Structure and Motion from Points, Lines and Conics with Affine Cameras

Abstract

In this paper we present an integrated approach that solves the structure and motion problem for affine cameras. Given images of corresponding points, lines and conics in any number of views, a reconstruction of the scene structure and the camera motion is calculated, up to an affine transformation. Starting with three views, two novel concepts are introduced. The first one is a quasi-tensor consisting of 20 components and the second one is another quasitensor consisting of 12 components. These tensors describe the viewing geometry for three views taken by an affine camera. It is shown how correspondences of points, lines and conics can be used to constrain the tensor components. A set of affine camera matrices compatible with the quasi-tensors can easily be calculated from the tensor components. The resulting camera matrices serve as an initial guess in a factorisation method, using points, lines and conics concurrently, generalizing the well-known factorisation method by Tomasi-Kanade. Finally, examples are given that illustrate the developed methods on both simulated and real data.