Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Active tracking of foveated feature clusters using affine structure
International Journal of Computer Vision
Euclidean Shape and Motion from Multiple Perspective Views by Affine Iterations
IEEE Transactions on Pattern Analysis and Machine Intelligence
A Paraperspective Factorization Method for Shape and Motion Recovery
IEEE Transactions on Pattern Analysis and Machine Intelligence
Geometric Information Criterion for Model Selection
International Journal of Computer Vision
EM algorithms for PCA and SPCA
NIPS '97 Proceedings of the 1997 conference on Advances in neural information processing systems 10
Linear and Incremental Acquisition of Invariant Shape Models From Image Sequences
IEEE Transactions on Pattern Analysis and Machine Intelligence
Principal Component Analysis with Missing Data and Its Application to Polyhedral Object Modeling
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
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
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
Affine Approximation for Direct Batch Recovery of Euclidian Structure and Motion from Sparse Data
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
2D-3D registration of deformable shapes with manifold projection
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
Successively alternate least square for low-rank matrix factorization with bounded missing data
Computer Vision and Image Understanding
Bilinear factorization via augmented lagrange multipliers
ECCV'10 Proceedings of the 11th European conference on Computer vision: Part IV
Adaptive metric registration of 3D models to non-rigid image trajectories
ECCV'10 Proceedings of the 11th European conference on computer vision conference on Computer vision: Part III
Multilinear model estimation with L2-regularization
DAGM'11 Proceedings of the 33rd international conference on Pattern recognition
Structure from motion and photometric stereo for dense 3D shape recovery
ICIAP'11 Proceedings of the 16th international conference on Image analysis and processing: Part I
A method for asteroids 3D surface reconstruction from close approach distances
ICVS'11 Proceedings of the 8th international conference on Computer vision systems
Optimal Metric Projections for Deformable and Articulated Structure-from-Motion
International Journal of Computer Vision
Joint estimation of segmentation and structure from motion
Computer Vision and Image Understanding
An algorithmic approach to missing data problem in modeling human aspects in software development
Proceedings of the 9th International Conference on Predictive Models in Software Engineering
Adaptive Non-rigid Registration and Structure from Motion from Image Trajectories
International Journal of Computer Vision
Recursive non-rigid structure from motion with online learned shape prior
Computer Vision and Image Understanding
A new framework for 3D face reconstruction for self-occluded images
International Journal of Computational Vision and Robotics
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Reconstructing a 3D scene from a moving camera is one of the most important issues in the field of computer vision. In this scenario, not all points are known in all images (e.g. due to occlusion), thus generating missing data. On the other hand, successful 3D reconstruction algorithms like Tomasi & Kanade's factorization method, require an orthographic model for the data, which is adequate in close-up views. The state-of-the-art handles the missing points in this context by enforcing rank constraints on the point track matrix. However, quite frequently, close-up views tend to capture planar surfaces producing degenerate data. Estimating missing data using the rank constraint requires that all known measurements are ''full rank'' in all images of the sequence. If one single frame is degenerate, the whole sequence will produce high errors on the reconstructed shape, even though the observation matrix verifies the rank 4 constraint. In this paper, we propose to solve the structure from motion problem with degenerate data, introducing a new factorization algorithm that imposes the full scaled-orthographic model in one single optimization procedure. By imposing all model constraints, a unique (correct) 3D shape is estimated regardless of the data degeneracies. Experiments show that remarkably good reconstructions are obtained with an approximate models such as orthography.