views, (3) recovering the scaling factor.