Uncertainty Modeling for Optimal Structure from Motion

The parameters estimated by Structure from Motion SFM contain inherent indeterminacies which we call gauge freedoms. Under a perspective camera, shape and motion parameters are only recovered up to an unknown similarity transformation. In this paper we investigate how covariance-based uncertainty can be represented under these gauge freedoms. Past work on uncertainty modeling has implicitly imposed gauge constraints on the solution before considering covariance estimation. Here we examine the e ect of selecting a particular gauge on the uncertainty of parameters. We show potentially dramatic e ects of gauge choice on parameter uncertainties. However the inherent geometric uncertainty remains the same irrespective of gauge choice. We derive a Geometric Equivalence Relationship with which covariances under different parametrizations and gauges can be compared, based on their true geometric uncertainty. We show that the uncertainty of gauge invariants exactly captures the geometric unce...

• Type: Conference
• Year: 1999
• Where: ICCVW
• Authors: Daniel D. Morris, Ken-ichi Kanatani, Takeo Kanade
• Keywords: Computer Vision, Gauge Freedoms, Geometric Equivalence Relationship, Geometric Uncertainty, ICCVW 1999