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
Linear fitting with missing data for structure-from-motion
Computer Vision and Image Understanding
IEEE Transactions on Software Engineering - Special section on the seventh international software metrics symposium
An Invitation to 3-D Vision: From Images to Geometric Models
An Invitation to 3-D Vision: From Images to Geometric Models
Reconstruction of a Scene with Multiple Linearly Moving Objects
International Journal of Computer Vision
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
A Unified Algebraic Approach to 2-D and 3-D Motion Segmentation and Estimation
Journal of Mathematical Imaging and Vision
On the Wiberg Algorithm for Matrix Factorization in the Presence of Missing Components
International Journal of Computer Vision
Perturbation Estimation of the Subspaces for Structure from Motion with Noisy and Missing Data
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
Multiframe Motion Segmentation with Missing Data Using PowerFactorization and GPCA
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
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part IV
Recovering the missing components in a large noisy low-rank matrix: application to SFM
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating Planar Surface Orientation Using Bispectral Analysis
IEEE Transactions on Image Processing
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
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A novel technique for missing data matrix rank estimation is presented. It is focused on matrices of trajectories, where every element of the matrix corresponds to an image coordinate from a feature point of a rigid moving object at a given frame; missing data are represented as empty entries. The objective of the proposed approach is to estimate the rank of a missing data matrix in order to fill in empty entries with some matrix completion method, without using or assuming neither the number of objects contained in the scene nor the kind of their motion. The key point of the proposed technique consists in studying the frequency behaviour of the individual trajectories, which are seen as 1D signals. The main assumption is that due to the rigidity of the moving objects, the frequency content of the trajectories will be similar after filling in their missing entries. The proposed rank estimation approach can be used in different computer vision problems, where the rank of a missing data matrix needs to be estimated. Experimental results with synthetic and real data are provided in order to empirically show the good performance of the proposed approach.