Relations between bundle-adjustment and epipolar-geometry-based approaches, and their applications to efficient structure from motion

Abstract

3D reconstruction from image correspondences has been studied in the two respects: one is the unifying framework, often called structure from motion, where motion and structure are estimated simultaneously, and the other is the decoupling framework, often called motion estimation, where motion is estimated separately from structure. The two approaches have both some advantages and disadvantages at the same time. So, in this paper, we first show the relations between structure from motion using bundle-adjustment, a representative approach in the unifying framework, and motion estimation using epipolar geometry, that in the decoupling framework. Based on the results we also present a computationally efficient algorithm solving the bundle-adjustment-based structure from motion problem, where motion and structure are estimated separately. Our research has some significance in the two respects. First, although some researchers have found the relations between the optimization criteria used in epipolar-geometry-based approaches, the results have rarely extended to those in other approaches, e.g. bundle-adjustment approach. Second, our proposed algorithm can take the advantages of the unifying and the decoupling frameworks, e.g., benefit of a low-dimensional search space and prevention of performance degradation in the decoupling framework.