Rigidity Checking of 3D Point Correspondences Under Perspective Projection

An algorithm is described which rapidly verifies the potential rigidity of three dimensional point correspondences from a pair of two dimensional views under perspective projection. The output of the algorithm is a simple yes or no answer to the question "Could these corresponding points from two views be the projection of a rigid configuration?" Potential applications include 3D object recognition from a single previous view and correspondence matching for stereo or motion over widely separated views. Our analysis begins with the observation that it is often the case that two views cannot provide an accurate structure-from-motion estimate because of ambiguity and ill- conditioning. However, it is argued that an accurate yes/no answer to the rigidity question is possible and experimental results support this assertion with as few as six pairs of corresponding points over a wide range of scene structures and viewing geometries. Rigidity checking verifies point correspondences by using 3D recovery equations as a matching condition. The proposed algorithm improves upon other methods that fall under this approach because it works with as few as six corresponding points under full perspective projection, handles correspondences from widely separated views, makes full use of the disparity of the correspondences, and is integrated with a linear algorithm for 3D recovery due to Kontsevich. The rigidity decision is based on the residual error of an integrated pair of linear and nonlinear structure-from-motion estimators. Results are given for experiments with synthetic and real image data. A complete implementation of this algorithm is being made publicly available.