Practical algorithms for stratified structure-from-motion

• Published in: Image and vision computing Vol. 20; no. 2; pp. 103 - 123
• Main Authors: Chen, George Q., Medioni, Gérard G.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.02.2002
• Subjects: Image-based-rendering and modeling; Matrix factorization; Self-calibration; Stratification; Structure-from-motion; Image-based-rendering and modeling; Self-calibration; Matrix factorization; Structure-from-motion; Stratification
• ISSN: 0262-8856; 1872-8138
• DOI: 10.1016/S0262-8856(01)00090-7

We present a set of multi-view structure-from-motion algorithms adapting the stratification paradigm, that is, projective reconstruction from correspondences only, followed by Euclidean upgrade using the zero-skew constraint. At each stratum, two algorithms are presented: one for initialization, one for the actual reconstruction. The latter is iterative in nature, thus requires good initial guesses. On the other hand, both initialization algorithms are actually independent algorithms—in noise-free cases they produce true reconstruction rather than an approximation. We formulate projective reconstruction as a bundle adjustment problem. But instead of using optimization techniques, we solve it as a serious of iterative eigen problems. Euclidean upgrade is obtained by estimating the projective distortion matrix. Self-calibration is a by-product, obtained in a subsequent step. Additionally, using our formulation, a closed-form solution is found. This approach departs from most existing ones which are based on the invariance property of the absolute quadric (or conic) under rigid motion. However, relationship between these two types of methods can be established. Experimental results on both synthetic and real data are presented. Potential applications are also demonstrated.