Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
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
Uncalibrated Perspective Reconstruction of Deformable Structures
ICCV '05 Proceedings of the Tenth IEEE International Conference on Computer Vision - Volume 2
A Closed-Form Solution to Non-Rigid Shape and Motion Recovery
International Journal of Computer Vision
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
Towards a measure of deformability of shape sequences
Pattern Recognition Letters
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Perspective Nonrigid Shape and Motion Recovery
ECCV '08 Proceedings of the 10th European Conference on Computer Vision: Part I
Rank Estimation in Missing Data Matrix Problems
Journal of Mathematical Imaging and Vision
Nonrigid shape and motion from multiple perspective views
ECCV'06 Proceedings of the 9th European conference on Computer Vision - Volume Part II
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This paper proposes a new algorithm to estimate automatically the number of deformation modes needed to describe a non-rigid object with the well-known low-rank shape model, focusing on the missing data case. The 3D shape is assumed to deform as a linear combination of K rigid shape bases according to time varying coefficients. One of the requirements of this formulation is that the number of bases must be known in advance. Most non-rigid structure from motion (NRSfM) approaches based on this model determine the value of K empirically. Our proposed approach is based on the analysis of the frequency spectra of the x and y coordinates corresponding to the individual image trajectories, which are seen as 1D signals. The frequency content of the 2D trajectories is encoded using the modulus of the Discrete Cosine Transform (DCT) of the signals. Our hypothesis is that the value of K that gives the best prediction of the missing data also provides the best 3D reconstruction. Our proposed approach does not assume any prior knowledge and is independent of the 3D reconstruction algorithm used. We validate our approach with experiments on synthetic and real sequences.