The main motivation in describing intrinsic shapes by Willmore energy is due to its ability to encode surface (i.e., image area in 2-D) with Möbius invariant features (translation, contrast, rotation, and inversion invariant). In addition to Willmore energy features that we adapt from Canham-Helfrich surface model, we have included seven different local shape features, which are parametrically related to Willmore energy formulation, into the proposed CAD system due to their some invariant properties and discriminative powers. Assume κ 1 and κ 2 indicate eigenvalues of the local Hessian matrix H e for any given local patch L , the following shape features are extracted: 1) shape index (SI), 2) Gaussian curvature, 3) mean curvature, 4) elongation, 5) distortion, 6) shear, 7) compactness.