Bilinear spatiotemporal basis models
ACM Transactions on Graphics (TOG)
The Journal of Machine Learning Research
Optimal templates for nonrigid surface reconstruction
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part I
Learning spatially-smooth mappings in non-rigid structure from motion
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part IV
Recursive non-rigid structure from motion with online learned shape prior
Computer Vision and Image Understanding
A Simple Prior-Free Method for Non-rigid Structure-from-Motion Factorization
International Journal of Computer Vision
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We address the classical computer vision problems of rigid and nonrigid structure from motion (SFM) with occlusion. We assume that the columns of the input observation matrix {\bf W} describe smooth 2D point trajectories over time. We then derive a family of efficient methods that estimate the column space of {\bf W} using compact parameterizations in the Discrete Cosine Transform (DCT) domain. Our methods tolerate high percentages of missing data and incorporate new models for the smooth time trajectories of 2D--points, affine and weak-perspective cameras, and 3D deformable shape. We solve a rigid SFM problem by estimating the smooth time trajectory of a single camera moving around the structure of interest. By considering a weak-perspective camera model from the outset, we directly compute euclidean 3D shape reconstructions without requiring postprocessing steps such as euclidean upgrade and bundle adjustment. Our results on real SFM data sets with high percentages of missing data compared positively to those in the literature. In nonrigid SFM, we propose a novel 3D shape trajectory approach that solves for the deformable structure as the smooth time trajectory of a single point in a linear shape space. A key result shows that, compared to state-of-the-art algorithms, our nonrigid SFM method can better model complex articulated deformation with higher frequency DCT components while still maintaining the low--rank factorization constraint. Finally, we also offer an approach for nonrigid SFM when {\bf W} is presented with missing data.