. Author manuscript; available in PMC: 2016 Sep 1.

Published in final edited form as: J Neuroimaging. 2015 May 4;25(5):728–737. doi: 10.1111/jon.12252

Table 2.

Intrinsic geometric cortical features and their definitions.

Geometric Measure

Mathematical formulas

Volume

\iint_{R^{3}} \int I_{D} (x, y, z) d x d y d z

Surface Area

\iint_{Ω} | {\overset{⇀}{r}}_{u} \times {\overset{⇀}{r}}_{v} | d u d v

Mean Curvature

\frac{1}{2} (k_{1} + k_{2})

Shape Index

\frac{2}{π} arctan (\frac{k_{2} + k_{1}}{k_{2} - k_{1}})

Curvedness

\sqrt{\frac{k_{1}^{2} + k_{2}^{2}}{2}}