| Brain imaging presents a multitude of fascinating and challenging problems for statisticians. Current techniques for analyzing such data either ignore inherent spatial correlation while delivering a whole brain analysis or properly model spatial correlation in hand-selected regions of interest (ROI). An approach that both produces a whole brain analysis and properly handles spatial correlation is needed. The proposed approach combines recursive partitioning with spatial kriging models to automate the placement of ROIs while properly accounting for spatial correlations.; The new technique starts with one spatial model for the entire image. For the two-dimensional implementation here, the algorithm searches through all bifurcations along each axis fitting a separate spatial kriging model in each region. All the models use a nonparametric variogram based on residuals after removing a localized estimate of the mean. Using an improved cross validation scheme, the split that produces the smallest hold-out overall sum of squares for error is retained. The process is started anew with the two new regions. Partitioning halts when some predetermined stopping criteria are met. The end result is a partitioned image with separate spatial kriging models fit within each region.; Several two-dimensional simulations of varying degrees of change in image smoothness and mean structure are discussed. Finally, an application on an axial slice of a SPECT scan is examined. |
