  A problem of current interest is the estimation of spatially distributed
processes at locations where measurements are missing. Linear interpolation
methods rely on the Gaussian assumption, which is often unrealistic in
practice, or normalizing transformations, which are successful only for mild
deviations from the Gaussian behavior. We propose to address the problem of
missing values estimation on two-dimensional grids by means of spatial
classification methods based on spin (Ising, Potts, clock) models. The "spin"
variables provide an interval discretization of the process values, and the
spatial correlations are captured in terms of interactions between the spins.
The spins at the unmeasured locations are classified by means of the "energy
matching" principle: the correlation energy of the entire grid (including
prediction sites) is estimated from the sample-based correlations. We
investigate the performance of the spin classifiers in terms of computational
speed, misclassification rate, class histogram and spatial correlations
reproduction using simulated realizations of spatial random fields, real
rainfall data, and a digital test image. We also compare the spin-based methods
with standard classifiers such as the k-nearest neighbor, the fuzzy k-nearest
neighbor, and the Support Vector Machine. We find that the spin-based
classifiers provide competitive choices.
