*Article* **Rate-Invariant Modeling in Lie Algebra for Activity Recognition**

### **Malek Boujebli 1,\*, Hassen Drira 2,3, Makram Mestiri 1 and Imed Riadh Farah 1**

1 Software Engineering, Distributed Applications, Decision Systems and Intelligent Imaging Research Laboratory (RIADI), National School of Computer Science (ENSI), University of Manouba, Manouba2010,Tunisia;mmestiri@gmail.com(M.M.);imed.riadh.farah@gmail.com(I.R.F.)


Received: 21 September 2020; Accepted: 4 November 2020; Published: 10 November 2020

**Abstract:** Human activity recognition is one of the most challenging and active areas of research in the computer vision domain. However, designing automatic systems that are robust to significant variability due to object combinations and the high complexity of human motions are more challenging. In this paper, we propose to model the inter-frame rigid evolution of skeleton parts as the trajectory in the Lie group *SE*(3) × ... × *SE*(3). The motion of the object is similarly modeled as an additional trajectory in the same manifold. The classification is performed based on a rate-invariant comparison of the resulting trajectories mapped to a vector space, the Lie algebra. Experimental results on three action and activity datasets show that the proposed method outperforms various state-of-the-art human activity recognition approaches.

**Keywords:** activity recognition; rate invariance; Lie group
