Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Mixtures of probabilistic principal component analyzers
Neural Computation
A new approach to dimensionality reduction: theory and algorithms
SIAM Journal on Applied Mathematics
An Integrated Bayesian Approach to Layer Extraction from Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Two-View Multibody Structure from Motion
International Journal of Computer Vision
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
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
Two-View Multibody Structure from Motion
International Journal of Computer Vision
Combined central and subspace clustering for computer vision applications
ICML '06 Proceedings of the 23rd international conference on Machine learning
A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation
Journal of Mathematical Imaging and Vision
Binet-Cauchy Kernels on Dynamical Systems and its Application to the Analysis of Dynamic Scenes
International Journal of Computer Vision
Scale adaptive visual attention detection by subspace analysis
Proceedings of the 15th international conference on Multimedia
Representing Images Using Nonorthogonal Haar-Like Bases
IEEE Transactions on Pattern Analysis and Machine Intelligence
Motion segmentation using GPCA techniques and optical flow
EATIS '07 Proceedings of the 2007 Euro American conference on Telematics and information systems
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
3D Perception and Environment Map Generation for Humanoid Robot Navigation
International Journal of Robotics Research
Translated Poisson Mixture Model for Stratification Learning
International Journal of Computer Vision
An Efficient K-Hyperplane Clustering Algorithm and Its Application to Sparse Component Analysis
ISNN '07 Proceedings of the 4th international symposium on Neural Networks: Part II--Advances in Neural Networks
Algebraic Identification of MIMO SARX Models
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Robust Multiple Structures Estimation with J-Linkage
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Spectral Curvature Clustering (SCC)
International Journal of Computer Vision
Patch-based video processing: a variational Bayesian approach
IEEE Transactions on Circuits and Systems for Video Technology
Analysis of multiple orientations
IEEE Transactions on Image Processing
Outliers in biometrical data: What's old, What's new
International Journal of Biometrics
Double sparsity: learning sparse dictionaries for sparse signal approximation
IEEE Transactions on Signal Processing
Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views
International Journal of Computer Vision
Image correspondence from motion subspace constraint and epipolar constraint
ACCV'07 Proceedings of the 8th Asian conference on Computer vision - Volume Part II
A prediction error compression method with tensor-PCA in video coding
MCAM'07 Proceedings of the 2007 international conference on Multimedia content analysis and mining
Video segmentation based on motion coherence of particles in a video sequence
IEEE Transactions on Image Processing
Computers in Biology and Medicine
PRICAI'10 Proceedings of the 11th Pacific Rim international conference on Trends in artificial intelligence
Fuzzy hyper-prototype clustering
KES'10 Proceedings of the 14th international conference on Knowledge-based and intelligent information and engineering systems: Part I
CC-RANSAC: Fitting planes in the presence of multiple surfaces in range data
Pattern Recognition Letters
Segmenting dynamic textures with ising descriptors, ARX models and level sets
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Non-manifold surface reconstruction from high-dimensional point cloud data
Computational Geometry: Theory and Applications
A novel probabilistic linear subspace approach for face applications
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
Local homology transfer and stratification learning
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Algebraic geometric comparison of probability distributions
The Journal of Machine Learning Research
A general framework for subspace detection in unordered multidimensional data
Pattern Recognition
Local and structural consistency for multi-manifold clustering
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Hybrid Linear Modeling via Local Best-Fit Flats
International Journal of Computer Vision
Dictionary based sparse representation for domain adaptation
Proceedings of the 21st ACM international conference on Information and knowledge management
Auto-grouped sparse representation for visual analysis
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Coherent filtering: detecting coherent motions from crowd clutters
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Robust and efficient subspace segmentation via least squares regression
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VII
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
A data driven approach for algebraic loop invariants
ESOP'13 Proceedings of the 22nd European conference on Programming Languages and Systems
Maximal cliques based rigid body motion segmentation with a RGB-D camera
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part II
Motion segmentation by velocity clustering with estimation of subspace dimension
ACCV'12 Proceedings of the 11th international conference on Computer Vision - Volume 2
Learning a subspace for clustering via pattern shrinking
Information Processing and Management: an International Journal
Editor's Choice Article: Motion-based segmentation of objects using overlapping temporal windows
Image and Vision Computing
A multi-manifold semi-supervised Gaussian mixture model for pattern classification
Pattern Recognition Letters
Greedy feature selection for subspace clustering
The Journal of Machine Learning Research
Hi-index | 0.15 |
This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high-dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.