Rigidity checking of 3D point correspondences under perspective projection

Abstract

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. Rigidity checking verifies point correspondences by using 3 0 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. Results are given for experiments with synthetic and real image data. A complete implementation of this algorithm is being made publicly available. 945 0-8186-7042-8195 $4.00 0 1995 IEEE

Structure from Recurrent Motion: From Rigidity to Recurrency

“…The latter condition (i.e., excluding homography) is to ensure 3D reconstruction is possible. Our algorithm is inspired by an early work of McReynolds and Lowe for the same task of rigidity-checking [27], however ours is much simpler-without involving complicated parameter tuning and non-linear refinement. Rigidity-checking was also applied for solving multi-view geometry problems without via camera motion [23].…”

Multi-view correspondence by enforcement of rigidity constraints

“…Earlier approaches exploiting rigidity have been made: in [15] an algorithm is devised that checks if corresponding points from two images could be the projection of a rigid scene (no correspondence calculation is made), while in [10] it is used for object detection. In [13] the authors use a cost function based on the determinant of the measurement matrix to match features in a pair of images.…”