Gyrification/Addendum

Commonly used measures of the exent of cortical folding include:
 * $ L^2 norms$:
 * $$LN_G = \tfrac{1}{4\pi} \textstyle \sqrt{\sum_A K^2}$$, with $$K = k_1 k_2$$ being the Gaussian curvature, computed from the two principal curvatures $$k_1$$ and $$k_2$$
 * $$LN_M =\tfrac{1}{4\pi} \textstyle \sum_A H^2$$, with $$H=\tfrac{1}{2}(k_1 + k_2)$$ being the Mean curvature and $$A$$ the area of the surface in question
 * Folding index
 * $$FI =\tfrac{1}{4\pi} \textstyle \sum_A k^{\ddagger}$$, with $$k^{\ddagger}=|k_1|(|k_1|-|k_2|)$$
 * Intrinsic curvature index
 * $$ICI =\tfrac{1}{4\pi} \textstyle \sum_A K^+$$, with $$K^+$$ being the positive Gaussian curvature


 * Gyrification index
 * $$GI(n) =\tfrac{A(n)_{pial}}{A(n)_{gc}}$$, with $$n$$ indicating the number of the slice, and $$A(n)_{pial}$$ and $$A(n)_{gc}$$ being the pial surface area in that slice and the surface area of the boundary between gray matter and cerebrospinal fluid, respectively
 * Gyrification-White index
 * $$GWI =\tfrac{A_{gw}}{A_{gc}}$$, with $$A_{gw}$$ being the surface area of the boundary between gray matter and white matter
 * White matter folding
 * $$WMF =\tfrac{A_{gw}}{{V_w}^{2/3}}$$, with $$V_w$$ being the volume of the white matter
 * Cortical complexity
 * Fractal dimension
 * Global gyrification index
 * Local gyrification index
 * Shape index
 * Curvedness
 * Roundness
 * $$Rn =\tfrac{A}{^3\sqrt{36 \pi V^2}}$$