In this paper, we aim to carry out a brief study of a new sets of Quaternion Discrete Moment Invariants (QDMI) in uniform lattice named: Quaternion Tchebichef Moment Invariants (QTMI), Quaternion Krawtchouk Moment Invariants (QKMI), and Quaternion Hahn Moment Invariants (QHMI), for hand gesture-based sign language recognition. For this purpose, we present briefly the principles of those moment invariants. Then, we test them on several datasets that contain challenging attributions, with regard to invariability and recognition under noise-free and noisy conditions. We conclude our paper by discussing the obtained results and the future works in this field.