Fig. 1: The spatial regression approach (Kriging).
From: The spatial layout of antagonistic brain regions is explicable based on geometric principles
Top, schematic of the spatial regression approach: A an illustration of a signal (elevation and color) in a 2D physical space, with black spheres indicating sampled points where the signal has been measured. B Distances and similarities of the signal between sampled points (black lines) can be used to approximate the spatial process of the continuous signal. This spatial process can be used to predict unsampled points (white sphere) based only on distance to sampled points (white lines). C 2D cut through, showing using samples (black points) from one extreme to predict the other extreme (white point). Bottom, application of the spatial regression approach to the cortical surface. D A cortical surface map is identified, for example, activations from a cognitive task. E The map is projected onto a sphere, and F thresholded to retain a subset of regions; here, those that show deactivation for the chosen task. Next, G a multiresolution regular lattice is created on the sphere, to estimate spatial covariance and H performs spatial prediction of the whole-brain map, including in particular the out-of-mask (task-positive) regions. Finally, these can be compared to the true out-of-mask values (i.e., observed task-positive activity).
