Shape and motion from image streams under orthography: a factorization method
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Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Two-View Multibody Structure from Motion
International Journal of Computer Vision
Motion segmentation with missing data using power factorization and GPCA
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Quasi-perspective structure factorization with missing data
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Successively alternate least square for low-rank matrix factorization with bounded missing data
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Enhanced Local Subspace Affinity for feature-based motion segmentation
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Rank Estimation in Missing Data Matrix Problems
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Sparse motion segmentation using multiple six-point consistencies
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume Part I
PCA document reconstruction for email classification
Computational Statistics & Data Analysis
Energy-Based Geometric Multi-model Fitting
International Journal of Computer Vision
A continuous max-flow approach to minimal partitions with label cost prior
SSVM'11 Proceedings of the Third international conference on Scale Space and Variational Methods in Computer Vision
Hybrid Linear Modeling via Local Best-Fit Flats
International Journal of Computer Vision
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
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We consider the problem of segmenting multiple rigid-body motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which point trajectories associated with each motion live in a linear subspace of dimension two, three or four. Our algorithm involves projecting all point trajectories onto a 5-dimensional subspace using the SVD, the PowerFactorization method, or RANSAC, and fitting multiple linear subspaces representing different rigid-body motions to the points in 驴5 using GPCA. Unlike previous work, our approach does not restrict the motion subspaces to be four-dimensional and independent. Instead, it deals gracefully with all the spectrum of possible affine motions: from two-dimensional and partially dependent to four-dimensional and fully independent. Our algorithm can handle the case of missing data, meaning that point tracks do not have to be visible in all images, by using the PowerFactorization method to project the data. In addition, our method can handle outlying trajectories by using RANSAC to perform the projection. We compare our approach to other methods on a database of 167 motion sequences with full motions, independent motions, degenerate motions, partially dependent motions, missing data, outliers, etc. On motion sequences with complete data our method achieves a misclassification error of less that 5% for two motions and 29% for three motions.