Optimal Estimation of Vanishing Points in a Manhattan World

In this paper, we present an analytical method for computing the globally optimal estimates of orthogonal vanishing points in a “Manhattan world” with a calibrated camera. We formulate this problem as constrained least-squares whose optimality conditions form a multivariate polynomial system. We solve this system analytically to compute all the critical points of the least-squares cost, and hence the global minimum, i.e., the globally optimal estimate for the orthogonal vanishing points. The same optimal estimator is used in conjunction with RANSAC to generate orthogonalvanishing-point hypotheses (from triplets of lines) and thus classify lines into parallel and mutually orthogonal groups. The proposed method is validated experimentally on the York Urban Database.

• Type: Journal
• Year: 2011
• Where: ICCV
• Authors: Faraz Mirzaei, Stergios Roumeliotis
• Keywords: Computer Vision, ICCV 2011, Multivariate Polynomial, Optimality Conditions, Polynomial System