Texture Classification Using RGGD Statistical Model of CNN Feature Maps Encoding

The symmetric positive definite (SPD) matrices play an important role in diverse domains, including computer vision and signal processing, due to their unique ability to capture the intrinsic structure of nonlinear data using Riemannian geometry. Despite their significance, a notable gap exists in the absence of statistical distributions capable of effectively characterizing the statistical properties within the SPD matrices space. This paper addresses this gap by introducing a novel Riemannian Generalized Gaussian distribution (RGGD). The primary aspect of this work includes presenting the precise expression for the probability density function (PDF) of the RGGD model, along with the parameter estimation method based on the maximum likelihood for this distribution. The second aspect of this work entails harnessing the second-order statistical information captured in the feature maps originating from the initial layers of deep convolutional neural networks (DCNNs) using the RGGD stochastic model within an image classification framework. The third aspect of this work includes also the comparison of the three-parameter RGGD model with its two-parameter predecessors, namely the Riemannian Gaussian distribution (RGD) and the Riemannian Laplacian distribution (RLD). Besides the mathematical foundations, the model's efficiency is validated through experiments conducted on the three well-known datasets, showcasing its effectiveness in capturing the underlying statistics of SPD matrices.