Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Affine analysis of image sequences
Affine analysis of image sequences
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recovery of Ego-Motion Using Region Alignment
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multi-Frame Structure-from-Motion Algorithm under Perspective Projection
International Journal of Computer Vision - Special issue on computer vision research at NEC Research Institute
Real-time motion analysis with linear programming
Computer Vision and Image Understanding - Special issue on robusst statistical techniques in image understanding
Heteroscedastic Regression in Computer Vision: Problems with Bilinear Constraint
International Journal of Computer Vision - Special issue on a special section on visual surveillance
Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Fast and Accurate Algorithms for Projective Multi-Image Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Multi-Frame Correspondence Estimation Using Subspace Constraints
International Journal of Computer Vision
Parallax Geometry of Pairs of Points for 3D Scene Analysis
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume I - Volume I
From Reference Frames to Reference Planes: Multi-View Parallax Geometry and Applications
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
Duality, Rigidity and Planar Parallax
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume II - Volume II
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 Factorization Method for Affine Structure from Line Correspondences
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Multi-body Factorization with Uncertainty: Revisiting Motion Consistency
International Journal of Computer Vision
Weighted and robust learning of subspace representations
Pattern Recognition
Journal of Mathematical Imaging and Vision
Clustering and Embedding Using Commute Times
IEEE Transactions on Pattern Analysis and Machine Intelligence
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Robust Factorization Methods Using a Gaussian/Uniform Mixture Model
International Journal of Computer Vision
Linear Quasi-Parallax SfM Using Laterally-Placed Eyes
International Journal of Computer Vision
An experimental evaluation of a Monte-Carlo algorithm for singular value decomposition
PCI'01 Proceedings of the 8th Panhellenic conference on Informatics
Rigid Structure from Motion from a Blind Source Separation Perspective
International Journal of Computer Vision
Robust object tracking based on uncertainty factorization subspace constraints optical flow
CIS'05 Proceedings of the 2005 international conference on Computational Intelligence and Security - Volume Part II
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Factorization using Singular Value Decomposition (SVD) is often used for recovering 3D shape and motion from feature correspondences across multiple views. SVD is powerful at finding the global solution to the associated least-square-error minimization problem. However, this is the correct error to minimize only when the x and y positional errors in the features are uncorrelated and identically distributed. But this is rarely the case in real data. Uncertainty in feature position depends on the underlying spatial intensity structure in the image, which has strong directionality to it. Hence, the proper measure to minimize is covariance-weighted squared-error (or the Mahalanobis distance). In this paper, we describe a new approach to covariance-weighted factorization, which can factor noisy feature correspondences with high degree of directional uncertainty into structure and motion. Our approach is based on transforming the raw-data into a covariance-weighted data space, where the components of noise in the different directions are uncorrelated and identically distributed. Applying SVD to the transformed data now minimizes a meaningful objective function in this new data space. This is followed by a linear but suboptimal second step to recover the shape and motion in the original data space. We empirically show that our algorithm gives very good results for varying degrees of directional uncertainty. In particular, we show that unlike other SVD-based factorization algorithms, our method does not degrade with increase in directionality of uncertainty, even in the extreme when only normal-flow data is available. It thus provides a unified approach for treating corner-like points together with points along linear structures in the image.