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
Structure from Motion Causally Integrated Over Time
IEEE Transactions on Pattern Analysis and Machine Intelligence
Detecting and Tracking Multiple Moving Objects Using Temporal Integration
ECCV '92 Proceedings of the Second European Conference on 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
Smoothness in Layers: Motion segmentation using nonparametric mixture estimation.
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
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 Robust Subspace Approach to Layer Extraction
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
ICCV '95 Proceedings of the Fifth International Conference on Computer Vision
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
Motion Segmentation and Tracking Using Normalized Cuts
ICCV '98 Proceedings of the Sixth 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
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
Generalized principal component analysis (GPCA)
CVPR'03 Proceedings of the 2003 IEEE computer society conference on Computer vision and pattern recognition
ISVC '08 Proceedings of the 4th International Symposium on Advances in Visual Computing, Part II
Robust Algebraic Segmentation of Mixed Rigid-Body and Planar Motions from Two Views
International Journal of Computer Vision
Learning spatio-temporal dependency of local patches for complex motion segmentation
Computer Vision and Image Understanding
Rank Estimation in Missing Data Matrix Problems
Journal of Mathematical Imaging and Vision
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In this paper, we present an analytic solution to the problem of estimating an unknown number of 2-D and 3-D motion models from two-view point correspondences or optical flow. The key to our approach is to view the estimation of multiple motion models as the estimation of a single multibody motion model. This is possible thanks to two important algebraic facts. First, we show that all the image measurements, regardless of their associated motion model, can be fit with a single real or complexpolynomial. Second, we show that the parameters of the individual motion model associated with an image measurement can be obtained from the derivatives of the polynomial at that measurement. This leads to an algebraic motion segmentation and estimation algorithm that applies to most of the two-view motion models that have been adopted in computer vision. Our experiments show that the proposed algorithm out-performs existing algebraic and factorization-based methods in terms of efficiency and robustness, and provides a good initialization for iterative techniques, such as Expectation Maximization, whose performance strongly depends on good initialization.