A comparison of spatial prediction techniques for an exploratory analysis of human cortical motor representations

We compare the use of two-dimensional Laplacian smoothing splines and median polish kriging for an exploratory analysis of spatial data sets. Splines were developed originally for modelling a process with determinstic mean structure, while median polish kriging was developed for predicting a spatial random process. We review the fundamentals of both methods, including smoothing parameter selection for splines and variogram estimation and solving the kriging equations for median polish kriging. We demonstrate application of the methods on maps of muscle representations on the human motor cortex (cortical maps). After applying both methods to 20 cortical maps (left and right hemispheres on each of 10 subjects), we compare the fitted surfaces on the basis of predictive ability, aesthetic appeal, and ease of computation.