  In this paper, we propose a method for characterizing 3D shapes from point
clouds and we show a direct application on a study of organ temporal
deformations. As an example, we characterize the behavior of a bladder during a
forced respiratory motion with a reduced number of 3D surface points: first, a
set of equidistant points representing the vertices of quadrilateral mesh for
the surface in the first time frame are tracked throughout a long dynamic MRI
sequence using a Large Deformation Diffeomorphic Metric Mapping (LDDMM)
framework. Second, a novel geometric feature which is invariant to scaling and
rotation is proposed for characterizing the temporal organ deformations by
employing an Eulerian Partial Differential Equations (PDEs) methodology. We
demonstrate the robustness of our feature on both synthetic 3D shapes and
realistic dynamic MRI data portraying the bladder deformation during forced
respiratory motions. Promising results are obtained, showing that the proposed
feature may be useful for several computer vision applications such as medical
imaging, aerodynamics and robotics.
