Conics-based stereo, motion estimation, and pose determination

Abstract

Stereo vision, motion and structure parameter estimation, and pose determination are three important problems in 3-D computer vision. The first step in all of these problems is to choose and to extract primitives and their features in images. In most of the previous work, people usually use edge points or straight line segments as primitives and their local properties as features. Few methods have been presented in the literature using more compact primitives and their global features. This article presents an approach using conics as primitives. For stereo vision, a closed-form solution is provided for both establishing the correspondence of conics in images and the reconstruction of conics in space. With this method, the correspondence is uniquely determined and the reconstruction is global. It is shown that the method can be extended for higher degree (degree≥3) planar curves.For motion and structure parameter estimation, it is shown that, in general, two sequential images of at least three conics are needed in order to determine the camera motion. A complicated nonlinear system must be solved in this case. In particular, if we are given two images of a pair of coplanar conics, a closed-form solution of camera motion is presented. In a CAD-based vision system, the object models are available, and this makes it possible to recognize 3-D objects and to determine their poses from a single image.For pose determination, it is shown that if there exist two conics on the surface of an object, the object's pose can be determined by an efficient one-dimensional search. In particular, if two conics are coplanar, a closed-form solution of the object's pose is presented.