Analytical computation of free vibration modes : application to non rigid motion analysis and animation in 3D images

In this paper, we concentrate on non rigid motion analysis and synthesis in 3D images using modal dynamics. Using the solid state physics formulation, we develop the analytic expression of eigenmodes of the multidimensional elastically-deformable model exposed in our previous publications. These analytic expressions are calculated for various topologies (plane, cylinder, torus). Thanks to these expressions, non rigid motion of a 3D deformable object can be approximated in modal space in real time, by superimposing a few number of low-frequency modes that can be computed in a straightforward manner, whatever the size of the structure. The power of the approach for analyzing 3D non rigid motion is demonstrated by a set of experimental results on a 3D time sequence of the human heart. Then the heart is animated between the diastole and the systole. Real-time animation capturing a high level of details is shown on a 3D magnetic resonance head data. Finally, the contribution of this paper is making modal analysis an efficient and easy-to-use tool for non rigid motion analysis and animation