Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Three-dimensional computer vision: a geometric viewpoint
Three-dimensional computer vision: a geometric viewpoint
Affine Structure and Motion from Points, Lines and Conics
International Journal of Computer Vision
Factorization with Uncertainty
International Journal of Computer Vision
A Unified Factorization Algorithm for Points, Line Segments and Planes with Uncertainty Models
ICCV '98 Proceedings of the Sixth International Conference on Computer Vision
ICCV '03 Proceedings of the Ninth IEEE International Conference on Computer Vision - Volume 2
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
A Blind Source Separation Approach to Structure from Motion
3DPVT '06 Proceedings of the Third International Symposium on 3D Data Processing, Visualization, and Transmission (3DPVT'06)
IEEE Transactions on Pattern Analysis and Machine Intelligence
A blind source separation technique using second-order statistics
IEEE Transactions on Signal Processing
Recovering the missing components in a large noisy low-rank matrix: application to SFM
IEEE Transactions on Pattern Analysis and Machine Intelligence
Recursive non-rigid structure from motion with online learned shape prior
Computer Vision and Image Understanding
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We present an information theoretic approach to define the problem of structure from motion (SfM) as a blind source separation one. Given that for almost all practical joint densities of shape points, the marginal densities are non-Gaussian, we show how higher-order statistics can be used to provide improvements in shape estimates over the methods of factorization via Singular Value Decomposition (SVD), bundle adjustment and Bayesian approaches. Previous techniques have either explicitly or implicitly used only second-order statistics in models of shape or noise. A further advantage of viewing SfM as a blind source problem is that it easily allows for the inclusion of noise and shape models, resulting in Maximum Likelihood (ML) or Maximum a Posteriori (MAP) shape and motion estimates. A key result is that the blind source separation approach has the ability to recover the motion and shape matrices without the need to explicitly know the motion or shape pdf. We demonstrate that it suffices to know whether the pdf is sub- or super-Gaussian (i.e., semi-parametric estimation) and derive a simple formulation to determine this from the data. We provide extensive experimental results on synthetic and real tracked points in order to quantify the improvement obtained from this technique.