SURFACE APPROXIMATION AND ON-LINE QUALITY ASSESSMENT IN DIGITAL TERRAIN MODELS (PHOTOGRAMMETRY)
Abstract
The properties of bicubic splines and their fitting to sets of observed terrain elevations are described. The fitting is done by applying the techniques of least squares adjustment. Particular attention is given to the case where the data points fall in a regular grid pattern. This condition permits the spline estimation to be performed by array algebra, which yields a computational advantage when compared to the more general case of observations at arbitrary locations. The techniques are applicable to data sets of any size; however, relatively small data sets (hundreds of points) are envisioned for an on-line application. The post adjustment analysis of the observation residuals for possible outliers is investigated. The necessity (imposed by array algebra) to locate all outliers in one pass, and the need to accommodate multiple outliers suggests an approach involving partial quadratic forms of the residuals. Externally studentized quadratic forms provide a means to construct test statistics which do not require the assumption of an a priori known reference variance, (sigma)(,0)('2). Restricting the test statistics to maximum occurrences is a useful strategy to locate the subset of observations which is corrupted by blunders. The distribution of this maximum statistic is approximated for various degrees of freedom by Monte Carlo simulation and by propagation of distributions. The effectiveness of this blunder detection strategy is investigated in a statistical experiment involving many terrain samples and four spline functions of different mesh density. The terrain samples are classified by finite difference descriptors into four classes corresponding to the four spline models. The choice of the model is found to be an important factor in the effectiveness of the blunder detection algorithm. It is believed that this approach to gross error detection is useful and very general, and it is recommended that experiments be made to study other photogrammetric adjustment problems. It is also recommended that the proposed method be implemented in an on-line collection system for DTM (digital terrain model) data.
Degree
Ph.D.
Subject Area
Civil engineering|Remote sensing
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