The paper presents a novel algorithm for pedestrian detection in still images using covariance matrices as object descriptors. The main challenge is that covariance matrices do not form a vector space, making classical machine learning techniques unsuitable. The authors propose a method that leverages the geometry of the space of nonsingular covariance matrices, which can be represented as a connected Riemannian manifold. The key contribution is a classification approach that incorporates the geometric properties of this manifold. The algorithm is tested on the INRIA and DaimlerChrysler pedestrian datasets, achieving superior detection rates compared to previous methods. The approach uses a boosting technique to train multiple weak classifiers on tangent spaces of the Riemannian manifold, combining them into a rejection cascade. The method is efficient, requiring fewer evaluations of descriptors for most test samples. Experiments show that the proposed method outperforms other approaches in terms of detection error trade-offs, especially at low false-positive rates. The covariance descriptors are also shown to be less sensitive to small translations and scalings of the target windows, making the detector more robust to variations in pose and scale.The paper presents a novel algorithm for pedestrian detection in still images using covariance matrices as object descriptors. The main challenge is that covariance matrices do not form a vector space, making classical machine learning techniques unsuitable. The authors propose a method that leverages the geometry of the space of nonsingular covariance matrices, which can be represented as a connected Riemannian manifold. The key contribution is a classification approach that incorporates the geometric properties of this manifold. The algorithm is tested on the INRIA and DaimlerChrysler pedestrian datasets, achieving superior detection rates compared to previous methods. The approach uses a boosting technique to train multiple weak classifiers on tangent spaces of the Riemannian manifold, combining them into a rejection cascade. The method is efficient, requiring fewer evaluations of descriptors for most test samples. Experiments show that the proposed method outperforms other approaches in terms of detection error trade-offs, especially at low false-positive rates. The covariance descriptors are also shown to be less sensitive to small translations and scalings of the target windows, making the detector more robust to variations in pose and scale.