| This thesis is concerned with the development of new methods to implement advanced spatial statistics procedures within Geographic Information Systems. Two approaches are investigated; the first uses Delaunay triangulation data structure to select an appropriate subset of the data and perform Ordinary Kriging interpolation. The second studies an advanced spatial statistics procedure, the optimal biased kriging, which is more efficient in terms of the Mean Squared Prediction Error.; Spatial statistical prediction, also called Kriging, has been proved to be an accurate and reliable interpolation method. However, geostatistical interpolation is a computationally very consuming process since it involves the inversion of a n*n matrix where n is the number of sampled points. The common way to overcome this problem is to include only “nearby” points in the Kriging process. Nevertheless, the choice of the Kriging points, we will call it support, has a significant effect on the accuracy of our prediction. Consequently, we will investigate the use of a well-established computational-geometry algorithm—the Delaunay triangulation—as a data structure to select our interpolation support. During this investigation we will develop an efficient algorithm and build up understanding about the statistical effect of a limited neighborhood on the interpolation. Moreover, we will test and evaluate the proposed innovative method using newly acquired aeromagnetic data collected at the West Antarctic mountains.; Optimal Biased Kriging is an efficient geostatistical method that gives up unbiasedness to gain improvement in the mean squared prediction error. We will apply this theory on a set of laser-scanning topographic data. In the implementation we will use a relatively new spatial coherency measure, the homeogram, also known as the non-centered covariance function. Moreover, we use a pre-interpolation spatial sorting to obtain a band-limited sparse coherency matrix. The sparseness of the coherency matrix is used to enhance the interpolation algorithm. |
