Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Artificial Intelligence - Special volume on computer vision
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Multibody Factorization Method for Independently Moving Objects
International Journal of Computer Vision
A morphable model for the synthesis of 3D faces
Proceedings of the 26th annual conference on Computer graphics and interactive techniques
Multiple view geometry in computer visiond
Multiple view geometry in computer visiond
International Journal of Computer Vision - Marr Prize Special Issue
Factorization Methods for Projective Structure and Motion
CVPR '96 Proceedings of the 1996 Conference on Computer Vision and Pattern Recognition (CVPR '96)
Segmentation of Dynamic Scenes from Image Intensities
MOTION '02 Proceedings of the Workshop on Motion and Video Computing
Vision-based control of 3D facial animation
Proceedings of the 2003 ACM SIGGRAPH/Eurographics symposium on Computer animation
Separability of Pose and Expression in Facial Tracking and Animation
ICCV '98 Proceedings of the Sixth International Conference on 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
A Feature-based Approach for Dense Segmentation and Estimation of Large Disparity Motion
International Journal of Computer Vision
Robust facial feature tracking under varying face pose and facial expression
Pattern Recognition
2D vs. 3D Deformable Face Models: Representational Power, Construction, and Real-Time Fitting
International Journal of Computer Vision
Multi-scale 3D scene flow from binocular stereo sequences
Computer Vision and Image Understanding
Extracting Average Shapes from Occluded Non-rigid Motion
IbPRIA '07 Proceedings of the 3rd Iberian conference on Pattern Recognition and Image Analysis, Part II
Perspective Nonrigid Shape and Motion Recovery
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
A Convex Approach to Low Rank Matrix Approximation with Missing Data
SCIA '09 Proceedings of the 16th Scandinavian Conference on Image Analysis
International Journal of Computer Vision
Convex optimization for nonrigid stereo reconstruction
IEEE Transactions on Image Processing
Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion
Image and Vision Computing
3D face reconstruction under imperfect tracking circumstances using shape model constraints
ISVC'07 Proceedings of the 3rd international conference on Advances in visual computing - Volume Part II
Quasi-perspective structure factorization with missing data
CAR'10 Proceedings of the 2nd international Asia conference on Informatics in control, automation and robotics - Volume 2
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
Piecewise quadratic reconstruction of non-rigid surfaces from monocular sequences
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Deterministic 3D human pose estimation using rigid structure
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Monocular template-based reconstruction of smooth and inextensible surfaces
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part III
Automatic estimation of the number of deformation modes in non-rigid SfM with missing data
SCIA'11 Proceedings of the 17th Scandinavian conference on Image analysis
Monocular Template-based Reconstruction of Inextensible Surfaces
International Journal of Computer Vision
Optimal Metric Projections for Deformable and Articulated Structure-from-Motion
International Journal of Computer Vision
ICSR'12 Proceedings of the 4th international conference on Social Robotics
Stratified Generalized Procrustes Analysis
International Journal of Computer Vision
3D shape regression for real-time facial animation
ACM Transactions on Graphics (TOG) - SIGGRAPH 2013 Conference Proceedings
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
EM-GPA: Generalized Procrustes analysis with hidden variables for 3D shape modeling
Computer Vision and Image Understanding
Forward non-rigid motion tracking for facial MoCap
The Visual Computer: International Journal of Computer Graphics
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Recovery of three dimensional (3D) shape and motion of non-static scenes from a monocular video sequence is important for applications like robot navigation and human computer interaction. If every point in the scene randomly moves, it is impossible to recover the non-rigid shapes. In practice, many non-rigid objects, e.g. the human face under various expressions, deform with certain structures. Their shapes can be regarded as a weighted combination of certain shape bases. Shape and motion recovery under such situations has attracted much interest. Previous work on this problem (Bregler, C., Hertzmann, A., and Biermann, H. 2000. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Brand, M. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition; Torresani, L., Yang, D., Alexander, G., and Bregler, C. 2001. In Proc. Int. Conf. Computer Vision and Pattern Recognition) utilized only orthonormality constraints on the camera rotations (rotation constraints). This paper proves that using only the rotation constraints results in ambiguous and invalid solutions. The ambiguity arises from the fact that the shape bases are not unique. An arbitrary linear transformation of the bases produces another set of eligible bases. To eliminate the ambiguity, we propose a set of novel constraints, basis constraints, which uniquely determine the shape bases. We prove that, under the weak-perspective projection model, enforcing both the basis and the rotation constraints leads to a closed-form solution to the problem of non-rigid shape and motion recovery. The accuracy and robustness of our closed-form solution is evaluated quantitatively on synthetic data and qualitatively on real video sequences.