Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Atomic Decomposition by Basis Pursuit
SIAM Journal on Scientific Computing
The Problem of Degeneracy in Structure and Motion Recovery from Uncalibrated Image Sequences
International Journal of Computer Vision - 1998 Marr Prize
Multibody Structure and Motion: 3-D Reconstruction of Independently Moving Objects
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part I
A multi-body factorization method for motion analysis
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
The least-squares error for structure from infinitesimal motion
International Journal of Computer Vision
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
Articulated Structure from Motion by Factorization
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Random Walks for Image Segmentation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Three-View Multibody Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
A Model-Selection Framework for Multibody Structure-and-Motion of Image Sequences
International Journal of Computer Vision
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
Sparse reconstruction by separable approximation
IEEE Transactions on Signal Processing
An iterative multiresolution scheme for SFM with missing data: Single and multiple object scenes
Image and Vision Computing
Multibody Structure-from-Motion in Practice
IEEE Transactions on Pattern Analysis and Machine Intelligence
Enhanced Local Subspace Affinity for feature-based motion segmentation
Pattern Recognition
Motion segmentation with missing data using power factorization and GPCA
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Simultaneous motion segmentation and Structure from Motion
WACV '11 Proceedings of the 2011 IEEE Workshop on Applications of Computer Vision (WACV)
Adaptive motion segmentation algorithm based on the principal angles configuration
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Bilinear Modeling via Augmented Lagrange Multipliers (BALM)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Low-Rank Matrix Approximation with Weights or Missing Data Is NP-Hard
SIAM Journal on Matrix Analysis and Applications
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We present a novel optimisation framework for the estimation of the multi-body motion segmentation and 3D reconstruction of a set of point trajectories in the presence of missing data. The proposed solution not only assigns the trajectories to the correct motion but it also solves for the 3D location of multi-body shape and it fills the missing entries in the measurement matrix. Such a solution is based on two fundamental principles: each of the multi-body motions is controlled by a set of metric constraints that are given by the specific camera model, and the shape matrix that describes the multi-body 3D shape is generally sparse. We jointly include such constraints in a unique optimisation framework which, starting from an initial segmentation, iteratively enforces these set of constraints in three stages. First, metric constraints are used to estimate the 3D metric shape and to fill the missing entries according to an orthographic camera model. Then, wrongly segmented trajectories are detected by using sparse optimisation of the shape matrix. A final reclassification strategy assigns the detected points to the right motion or discards them as outliers. We provide experiments that show consistent improvements to previous approaches both on synthetic and real data.