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

Accepted in ICCV 2021

References in corpus (8)

• NTU RGB+D 120: A Large-Scale Benchmark for 3D Human Activity Understanding
• Riemannian Adaptive Optimization Methods
• A Riemannian Network for SPD Matrix Learning
• Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation
• Riemannian Geometry of Symmetric Positive Definite Matrices via Cholesky Decomposition
• A Survey on 3D Skeleton-Based Action Recognition Using Learning Method
• Riemannian batch normalization for SPD neural networks
• Statistics on the (compact) Stiefel manifold: Theory and Applications