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Characterizing Humans on Riemannian Manifolds

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4 Author(s)
Diego Tosato ; University of Verona, Verona ; Mauro Spera ; Marco Cristani ; Vittorio Murino

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.

Published in:

IEEE Transactions on Pattern Analysis and Machine Intelligence  (Volume:35 ,  Issue: 8 )