Spatiotemporal coupling with the 3D+t motion Laplacian

Motion editing requires the preservation of spatial and temporal information of the motion. During editing, this information should be preserved at best. We propose a new representation of the motion based on the Laplacian expression of a 3D+t graph: the set of connected graphs given by the skeleton over time. Through this Laplacian representation of the motion, we propose an application which allows an easy and interactive editing, correction or retargeting of a motion. The new created motion is the result of the combination of two minimizations, linear and non-linear: the first penalizes the difference of energy between the Laplacian coordinates from an animation to the desired one. The other one preserves the length of segments. Using several examples, we demonstrate the benefits of our method and in particularly the preservation of the spatiotemporal properties of the motion in an interactive context.