Exceedence Probabilities of Local Maxima of Non-isotropic Random Elds, with an Application to Shape Analysis via Surface Displacements

Data used for the analysis of shape change has been modeled as non-isotropic Gaussian random elds, and local changes in shape are detected by local maxima of a random eld of test statistics derived from this data. In this paper we use the Sampson & Guttorp (1992) model for non-isotropy in which their exists an unknown mapping of the support of the data to a space in which the random elds are isotropic. We derive a simple estimator of this mapping, and use it to derive estmators of parameters required to nd the exceedence probability of local maxima based on the expected Euler characteristic of the excursion set of the test statistic random eld. The results are used to detect shape changes in the outer cortical surface of the brain.