| This thesis contains two parts. In Part I we develop a parallel algorithm to generate realizations in a rectangular or domain of a stochastic, isotropic, scalar field which is conditioned pointwise to a set of measurements using a kriging procedure. The field is characterized by heterogeneity variation described either by a two point covariance function C(r) or semivariogram γ( r) for pairs of points separated by distance r. We describe the implementation of the algorithms and present numerical examples with discussion.; In Part II we apply the theory of kriging to the problem of image segmentation. Consider a digitized (2D or 3D) image consisting of two univariate populations. Assume a-priori knowledge allows incomplete assignment of voxels in the image, in the sense that a fraction of the voxels can be identified as belonging to population Π0, a second fraction to Π1, and the remaining fraction have no a-priori identification. Based upon estimates of the short-length scale spatial covariance of the image, we develop a method based upon indicator kriging to complete the image segmentation. |
