Distortion is an algebraic quantity defined as the difference of eigenvalues (i.e., |κ 1 − κ 2 |) of the local Hessian matrix H e . Distortion is a valuable image analysis property revealed by magnitude difference of principal curvatures. Distortion measure captures the deviation of principal curvatures, thus nonplanarity of a region. Together with Gaussian or mean curvature, distortion measure brings further information into encoding of local shape. Distortion measure is translation and rotation invariant, but not scale invariant. 6) Shear: The shear is another algebraic distortion quantity defined as proportional to the normalized distortion: (κ 1 − κ 2 ) 2 /4. The physical information contained in the shear is basically the same as that of the distortion; it is related to distortion with powers of the difference of principal curvatures. Different than distortion, shear descriptor captures higher degree of nonplanarity of a region due to having more robustness against noise. 7) Compactness: Compactness feature measures the similarity between shape of interest and a perfect ellipse, and is defined as 1/(4π √ κ 1 κ 2 ). Note that this ratio is a dimensionless ratio between the area of the shape (1 for a normalized shape) and the area of the best ellipse fitting the shape. Note also that the compactness measure is invariant to affine transformations and parametrically related to Gaussian curvature. Given a single-axial CT slice of left lung, Fig. 6 (b) indicates a thresholded (i.e., selected candidate patterns) b-scale scene encoded from the corresponding gray-level CT slice shown in Fig. 6(a) . Furthermore, Fig. 6 (c) and (d) shows mean and Gaussian curvature maps from which all the other local shape features are extracted, respectively. In addition, Fig. 6 (e) and (f) shows Willmore energy maps using both mean and Gaussian curvature maps as formulated in (4) and shown in Fig. 6(c) and (d) .