Estimation of compressible or incompressible deformable motions for density images

When deformable motion is considered, the conventional “smoothness” constraint are not suitable. Since the deformation information lies on the derivatives of the displacement components, an ill-chosen minimization over the spatial derivatives of the now field can distort the estimated vector field. So we propose to use the small displacement theory of elasticity to define a new penalty function for 2D or 3D deformable motion estimation. This penalty function depends on two parameters. The study of these parameters shows the ability of the proposed functional to take into account compressible or incompressible deformations