Abstract-In this paper we aim at increasing the descriptive power of the covariance matrix, limited in capturing linear mutual dependencies between variables only. We present a rigorous and principled mathematical pipeline to recover the kernel trick for computing the covariance matrix, enhancing it to model more complex, non-linear relationships conveyed by the raw data. To this end, we propose Kernelized-COV, which generalizes the original covariance representation without compromising the efficiency of the computation. In the experiments, we validate the proposed framework against many previous approaches in the literature, scoring on par or superior with respect to the state of the art on benchmark datasets for 3D action recognition.Publicly available code: https://www.iit.it/pavis/code/kcar

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Characterizing an image region by its feature inter-correlations is a modern trend in computer vision. In this paper, we introduce a new image descriptor that can be seen as a natural extension of a covariance descriptor with the advantage of capturing nonlinear and non-monotone dependencies. Inspired from the recent advances in mathematical statistics of Brownian motion, we can express highly complex structural information in a compact and computationally efficient manner. We show that our Brownian covariance descriptor can capture richer image characteristics than the covariance descriptor. Additionally, a detailed analysis of the Brownian manifold reveals that in opposite to the classical covariance descriptor, the proposed descriptor lies in a relatively flat manifold, which can be treated as a Euclidean. This brings significant boost in the efficiency of the descriptor. The effectiveness and the generality of our approach is validated on two challenging vision tasks, pedestrian classification and person re-identification. The experiments are carried out on multiple datasets achieving promising results.

Capturing the essential characteristics of visual objects by considering how their features are inter-related is a recent philosophy of object classification. In this paper, we embed this principle in a novel image descriptor, dubbed Heterogeneous Auto-Similarities of Characteristics (HASC). HASC is applied to heterogeneous dense features maps, encoding linear relations by covariances and nonlinear associations through information-theoretic measures such as mutual information and entropy. In this way, highly complex structural information can be expressed in a compact, scale invariant and robust manner. The effectiveness of HASC is tested on many diverse detection and classification scenarios, considering objects, textures and pedestrians, on widely known benchmarks Brodatz,