What can two images tell us about a third one?

Abstract

This paper discusses the problem of predicting image features in an image from image features in two other images and the epipolar geometry between the three images. We adopt the most general camera model of perpective projection and show that a point can be predicted in the third image as a bilinear function of its images in the first two cameras, that the tangents to three corresponding curves are related by a trilinear function, and that the curvature of a curve in the third image is a linear function of the curvatures at the corresponding points in the other two images. We thus answer completely the following question: given two views of an object, what would a third view look like? We show that in the special case of orthographic projection our results for points reduce to those of Unman and Basri [19]. We demonstrate on synthetic as well as on real data the applicability of our theory.