Temporal Reflection Symmetry of Human Actions: A Riemannian Analysis

Abstract

While spatial symmetry of objects is studied frequently, the problem of measuring temporal symmetry has rarely been explored. In this paper we present a mathematical framework that utilizes a recently developed differential geometric approach to quantify temporal reflection symmetry in movements from video data, in which human movements are modeled as trajectories on Riemannian manifolds. Using the recently proposed transport square-root velocity functions (TSRVF) representation, the amounts of temporal asymmetry in movements are decomposed into a spatial component and a temporal one, each of which is quantified by an asymmetry score.