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Characterizing Humans on Riemannian Manifolds
Aug. 2013 (vol. 35 no. 8)
pp. 1972-1984
Diego Tosato, University of Verona, Verona
Mauro Spera, University of Verona, Verona
Marco Cristani, University of Verona, Verona
Vittorio Murino, University of Verona, Verona
In surveillance applications, head and body orientation of people is of primary importance for assessing many behavioral traits. Unfortunately, in this context people are often encoded by a few, noisy pixels so that their characterization is difficult. We face this issue, proposing a computational framework which is based on an expressive descriptor, the covariance of features. Covariances have been employed for pedestrian detection purposes, actually a binary classification problem on Riemannian manifolds. In this paper, we show how to extend to the multiclassification case, presenting a novel descriptor, named weighted array of covariances, especially suited for dealing with tiny image representations. The extension requires a novel differential geometry approach in which covariances are projected on a unique tangent space where standard machine learning techniques can be applied. In particular, we adopt the Campbell-Baker-Hausdorff expansion as a means to approximate on the tangent space the genuine (geodesic) distances on the manifold in a very efficient way. We test our methodology on multiple benchmark datasets, and also propose new testing sets, getting convincing results in all the cases.
Index Terms:
Manifolds,Symmetric matrices,Head,Magnetic heads,Covariance matrix,Humans,Estimation,Riemannian manifolds,Pedestrian characterization,covariance descriptors
Citation:
Diego Tosato, Mauro Spera, Marco Cristani, Vittorio Murino, "Characterizing Humans on Riemannian Manifolds," IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 35, no. 8, pp. 1972-1984, Aug. 2013, doi:10.1109/TPAMI.2012.263
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