In this paper, we present a 3D motion correction system posterior to 3D pose estimation from video. Our approach, relying on a 3D human pose estimator taken from the literature, consists of a motion correction system using deep learning techniques coupled with Laplacian motion modeling. The system affects the temporal features of the movement to obtain temporally better reconstructed motion, and ensures the preservation of the static skeletal structure throughout the movement. The approach is built upon two deep neural networks. The first neural network uses a 3D+t graph representation of motion associated with the discrete Laplacian operator to improve the spatio-temporal structural deformation of the skeleton over time. The second neural network, meanwhile, estimates fixed lengths for the bones of the skeletal structure. This enables the correction process to produce skeletal consistency in the motion while reducing the error on the lengths of the bones in the previously estimated motion. Compared to competitive state-of-the-art approaches, we show that our correction system improves both the spatial and temporal characteristics of the reconstructed motion, for better use in data-driven animation applications.