Nonlinear component analysis as a kernel eigenvalue problem
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A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Mixtures of probabilistic principal component analyzers
Neural Computation
Segmentation of Dynamic Scenes from Image Intensities
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
Generalized principal component analysis (gpca): an algebraic geometric approach to subspace clustering and motion segmentation
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
Robust subspace analysis for detecting visual attention regions in images
Proceedings of the 13th annual ACM international conference on Multimedia
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two-View Multibody Structure from Motion
International Journal of Computer Vision
A unifying geometric representation for central projection systems
Computer Vision and Image Understanding - Special issue on omnidirectional vision and camera networks
A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation
Journal of Mathematical Imaging and Vision
Detection of visual attention regions in images using robust subspace analysis
Journal of Visual Communication and Image Representation
Dichromatic illumination estimation without pre-segmentation
Pattern Recognition Letters
Using subspace analysis for event detection from web click-through data
Proceedings of the 17th international conference on World Wide Web
International Journal of Remote Sensing
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
Seeing the Objects Behind the Dots: Recognition in Videos from a Moving Camera
International Journal of Computer Vision
ECML PKDD '09 Proceedings of the European Conference on Machine Learning and Knowledge Discovery in Databases: Part II
Analysis of multiple orientations
IEEE Transactions on Image Processing
Bayesian approaches to motion-based image and video segmentation
IWCM'04 Proceedings of the 1st international conference on Complex motion
3D motion segmentation from straight-line optical flow
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Robust height estimation of moving objects from uncalibrated videos
IEEE Transactions on Image Processing
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
Minimum effective dimension for mixtures of subspaces: a robust GPCA algorithm and its applications
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Inference of multiple subspaces from high-dimensional data and application to multibody grouping
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
Nonparametric estimation of multiple structures with outliers
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
Spatial segmentation of temporal texture using mixture linear models
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Subspace estimation using projection based m-estimators over grassmann manifolds
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
An approach to the compression of residual data with GPCA in video coding
PCM'06 Proceedings of the 7th Pacific Rim conference on Advances in Multimedia Information Processing
Background subtraction using low rank and group sparsity constraints
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Robust integrated locally linear embedding
CCBR'12 Proceedings of the 7th Chinese conference on Biometric Recognition
Location-Aware Caching for Semantic-Based Image Queries in Mobile AD HOC Networks
International Journal of Multimedia Data Engineering & Management
Finding multiple global linear correlations in sparse and noisy data sets
Knowledge-Based Systems
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We propose an algebraic geometric approach to the problem of estimating a mixture of linear subspaces from sample data points, the so-called Generalized Principal Component Analysis (GPCA) problem. In the absence of noise, we show that GPCA is equivalent to factoring a homogeneous polynomial whose degree is the number of subspaces and whose factors (roots) represent normal vectors to each subspace. We derive a formula for the number of subspaces n and provide an analytic solution to the factorization problem using linear algebraic techniques. The solution is closed form if and only if n ≤ 4. In the presence of noise, we cast GPCA as a constrained nonlinear least squares problem and derive an optimal function from which the subspaces can be directly recovered using standard nonlinear optimization techniques. We apply GPCA to the motion segmentation problem in computer vision, i.e. the problem of estimating a mixture of motion models from 2-D imagery.