Pedestrian Detection via Classification on Riemannian Manifolds

Abstract

We present a new algorithm to detect pedestrians in still images utilizing covariance matrices as object descriptors. Since the descriptors do not form a vector space, well-known machine learning techniques are not well suited to learn the classifiers. The space of d-dimensional nonsingular covariance matrices can be represented as a connected Riemannian manifold. The main contribution of the paper is a novel approach for classifying points lying on a connected Riemannian manifold using the geometry of the space. The algorithm is tested on the INRIA and DaimlerChrysler pedestrian data sets where superior detection rates are observed over the previous approaches. IEEE Transaction on PAMI 2008This work may not be copied or reproduced in whole or in part for any commercial purpose. Permission to copy in whole or in part without payment of fee is granted for nonprofit educational and research purposes provided that all such whole or partial copies include the following: a notice that such copying is by permission of Mitsubishi Electric Research Laboratories, Inc.; an acknowledgment of the authors and individual contributions to the work; and all applicable portions of the copyright notice. Copying, reproduction, or republishing for any other purpose shall require a license with payment of fee to Mitsubishi Electric Research Laboratories, Inc. All rights reserved. Abstract-We present a new algorithm to detect pedestrians in still images utilizing covariance matrices as object descriptors. Since the descriptors do not form a vector space, well-known machine learning techniques are not well suited to learn the classifiers. The space of d-dimensional nonsingular covariance matrices can be represented as a connected Riemannian manifold. The main contribution of the paper is a novel approach for classifying points lying on a connected Riemannian manifold using the geometry of the space. The algorithm is tested on the INRIA and DaimlerChrysler pedestrian data sets where superior detection rates are observed over the previous approaches.

Pedestrian Recognition with a Learned Metric

“…Pedestrians are by definition upright people figures with limited configurations. Therefore template based approaches with a sliding window classifier produce favorable results [2,3]. In addition, there exists a number of strong and relatively easy to detect contextual cues, such as the presence of ground and other rigid objects (e.g., cars), which can be integrated into the decision process to significantly improve the detection performance [4].…”

Kernel Learning for Extrinsic Classification of Manifold Features

“…One such Euclidean space is the tangent-space. In [22], a LogitBoost classifier was developed using weak classifiers learned on tangent spaces, and then used for pedestrian detection with covariance features. Tangent spaces only preserves the local structure of the manifold and can often lead to sub-optimal performance.…”

“…Such data often lie in non-Euclidean spaces. For instance, popular features and models in computer vision like shapes [10], histograms, covariance features [22] , linear dynamical systems (LDS) [6], etc., are known to lie on Riemannian manifolds. In such cases, one needs good classification techniques that make use of the underlying manifold structure.…”

“…Hence, classification is often performed in an extrinsic manner by first mapping the manifold to an Euclidean space, and then learning classifiers in the new space. One such popularly used Euclidean space is the tangent space at the mean sample [22,23]. However, tangent spaces preserves only the local structure of the manifold and can often lead to sub-optimal performance.…”

Learning to Match Appearances by Correlations in a Covariance Metric Space

“…However, learning on a manifold space is a di cult and unsolved challenge. Methods [2,20] perform classi cation by regression over the mappings from the training data to a suitable tangent plane. De ning tangent plane over the Karcher mean of the positive training data points, we can preserve a local structure of the points.…”