Trajectory Triangulation: 3D Reconstruction of Moving Points from a Monocular Image Sequence
IEEE Transactions on Pattern Analysis and Machine Intelligence
An Integrated Bayesian Approach to Layer Extraction from Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
Optimization Criteria and Geometric Algorithms for Motion and Structure Estimation
International Journal of Computer Vision
Structure and Motion for Dynamic Scenes - The Case of Points Moving in Planes
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part II
Evaluation and Selection of Models for Motion Segmentation
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part III
Scene Segmentation from 3D Motion
CVPR '98 Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition
Segmentation of Dynamic Scenes from Image Intensities
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
A multi-body factorization method for motion analysis
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
An Invitation to 3-D Vision: From Images to Geometric Models
An Invitation to 3-D Vision: From Images to Geometric Models
Generalized Principal Component Analysis (GPCA)
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
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
Form representions and means for landmarks: a survey and comparative study
Computer Vision and Image Understanding
A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation
Journal of Mathematical Imaging and Vision
International Journal of Robotics Research
International Journal of Robotics Research
Consistency of robust estimators in multi-structural visual data segmentation
Pattern Recognition
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
International Journal of Computer Vision
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Conditions for Segmentation of 2D Translations of 3D Objects
ICIAP '09 Proceedings of the 15th International Conference on Image Analysis and Processing
Detection of object motion regions in aerial image pairs with a multilayer Markovian model
IEEE Transactions on Image Processing
Conditions for Segmentation of Motion with Affine Fundamental Matrix
ISVC '09 Proceedings of the 5th International Symposium on Advances in Visual Computing: Part I
Journal of Mathematical Imaging and Vision
Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views
International Journal of Computer Vision
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
Realtime motion segmentation based multibody visual SLAM
Proceedings of the Seventh Indian Conference on Computer Vision, Graphics and Image Processing
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
3D dense reconstruction from 2D video sequence via 3D geometric segmentation
Journal of Visual Communication and Image Representation
SAMT'10 Proceedings of the 5th international conference on Semantic and digital media technologies
Multi-body segmentation and motion number estimation via over-segmentation detection
ACCV'10 Proceedings of the 2010 international conference on Computer vision - Volume part II
Multi-way clustering using super-symmetric non-negative tensor factorization
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
View synthesis of scenes with multiple independently translating objects from uncalibrated views
ACCV'06 Proceedings of the 7th Asian conference on Computer Vision - Volume Part I
Nonrigid shape and motion from multiple perspective views
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Bifocal matching using multiple geometrical solutions
PSIVT'11 Proceedings of the 5th Pacific Rim conference on Advances in Image and Video Technology - Volume Part II
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We present an algebraic geometric approach to 3-D motion estimation and segmentation of multiple rigid-body motions from noise-free point correspondences in two perspective views. Our approach exploits the algebraic and geometric properties of the so-called multibody epipolar constraint and its associated multibody fundamental matrix, which are natural generalizations of the epipolar constraint and of the fundamental matrix to multiple motions. We derive a rank constraint on a polynomial embedding of the correspondences, from which one can estimate the number of independent motions as well as linearly solve for the multibody fundamental matrix. We then show how to compute the epipolar lines from the first-order derivatives of the multibody epipolar constraint and the epipoles by solving a plane clustering problem using Generalized PCA (GPCA). Given the epipoles and epipolar lines, the estimation of individual fundamental matrices becomes a linear problem. The clustering of the feature points is then automatically obtained from either the epipoles and epipolar lines or from the individual fundamental matrices. Although our approach is mostly designed for noise-free correspondences, we also test its performance on synthetic and real data with moderate levels of noise.