Regional Type II multivariate Laplace descriptor based on Lie group

Abstract

Feature descriptors play a pivotal role in image classification and target detection. This paper introduces three categories of Type II multivariate Laplace region image descriptors based on Lie group theory. Through Lie group theory, we have demonstrated that the Laplace distribution function space is a unique type of Riemannian manifold, specifically a Lie group. Subsequently, we have proven the equivalence between two categories of partitions obtained through isomorphic mapping, leading to the left (or right) coset. Following this, the left (or right) polar decomposition leads to the symmetric positive definite matrix Lie group. Finally, based on the homeomorphic mapping, we obtain the feature descriptor on the Lie algebra at the mean $\mu$ of the embedded matrix. The Laplace descriptors are constructed by selecting $d$ low-level or mid-level original features on each pixel. This method is able to handle low-dimensional or high-dimensional features based on actual requirements more effectively. We have conducted image classification experiments on two benchmark datasets and carried out ship target detection tasks on a public naval image set to validate the effectiveness of the Laplace region image descriptors. The results have demonstrated a certain degree of expressiveness and universality, offering a novel method for image information extraction.