Structure and Motion from Points, Lines and Conics with Affine Cameras 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 quasitensor 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 quasitensors 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 wellknown factorisation method by TomasiKanade (1992). Finally, examples are given that illustrate the developed methods on both simulated and real data

Variable elimination for 3D from 2D Accurately reconstructing the 3D geometry of a scene or object observed on 2D images is a difficult problem: there are many unknowns involved (camera pose, scene structure, depth factors) and solving for all these unknowns simultaneously is computationally intensive and suffers from numerical instability. In this paper, we algebraically decouple some of the unknowns so that they can be solved for independently. Decoupling the pose from the other variables has been previously discussed in the literature. Unfortunately, pose estimation is an illconditioned problem. In this paper, we algebraically eliminate all the camera pose parameters (i.e., position and orientation) from the structurefrommotion equations for an internally calibrated camera. We then also fully eliminate the structure coordinates from the equations. This yields a very simple set of homogeneous polynomial equations of low degree involving only the depths of the observed points. When considering a small number of tracked points and pictures (e.g., five points on two pictures), these equations can be solved using the sparse resultant method.