文章基本信息

标题：Surface Reconstruction via Total Least-Squares Adjustment of the Semi-Variogram
本地全文：下载
作者：Burkhard Schaffrin ; Sibel Uzun
期刊名称：ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences
印刷版ISSN：2194-9042
电子版ISSN：2194-9050
出版年度：2008
卷号：XXXVII Part B3b
页码：141-148
出版社：Copernicus Publications
摘要：One well established technique to construct a surface that best fits to an observed scattered point cloud is based on the Kriging methodology that uses semi-variograms. It somewhat resembles least-squares collocation which, however, uses the covariance function to define spatial coherency. This approach requires the assumption of ergodicity for the underlying spatial process that ultimately determines the surface in need for reconstruction by pointwise spatial prediction and, thereby, avoids the restrictions that come with a parametric surface description. An essential part of the Kriging approach, though, is the estimation of the empirical semi-variogram which is usually found by employing a weighted least-squares technique to best fit a number of representative values, derived from the data set, that describe the average loss of similarity between surface heights over growing distances. As this semi-variogram regularly turns out to have a steep slope near the origin - where it matters most -, a better idea seems to be seeking a best fit on the basis of the Total Least-Squares (TLS) principle. This approach does guarantee that any measures of misfit are taken perpendicular to the adjusted curve rather then in the vertical direction. In the present contribution, an attempt will be made to quantify the improvement, due to the TLS adjustment, over the traditional weighted least-squares fit. An exemplary set of aeromagnetic data from West Antarctica will serve as a realistic application case for this novel approach to surface reconstruction
关键词：Surface reconstruction; Kriging; Semi-variogram; TLS