Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Linear fitting with missing data for structure-from-motion
Computer Vision and Image Understanding
Statistical Optimization for Geometric Computation: Theory and Practice
Statistical Optimization for Geometric Computation: Theory and Practice
Incremental Singular Value Decomposition of Uncertain Data with Missing Values
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Damped Newton Algorithms for Matrix Factorization with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Recovering the missing components in a large noisy low-rank matrix: application to SFM
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Computing a 1-dimensional linear subspace is an important problem in many computer vision algorithms. Its importance stems from the fact that maximizing a linear homogeneous equation system can be interpreted as subspace fitting problem. It is trivial to compute the solution if all coefficients of the equation system are known, yet for the case of incomplete data, only approximation methods based on variations of gradient descent have been developed. In this work, an algorithm is presented in which the data is embedded in projective spaces. We prove that the intersection of these projective spaces is identical to the desired subspace. Whereas other algorithms approximate this subspace iteratively, computing the intersection of projective spaces defines a linear problem. This solution is therefore not an approximation but exact in the absence of noise. We derive an upper boundary on the number of missing entries the algorithm can handle. Experiments with synthetic data confirm that the proposed algorithm successfully fits subspaces to data even ifmore than 90% of the data is missing. We demonstrate an example application with real image sequences.