A functional for compressible or incompressible elastic deformation estimation

When deformable motion is considered, the conventional "smoothness" constraints are not suitable since the deformation information lies on the derivatives of the displacement components. So we propose to use the small displacement theory of elasticity to define a new penalty function for two-dimensional (2-D) or three-dimensional (3-D) 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.