Figure 3.

Validation : a simulated cross-sectional study between the group of cortical surfaces (interface between GM and WM) of 20 BrainWeb [Aubert-Broche et al. (2006)] images and a second group created by moderately smoothing the 20 BrainWeb surfaces. For all plots in this paper, horizontal axis ≡ S, vertical axis ≡ C, coordinates for the bottom left corner : (C, S) = (c_min, −1); bottom right corner : (C, S) = (c_min, 1); top left corner : (C, S) = (c_max, −1). (a)-(b) Mean of the multivariate surface descriptors $P_{{\mathcal{M}}^n}(C,S)$ for the n = 1, . . . , 20 original and smoothed surfaces, respectively, as proposed in Section 2.1; red≡high and blue≡low values. (c) The t-statistic map for the original and smoothed surfaces; t > 0 ⇒ P_original > P_smoothed. Expectedly, the map indicates that the original surfaces have larger mass (red/yellow) in high-curvedness regions as compared to the smoothed surfaces. (d) The significant locations (p < 0.05) produced via permutation testing [Fisher (1935); Nichols and Holmes (2002)]. For all plots in this paper, p values (corrected; permutation testing) for significant locations/clusters are visualized by coloring them by the associated z score [Papoulis and Pillai (2001)], e.g. z(p = 0.05) = 1.65, z(p = 0.005) = 2.58.