@conference {14227,
	title = {Learning shift-invariant sparse representation of actions},
	booktitle = {2010 IEEE Conference on Computer Vision and Pattern Recognition (CVPR)},
	year = {2010},
	month = {2010/06/13/18},
	pages = {2630 - 2637},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {A central problem in the analysis of motion capture (MoCap) data is how to decompose motion sequences into primitives. Ideally, a description in terms of primitives should facilitate the recognition, synthesis, and characterization of actions. We propose an unsupervised learning algorithm for automatically decomposing joint movements in human motion capture (MoCap) sequences into shift-invariant basis functions. Our formulation models the time series data of joint movements in actions as a sparse linear combination of short basis functions (snippets), which are executed (or {\textquotedblleft}activated{\textquotedblright}) at different positions in time. Given a set of MoCap sequences of different actions, our algorithm finds the decomposition of MoCap sequences in terms of basis functions and their activations in time. Using the tools of L1 minimization, the procedure alternately solves two large convex minimizations: Given the basis functions, a variant of Orthogonal Matching Pursuit solves for the activations, and given the activations, the Split Bregman Algorithm solves for the basis functions. Experiments demonstrate the power of the decomposition in a number of applications, including action recognition, retrieval, MoCap data compression, and as a tool for classification in the diagnosis of Parkinson (a motion disorder disease).},
	keywords = {action characterization, Action recognition, action retrieval, action synthesis, Character recognition, data compression, human motion capture, HUMANS, Image matching, Image motion analysis, image representation, Image sequences, Information retrieval, joint movements, large convex minimizations, learning (artificial intelligence), learning shift-invariant sparse representation, Matching pursuit algorithms, minimisation, Minimization methods, MoCap data compression, Motion analysis, motion capture analysis, motion disorder disease, motion sequences, orthogonal matching pursuit, Parkinson diagnosis, Parkinson{\textquoteright}s disease, Pursuit algorithms, shift-invariant basis functions, short basis functions, snippets, sparse linear combination, split Bregman algorithm, time series, time series data, Unsupervised learning, unsupervised learning algorithm},
	isbn = {978-1-4244-6984-0},
	doi = {10.1109/CVPR.2010.5539977},
	author = {Li,Yi and Ferm{\"u}ller, Cornelia and Aloimonos, J. and Hui Ji}
}
@article {14182,
	title = {A 3D shape constraint on video},
	journal = {IEEE Transactions on Pattern Analysis and Machine Intelligence},
	volume = {28},
	year = {2006},
	month = {2006/06//},
	pages = {1018 - 1023},
	abstract = {We propose to combine the information from multiple motion fields by enforcing a constraint on the surface normals (3D shape) of the scene in view. The fact that the shape vectors in the different views are related only by rotation can be formulated as a rank = 3 constraint. This constraint is implemented in an algorithm which solves 3D motion and structure estimation as a practical constrained minimization. Experiments demonstrate its usefulness as a tool in structure from motion providing very accurate estimates of 3D motion.},
	keywords = {3D motion estimation, algorithms, Artificial intelligence, CAMERAS, decoupling translation from rotation, Estimation error, Fluid flow measurement, Image Enhancement, Image Interpretation, Computer-Assisted, Image reconstruction, Imaging, Three-Dimensional, Information Storage and Retrieval, integration of motion fields, Layout, minimisation, Minimization methods, Motion estimation, multiple motion fields, parameter estimation, Pattern Recognition, Automated, Photography, practical constrained minimization, SHAPE, shape and rotation., shape vectors, stability, structure estimation, surface normals, Three-dimensional motion estimation, video 3D shape constraint, Video Recording, video signal processing},
	isbn = {0162-8828},
	doi = {10.1109/TPAMI.2006.109},
	author = {Hui Ji and Ferm{\"u}ller, Cornelia}
}
@conference {11974,
	title = {Optimal motion estimation},
	booktitle = {Workshop on Visual Motion, 1989.,Proceedings},
	year = {1989},
	month = {1989/03/20/22},
	pages = {229 - 237},
	publisher = {IEEE},
	organization = {IEEE},
	abstract = {The problem of using feature correspondences to recover the structure and 3D motion of a moving object from its successive images is analyzed. They formulate the problem as a quadratic minimization problem with a nonlinear constraint. Then they derive the condition for the solution to be optimal under the assumption of Gaussian noise in the input, in the maximum-likelihood-principle sense. The authors present two efficient ways to approximate it and discuss some inherent limitations of the structure-from-motion problem when two frames are used that should be taken into account in robotics applications that involve dynamic imagery. Finally, it is shown that some of the difficulties inherent in the two-frame approach disappear when redundancy in the data is introduced. This is concluded from experiments using a structure-from-motion algorithm that is based on multiple frames and uses only the rigidity assumption},
	keywords = {3D motion interpretation, Automation, Computer vision, computerised pattern recognition, computerised picture processing, constraint minimization, dynamic imagery, Educational institutions, feature correspondences, Gaussian noise, Image motion analysis, Laboratories, maximum-likelihood-principle, Minimization methods, Motion analysis, Motion estimation, motion parameters, moving object, multiple frames, nonlinear constraint, Optical computing, optimal motion estimation, parameter estimation, quadratic minimization, quadratic programming, redundancy, rigidity assumption, robotics applications, structure-from-motion, successive images, two-frame},
	isbn = {0-8186-1903-1},
	doi = {10.1109/WVM.1989.47114},
	author = {Spetsakis, M. E and Aloimonos, J.}
}
