The algebraic eigenvalue problem
The algebraic eigenvalue problem
Motion and Structure From Two Perspective Views: Algorithms, Error Analysis, and Error Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Geometric invariance in computer vision
Geometric invariance in computer vision
Self-calibration of an affine camera from multiple views
International Journal of Computer Vision
A Paraperspective Factorization Method for Shape and Motion Recovery
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
A Sequential Factorization Method for Recovering Shape and Motion From Image Streams
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Linear and Incremental Acquisition of Invariant Shape Models From Image Sequences
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
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
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This paper is focused on error characterization of the factorization approach to shape and motion recovery from image sequence using results from matrix perturbation theory and covariance propagation for linear models. Given the 2-D projections of a set of points across multiple image frames and small perturbation on image coordinates, first order perturbation and covariance matrices for 3-D affine/Euclidean shape and motion are derived and validated with the ground truth. The propagation of the small perturbation and covariance matrix provides better understanding of the factorization approach and its results, provides error sensitivity information for 3-D affine/Euclidean shape and motion subject to small image error. Experimental results are demonstrated to support the analysis and show how the error analysis and error measures can be used.