Estimating the Kinematics and Structure of a Rigid Object from a Sequence of Monocular Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Shape and motion from image streams: a factorization method
Shape and motion from image streams: a factorization method
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Sequential Factorization Method for Recovering Shape and Motion From Image Streams
IEEE Transactions on Pattern Analysis and Machine Intelligence
Efficient Region Tracking With Parametric Models of Geometry and Illumination
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
Model-Based Brightness Constraints: On Direct Estimation of Structure and Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
Artificial Vision for Mobile Robots: Stereo Vision and Multisensory Perception
Artificial Vision for Mobile Robots: Stereo Vision and Multisensory Perception
Optimal Motion and Structure Estimation
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recursive Estimation of Motion, Structure, and Focal Length
IEEE Transactions on Pattern Analysis and Machine Intelligence
Hierarchical Model-Based Motion Estimation
ECCV '92 Proceedings of the Second European Conference on Computer Vision
A Factorization Based Algorithm for Multi-Image Projective Structure and Motion
ECCV '96 Proceedings of the 4th European Conference on Computer Vision-Volume II - Volume II
A Factorization Method for Affine Structure from Line Correspondences
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
Three-dimensional modeling from two-dimensional video
IEEE Transactions on Image Processing
Journal of Mathematical Imaging and Vision
Geometrical recovery of missing data for shape from motion
International Journal of Computer Mathematics
Optimization Algorithms on Subspaces: Revisiting Missing Data Problem in Low-Rank Matrix
International Journal of Computer Vision
Rank Constraints for Homographies over Two Views: Revisiting the Rank Four Constraint
International Journal of Computer Vision
Geometrical fitting of missing data for shape from motion under noise distribution
ICNC'06 Proceedings of the Second international conference on Advances in Natural Computation - Volume Part II
Uncertainty analysis using geometrical property between 2d-to-3d under affine projection
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
A novel recovery algorithm of incomplete observation matrix for converting 2-d video to 3-d content
IWICPAS'06 Proceedings of the 2006 Advances in Machine Vision, Image Processing, and Pattern Analysis international conference on Intelligent Computing in Pattern Analysis/Synthesis
Efficient methods for point matching with known camera orientation
ICIAR'10 Proceedings of the 7th international conference on Image Analysis and Recognition - Volume Part I
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The paper describes the rank 1 weighted factorization solution to the structure from motion problem. This method recovers the 3D structure from the factorization of a data matrix that is rank 1 rather than rank 3. This matrix collects the estimates of the 2D motions of a set of feature points of the rigid object. These estimates are weighted by the inverse of the estimates error standard deviation so that the 2D motion estimates for "sharper" features, which are usually well-estimated, are given more weight, while the noisier motion estimates for "smoother" features are weighted less. We analyze the performance of the rank 1 weighted factorization algorithm to determine what are the most suitable 3D shapes or the best 3D motions to recover the 3D structure of a rigid object from the 2D motions of the features. Our approach is developed for the orthographic camera model. It avoids expensive singular value decompositions by using the power method and is suitable to handle dense sets of feature points and long video sequences. Experimental studies with synthetic and real data illustrate the good performance of our approach.