SURFACE RECONSTRUCTION VIA TOTAL LEAST-SQUARES ADJUSTMENT OF THE SEMI-VARIOGRAM
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 appr...
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| Format: | Text |
| Language: | English |
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| Online Access: | http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.182.6579 http://www.isprs.org/proceedings/XXXVII/congress/3b_pdf/25a.pdf |
| Summary: | 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. |
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