Abstract: We present a method to construct a group of isometric and scaling invariant shape descriptors for shape analysis.Firstly,we construct a kernel function based on Biharmonic distance.Then Lebesgue integral is employed to produce a group of isometric shape descriptors.In the following step,Lebesgue measure of the surface is applied to smooth away their scaling factors.Thus we get one group of isometric and scaling invariant shape descriptors on 2D manifold,which reflect some intrinsic properties of shapes.Several experiments are done on the human hand models.The results show that objects can be recognized and distinguished using these shape descriptors with high efficiency.