Recognition by Linear Combinations of Models
IEEE Transactions on Pattern Analysis and Machine Intelligence - Special issue on interpretation of 3-D scenes—part I
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
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
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
Exact Matrix Completion via Convex Optimization
Foundations of Computational Mathematics
A Singular Value Thresholding Algorithm for Matrix Completion
SIAM Journal on Optimization
Multiview Stereo and Silhouette Consistency via Convex Functionals over Convex Domains
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Many challenging computer vision problems can be formulated as a multilinear model. Classical methods like principal component analysis use singular value decomposition to infer model parameters. Although it can solve a given problem easily if all measurements are known this prerequisite is usually violated for computer vision applications. In the current work, a standard tool to estimate singular vectors under incomplete data is reformulated as an energy minimization problem. This admits for a simple and fast gradient descent optimization with guaranteed convergence. Furthermore, the energy function is generalized by introducing an L2-regularization on the parameter space. We show a quantitative and qualitative evaluation of the proposed approach on an application from structure-from-motion using synthetic and real image data, and compare it with other works.