Analysis of 2D intrinsic mode function

The definition of 2D IMF is very important for bidimensional empirical mode decomposition of images. V. Vatchev analyzed 1D IMF in his doctoral dissertation, and introduced the concept of weak-IMF which point out that the solution of Sturm-Liouville equations can be regarded as 1D weak-IMF. In this paper we try to give the definition of 2D IMF and investigate the relations between the vibration theory of thin plate and 2D IMF. Three types of bivariate splines with certain mechanical meanings can be defined as 2D weak-IMF.