Dipartimento di Informatica, University of Verona, Strada le Grazie 15, 37134 Verona, Italy.
IEEE Trans Pattern Anal Mach Intell. 2013 Aug;35(8):1972-84. doi: 10.1109/TPAMI.2012.263.
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.
在监控应用中，人的头部和身体方向对于评估许多行为特征至关重要。不幸的是，在这种情况下，人们通常只被几个嘈杂的像素编码，因此很难对其进行特征描述。我们提出了一个基于表达性描述符协方差的计算框架来解决这个问题，协方差已经被用于行人检测，实际上是黎曼流形上的二元分类问题。在本文中，我们展示了如何将其扩展到多分类情况，提出了一种新的描述符，称为加权协方差数组，特别适合处理微小的图像表示。这种扩展需要一种新的微分几何方法，其中协方差被投影到一个唯一的切空间上，可以在该切空间上应用标准的机器学习技术。具体来说，我们采用 Campbell-Baker-Hausdorff 扩展作为一种方法，以非常有效的方式在切空间上逼近流形上的真实（测地线）距离。我们在多个基准数据集上测试了我们的方法，还提出了新的测试集，在所有情况下都得到了令人信服的结果。
