Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Learning with Kernels: Support Vector Machines, Regularization, Optimization, and Beyond
Multiple View Geometry in Computer Vision
Multiple View Geometry in 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
Nonrigid Structure-from-Motion: Estimating Shape and Motion with Hierarchical Priors
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Rotation Invariant Kernels and Their Application to Shape Analysis
IEEE Transactions on Pattern Analysis and Machine Intelligence
Trajectory Space: A Dual Representation for Nonrigid Structure from Motion
IEEE Transactions on Pattern Analysis and Machine Intelligence
IEEE Transactions on Pattern Analysis and Machine Intelligence
Non-rigid structure from motion with complementary rank-3 spaces
CVPR '11 Proceedings of the 2011 IEEE Conference on Computer Vision and Pattern Recognition
Automated articulated structure and 3D shape recovery from point correspondences
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Kernel non-rigid structure from motion
ICCV '11 Proceedings of the 2011 International Conference on Computer Vision
Salient and non-salient fiducial detection using a probabilistic graphical model
Pattern Recognition
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Non-rigid structure from motion (NRSFM) is a classical underconstrained problem in computer vision. A common approach to make NRSFM more tractable is to constrain 3D shape deformation to be smooth over time. This constraint has been used to compress the deformation model and reduce the number of unknowns that are estimated. However, temporal smoothness cannot be enforced when the data lacks temporal ordering and its benefits are less evident when objects undergo abrupt deformations. This paper proposes a new NRSFM method that addresses these problems by considering deformations as spatial variations in shape space and then enforcing spatial, rather than temporal, smoothness. This is done by modeling each 3D shape coefficient as a function of its input 2D shape. This mapping is learned in the feature space of a rotation invariant kernel, where spatial smoothness is intrinsically defined by the mapping function. As a result, our model represents shape variations compactly using custom-built coefficient bases learned from the input data, rather than a pre-specified set such as the Discrete Cosine Transform. The resulting kernel-based mapping is a by-product of the NRSFM solution and leads to another fundamental advantage of our approach: for a newly observed 2D shape, its 3D shape is recovered by simply evaluating the learned function.