where ds is the length metric on ∂Σ. The resultant energy of a surface can be regarded as a function H and K, and captures the deviation of a surface from local sphericity [22] such that a sphere has zero Willmore energy. Note also that the Willmore energy is always nonnegative. Since a homogeneity region that a typical TIB pattern appears is small in size, total curvature (or energy) of that region is high and can be used as a discriminative feature.