Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
MLESAC: a new robust estimator with application to estimating image geometry
Computer Vision and Image Understanding - Special issue on robusst statistical techniques in image understanding
Linear fitting with missing data for structure-from-motion
Computer Vision and Image Understanding
Bayesian Model Estimation and Selection for Epipolar Geometry and Generic Manifold Fitting
International Journal of Computer Vision
ECCV '02 Proceedings of the 7th European Conference on Computer Vision-Part I
Multiple View Geometry in Computer Vision
Multiple View Geometry in Computer Vision
3D Reconstruction by Fitting Low-Rank Matrices with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A Measure of Deformability of Shapes, with Applications to Human Motion Analysis
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 1 - Volume 01
A Direct Method for 3D Factorization of Nonrigid Motion Observed in 2D
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Damped Newton Algorithms for Matrix Factorization with Missing Data
CVPR '05 Proceedings of the 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) - Volume 2 - Volume 02
Non-Rigid Metric Shape and Motion Recovery from Uncalibrated Images Using Priors
CVPR '06 Proceedings of the 2006 IEEE Computer Society Conference on Computer Vision and Pattern Recognition - Volume 1
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
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
A batch algorithm for implicit non-rigid shape and motion recovery
WDV'05/WDV'06/ICCV'05/ECCV'06 Proceedings of the 2005/2006 international conference on Dynamical vision
Nonrigid shape and motion from multiple perspective views
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
Special Issue on Tribute Workshop for Peter Johansen
Journal of Mathematical Imaging and Vision
Sequential non-rigid structure-from-motion with the 3D-implicit low-rank shape model
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part II
Monocular template-based reconstruction of smooth and inextensible surfaces
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Monocular Template-based Reconstruction of Inextensible Surfaces
International Journal of Computer Vision
Simultaneous compaction and factorization of sparse image motion matrices
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
A unified view on deformable shape factorizations
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part VI
Non-rigid self-calibration of a projective camera
ACCV'12 Proceedings of the 11th Asian conference on Computer Vision - Volume Part IV
Adaptive Non-rigid Registration and Structure from Motion from Image Trajectories
International Journal of Computer Vision
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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This paper describes an approach to implicit Non-Rigid Structure-from-Motion based on the low-rank shape model. The main contributions are the use of an implicit model, of matching tensors, a rank estimation procedure, and the theory and implementation of two smoothness priors. Contrarily to most previous methods, the proposed method is fully automatic: it handles a substantial amount of missing data as well as outlier contaminated data, and it automatically estimates the degree of deformation. A major problem in many previous methods is that they generalize badly. Although the estimated model fits the visible training data well, it often predicts the missing data badly. To improve generalization a temporal smoothness prior and a surface shape prior are developed. The temporal smoothness prior constrains the camera trajectory and the configuration weights to behave smoothly. The surface shape prior constrains consistently close image point tracks to have similar implicit structure. We propose an algorithm for achieving a Maximum A Posteriori (map) solution and show experimentally that the map-solution generalizes far better than the prior-free Maximum Likelihood (ml) solution.