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Ph.D. Theses

Contours to Digital Elevation Models: Grid-Based Surface Reconstruction Methods

By Michael B. Gousie
Advisor: W. R. Franklin
April 9, 1998

This thesis presents several new approaches to the problem of creating a terrain surface from contours on a regular grid. Previous solutions often generate surfaces with several kinds of artifacts, most notably terraces. The solutions presented in this thesis minimize the terracing effect while creating surfaces that are globally accurate.

The first technique improves upon previous thin plate approximations. The Intermediate Contours method creates additional contour lines in between the existing contours to alleviate the terracing problem. The Maximum Intermediate Contours method extends this idea to the creation of an initial surface by continually computing intermediate contours. Because peaks can not be computed by intermediate contours, a novel approach for computing such areas using Hermite splines is presented. Gaussian smoothing is applied to smooth the final surface.

The second technique makes use of slope information in an initial surface approximation to create ``gradient lines." These gradient lines are paths that follow the steepest slope from local minima to local maxima. An interpolating spline is fit along the paths to create a surface. Thin plate approximation techniques are applied to produce the final, smooth result.

Finally, an interpolating spline method is presented which computes good quality surfaces faster than the aforementioned techniques. Catmull-Rom splines are computed in the horizontal and vertical directions to create an initial surface which is then smoothed with the Gaussian smoothing function.

All of the surfaces created by the new methods are qualitatively analyzed. The generated surfaces are also compared to current US Geological Survey standards. Accuracy and smoothness criteria show that the surfaces computed by the new methods are quantitatively superior than previous techniques.

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