Shape and motion from image streams under orthography: a factorization method
International Journal of Computer Vision
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
Rank-deficient and discrete ill-posed problems: numerical aspects of linear inversion
International Journal of Computer Vision
Bundle Adjustment - A Modern Synthesis
ICCV '99 Proceedings of the International Workshop on Vision Algorithms: Theory and Practice
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
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
Photometric Stereo with General, Unknown Lighting
International Journal of Computer Vision
Non-rigid structure from motion using ranklet-based tracking and non-linear optimization
Image and Vision Computing
Implicit Non-Rigid Structure-from-Motion with Priors
Journal of Mathematical Imaging and Vision
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
Estimating 3D shape from degenerate sequences with missing data
Computer Vision and Image Understanding
Real-time combined 2D+3D active appearance models
CVPR'04 Proceedings of the 2004 IEEE computer society conference on Computer vision and pattern recognition
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
Bilinear Modeling via Augmented Lagrange Multipliers (BALM)
IEEE Transactions on Pattern Analysis and Machine Intelligence
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This paper addresses the problem of registering a known 3D model to a set of 2D deforming image trajectories. The proposed approach can adapt to a scenario where the 3D model to register is not an exact description of the measured image data. This results in finding a 2D---3D registration, given the complexity of having both 2D deforming data and a coarse description of the image observations. The method acts in two distinct phases. First, an affine step computes a factorization for both the 2D image data and the 3D model using a joint subspace decomposition. This initial solution is then upgraded by finding the best projection to the image plane complying with the metric constraints given by a scaled orthographic camera. Both steps are computed efficiently in closed-form with the additional feature of being robust to degenerate motions which may possibly affect the 2D image data (i.e. lack of relevant rigid motion). A further extension of the approach allows to compute the full 3D deformations of the shape given the first initial (rigid) registration. This step results in solving a Non-rigid Structure from Motion (NRSfM) problem using the 3D known shape as a prior. Experimental results show the robustness of the method in registration tasks such as pose estimation and 3D reconstruction when degenerate image motion is present.