Rate invariant action recognition in Lie algebra

Human action recognition is currently a hot topic research domain including a variety of applications such as human HMI, rehabilitation and surveillance. The majority of existing approaches are based on the skeleton. They utilize either the joint locations or the joint angles in order to present a human skeleton. This study introduce a novel framework, which allows compact representation, quick comparison and accurate recognition of human action in video sequences from depth sensors. First, we represent the evolution of body parts in successive frames by rotations and translations. Mathematically, in 3D space, rigid body transformations are members of the special Euclidean group SE(3). We can represent the actions by trajectories in the Lie group SE(3) ×…× SE(3) with the proposed skeleton representation. We map these trajectories from Lie group to the corresponding Lie algebra se(3) ×…× se(3), by using the identity element of the group in the tangent space group. We propose then to use an elastic shape analysis framework to compare the resulting trajectories in the lie algebra, thus the comparison is invariant to the rate of execution of the action. Finally, a Hoeffding tree (VFDT)-based classification is performed. Experimentations on two challenging action datasets show that our proposed approach operates equally well or better when compared to state of the art.