Human action representation, recognition and learning is of importance to guarantee a fruitful human-robot cooperation. In this paper, we propose a novel coordinate-free, scale invariant representation of 6D (position and orientation) motion trajectories. The advantages of the proposed invariant representation are twofold. First the performance of gesture recognition can be improved thanks to its invariance to different viewpoints and different body sizes of the actors. Secondly, the proposed representation is bi-directional. Not only the original Cartesian trajectory can be converted into the 6 invariant values, but also the motion in the original space can be retrieved back from the invariants. While the former aspect handles robust human gesture recognition, the latter allows the execution of robot motions without the need to store the Cartesian data. Experimental results illustrate the effectiveness of the proposed invariant representation for gesture recognition and accurate trajectory reconstruction.

In this paper we propose a new bidirectional invariant motion descriptor of a rigid body. The proposed invariant representation is not affected by rotations, translations, time, linear and angular scaling. Invariant properties of the proposed representation enable to recognize gestures in realistic scenarios with unexpected variations (e.g., changes in user's initial pose, execution time or an observation point), while Cartesian trajectories are sensitive to these changes. The proposed invariant representation also allows reconstruction of the original motion trajectory, which is useful for human-robot interaction applications where a robot recognizes human actions and executes robot's proper behaviors using same descriptors. By removing the dependency on absolute pose and scaling factors of the Cartesian trajectories the proposed descriptor achieves flexibility to generate different motion instances from the same invariant representation. In order to illustrate the effectiveness of our proposed descriptor in motion recognition and generation, it is tested on three datasets and experiments on a NAO humanoid robot and a KUKA LWR IV+ manipulator and compared with other existing invariant representations.

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In this paper we face the issue of the most effective implementation of multistage decimators in terms of group delay minimization. Here we derive the design criteria to minimize the group delay of multistage decimators and we check their validity comparing the analytical outcomes with the "experimental" outcomes obtained through the design of a variety of decimators.

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