Advances in matrix manifolds for computer vision
Image and Vision Computing
Sparse Modeling of Human Actions from Motion Imagery
International Journal of Computer Vision
Sparse coding and dictionary learning for symmetric positive definite matrices: a kernel approach
ECCV'12 Proceedings of the 12th European conference on Computer Vision - Volume Part II
Human action recognition in video by fusion of structural and spatio-temporal features
SSPR'12/SPR'12 Proceedings of the 2012 Joint IAPR international conference on Structural, Syntactic, and Statistical Pattern Recognition
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A novel approach to action recognition in video based onthe analysis of optical flow is presented. Properties of opticalflow useful for action recognition are captured usingonly the empirical covariance matrix of a bag of featuressuch as flow velocity, gradient, and divergence. The featurecovariance matrix is a low-dimensional representationof video dynamics that belongs to a Riemannian manifold.The Riemannian manifold of covariance matrices is transformedinto the vector space of symmetric matrices underthe matrix logarithm mapping. The log-covariance matrixof a test action segment is approximated by a sparse linearcombination of the log-covariance matrices of training actionsegments using a linear program and the coefficients ofthe sparse linear representation are used to recognize actions.This approach based on the unique blend of a logcovariance-descriptor and a sparse linear representation istested on the Weizmann and KTH datasets. The proposedapproach attains leave-one-out cross validation scores of94.4% correct classification rate for the Weizmann datasetand 98.5% for the KTH dataset. Furthermore, the methodis computationally efficient and easy to implement.