Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Mixtures of probabilistic principal component analyzers
Neural Computation
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
Evaluation and Selection of Models for Motion Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
A multi-body factorization method for motion analysis
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Segmentation Using Eigenvectors: A Unifying View
ICCV '99 Proceedings of the International Conference on Computer Vision-Volume 2 - Volume 2
Two-View Multibody Structure from Motion
International Journal of Computer Vision
Clustering appearances of objects under varying illumination conditions
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Generalized principal component analysis (GPCA)
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Closed-Form Solution to Non-Rigid Shape and Motion Recovery
International Journal of Computer Vision
Two-View Multibody Structure from Motion
International Journal of Computer Vision
Wide Baseline Matching between Unsynchronized Video Sequences
International Journal of Computer Vision
A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation
Journal of Mathematical Imaging and Vision
Journal of Mathematical Imaging and Vision
Incorporating non-motion cues into 3D motion segmentation
Computer Vision and Image Understanding
Rotation constrained power factorization for structure from motion of nonrigid objects
Pattern Recognition Letters
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
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Extraction and temporal segmentation of multiple motion trajectories in human motion
Image and Vision Computing
Motion Segmentation from Feature Trajectories with Missing Data
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
Segmentation of Rigid Motion from Non-rigid 2D Trajectories
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part I
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
Robust Factorization Methods Using a Gaussian/Uniform Mixture Model
International Journal of Computer Vision
Proceedings of the 2008 conference on Artificial Intelligence Research and Development: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence
International Journal of Computer Vision
Non-rigid metric reconstruction from perspective cameras
Image and Vision Computing
Video segmentation based on motion coherence of particles in a video sequence
IEEE Transactions on Image Processing
Enhanced Local Subspace Affinity for feature-based motion segmentation
Pattern Recognition
Visibility subspaces: uncalibrated photometric stereo with shadows
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Motion segmentation using the hadamard product and spectral clustering
WMVC'09 Proceedings of the 2009 international conference on Motion and video computing
Rank Estimation in Missing Data Matrix Problems
Journal of Mathematical Imaging and Vision
Adaptive motion segmentation algorithm based on the principal angles configuration
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
The space of multibody fundamental matrices: rank, geometry and projection
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Articulated motion segmentation using RANSAC with priors
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Trajectory Analysis and Semantic Region Modeling Using Nonparametric Hierarchical Bayesian Models
International Journal of Computer Vision
Perspective n-view multibody structure-and-motion through model selection
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part I
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Recovering articulated non-rigid shapes, motions and kinematic chains from video
AMDO'06 Proceedings of the 4th international conference on Articulated Motion and Deformable Objects
Non-rigid face modelling using shape priors
AMFG'05 Proceedings of the Second international conference on Analysis and Modelling of Faces and Gestures
Incorporating non-motion cues into 3d motion segmentation
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part III
3D motion segmentation using intensity trajectory
ACCV'09 Proceedings of the 9th Asian conference on Computer Vision - Volume Part I
Application dependency discovery using matrix factorization
Proceedings of the 2012 IEEE 20th International Workshop on Quality of Service
Deformation weight constraint and 3D reconstruction of nonrigid objects
ICIAR'07 Proceedings of the 4th international conference on Image Analysis and Recognition
Multi-scale clustering of frame-to-frame correspondences for motion segmentation
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
SuperFloxels: a mid-level representation for video sequences
ECCV'12 Proceedings of the 12th international conference on Computer Vision - Volume Part III
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
Finding multiple global linear correlations in sparse and noisy data sets
Knowledge-Based Systems
Hybrid structure for robust dimensionality reduction
Neurocomputing
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We consider the problem of segmenting multiple rigid motions from point correspondences in multiple affine views. We cast this problem as a subspace clustering problem in which the motion of each object lives in a subspace of dimension two, three or four. Unlike previous work, we do not restrict the motion subspaces to be four-dimensional or linearly independent. Instead, our approach deals gracefully with all the spectrum of possible affine motions: from twodimensional and partially dependent to four-dimensional and fully independent. In addition, our method handles the case of missing data, meaning that point tracks do not have to be visible in all images. Our approach involves projecting the point trajectories of all the points into a 5- dimensional space, using the PowerFactorization method to fill in missing data. Then multiple linear subspaces representing independent motions are fitted to the points in R5using GPCA. We test our algorithm on various real sequences with degenerate and nondegenerate motions, missing data, perspective effects, transparent motions, etc. Our algorithm achieves a misclassification error of less than 5% for sequences with up to 30% of missing data points.