results for au:Biagio_M in:cs
Sep 30 2016 cs.CV
This paper presents a novel framework for visual object recognition using infinite-dimensional covariance operators of input features in the paradigm of kernel methods on infinite-dimensional Riemannian manifolds. Our formulation provides in particular a rich representation of image features by exploiting their non-linear correlations. Theoretically, we provide a finite-dimensional approximation of the Log-Hilbert-Schmidt (Log-HS) distance between covariance operators that is scalable to large datasets, while maintaining an effective discriminating capability. This allows us to efficiently approximate any continuous shift-invariant kernel defined using the Log-HS distance. At the same time, we prove that the Log-HS inner product between covariance operators is only approximable by its finite-dimensional counterpart in a very limited scenario. Consequently, kernels defined using the Log-HS inner product, such as polynomial kernels, are not scalable in the same way as shift-invariant kernels. Computationally, we apply the approximate Log-HS distance formulation to covariance operators of both handcrafted and convolutional features, exploiting both the expressiveness of these features and the power of the covariance representation. Empirically, we tested our framework on the task of image classification on twelve challenging datasets. In almost all cases, the results obtained outperform other state of the art methods, demonstrating the competitiveness and potential of our framework.
Apr 25 2016 cs.CV
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.