Refining 3D reconstruction: a theoretical and experimental study of the effect of cross-correlations
CVGIP: Image Understanding
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape Ambiguities in Structure From Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Affine Structure from Line Correspondences With Uncalibrated Affine Cameras
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric Information Criterion for Model Selection
International Journal of Computer Vision
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
Euclidean Reconstruction from Uncalibrated Views
Proceedings of the Second Joint European - US Workshop on Applications of Invariance in Computer Vision
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Quasi-Dense Reconstruction from Image Sequence
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Gauge Independence in Optimization Algorithms for 3D Vision
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
Journal of Signal Processing Systems
Geometrical fitting of missing data for shape from motion under noise distribution
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Uncertainty analysis using geometrical property between 2d-to-3d under affine projection
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
A novel recovery algorithm of incomplete observation matrix for converting 2-d video to 3-d content
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
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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 effect of selecting a particular gauge on the uncertainty of parameters. We show potentially dramatic effects 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 uncertainty of the solution, and hence provides useful measures for evaluating the uncertainty of the solution. Finally we propose a fast method for covariance estimation and show its correctness using the Geometric Equivalence Relationship.