. Author manuscript; available in PMC: 2012 Feb 3.

Published in final edited form as: IEEE Trans Med Imaging. 2010 Sep 16;30(2):266–278. doi: 10.1109/TMI.2010.2076300

Table I.

Basic shapes and associated characteristics of principal curvatures

Basic Shapes	Examples	C_max	C_min	D_max	D_min
plane	fissures	0	0	random	random
convex cylinder	vascular tree	1/r	0	orthogonal to axis	parallel to axis
concave cylinder	inner airway wall	−1/r	0	orthogonal to axis	parallel to axis
convex sphere	nodules	1/r	1/r	random	random
concave sphere	n/a	−1/r	−1/r	random	random

C_max: the maximum curvature;

C_mix: the minimum curvature;

r: the radius of a cylinder or a sphere;

D_max: the principal direction associated C_max;

D_min: the principal direction associated C_min;

n/a: no example available.