The Projective Invariants of Six 3D Points from Three 2D Uncalibrated Images

Abstract

A basic problem in computer vision is to recover the projective structure of a set of 3D points from its 2D images. It is known that 3D projective invariants of six points can be computed from three uncalibrated view images. In the previous method, three homogeneous polynomial equations in four variables relating the geometry of the six 3D points and their 2D projections were derived first. Then an eighth degree polynomial equation in single variable was derived by means of the classical resultant technique. Numerical method was applied to obtain an equation of a third degree. So the form of the equation is implicit and hard to apply in real applications. This paper adopts a novel method to eliminate variables. A third degree polynomial equation in single variable is derived symbolically. The equation is presented in explicit form. It can be used in real applications directly.