GeomNet: A Neural Network Based on Riemannian Geometries of SPD Matrix Space and Cholesky Space for 3D Skeleton-Based Interaction Recognition

TL;DR

This paper introduces GeomNet, a neural network leveraging Riemannian geometry of SPD matrices and Cholesky space to improve 3D skeleton-based interaction recognition by capturing high-order statistics.

Contribution

It develops a novel approach for representing and classifying 3D skeleton interactions using Gaussian distributions embedded in Riemannian manifolds, based on Lie groups and symmetric spaces.

Findings

Achieves competitive results on three 3D human activity benchmarks.

Effectively encodes high-order statistics from 3D joint positions.

Utilizes Riemannian geometry for improved interaction recognition.

Abstract

In this paper, we propose a novel method for representation and classification of two-person interactions from 3D skeleton sequences. The key idea of our approach is to use Gaussian distributions to capture statistics on R n and those on the space of symmetric positive definite (SPD) matrices. The main challenge is how to parametrize those distributions. Towards this end, we develop methods for embedding Gaussian distributions in matrix groups based on the theory of Lie groups and Riemannian symmetric spaces. Our method relies on the Riemannian geometry of the underlying manifolds and has the advantage of encoding high-order statistics from 3D joint positions. We show that the proposed method achieves competitive results in two-person interaction recognition on three benchmarks for 3D human activity understanding.