IMPROVING DIGITAL ELEVATION MODELS THROUGH BETTER SAMPLING METHODS 
Walker Gomes MSc 
Head of Atmospheric Science Division 
Centro Tecnico Aeroespacial 
12225 - Säo José dos Campos - Säo Paulo 
Brazil 
Commission IV 
ABSTRACT : 
This paper presents a new method for acquiring data points from topographic charts to be used on Digital 
Elevation Models (DEM's) generation. The DEM's accuracy are strongly influenced by the original data Points 
position and grid regularization procedures (to obtain a rectangular grid). The first step was the 
understanding of the errors sources and their propagation. In order to put into practical use the new 
method, it was tested on a Geographical Information System which had a traditional data point acquisition 
method; based on nearest neighbors interpolation. The new method is based on fact that some algorithms first 
check the data input. If the original data are on unfavorable positions it automatically, through special 
procedures, chooses other data inputs. A linear interpolation is used on favorable circumstances, and Akima 
cubics interpolator on more difficult situations. It was used an IBM-PC-XT compatible computer, and the 
algorithms are fast enough for practical use. The examples have shown an excellent improvement over the 
traditional nearest neighbors interpolations. 
KEY WORDS: MDE, GIS, 3-D, computer graphics. 
1. INTRODUCTION Although this approach is largely used in other 
types of modelling, it is not adequate for modelling 
It is well known that there isn't a single perfect from contour lines. 
interpolation method, and that the required 
Precision is a function of the model ‘'s application. 2) Maybe the most popular of all is a linear 
While a given model can prove excellent for some interpolation along certain axes. The number of axes 
usages, it can be inadequate or even useless for may be one, two or four, and interpolation is based 
others. on a weight average of the elevations of the 
supporting contour lines. When it's used one axis 
In this sense, it's believed that there can be a the sampling would be very poor on some regions, 
large number of users interested in a DEM generation compromising the interpolator per formance 
technique with the following characteristics: (Gomes, 1990a). On two axes, sampling is generally 
good, but in some cases it causes serious errors as 
- Low cost. shown in Gomes, 1990a. These problems are 
- Contour lines extracted from topographic charts significantly reduced on four axes, but some errors 
as data source. still can be found in some few places, apart from 
- IBM-PC-XT hardware or better. the considerable increase in computing time. 
- Very high resolution for a large number of 
applications. 3) The most recent works make use of four axes 
sampling, and use the steepest profile together with 
The Proposed method is designed to be a specialized cubic interpolation.  (Legates & Willmott,1986). The 
system intended for use under the constraints performance of these methods has shown to be better 
mentioned above. Within this frame, a method was than the former ones, but they significantly 
searched that could be both accurate and simple increase the computing effort. 
enough to be compatible with the data source and 
hardware used. 3. ERROR TYPES 
The quality of DEMs is closely dependent on sampling In general terms, the errors associated to grid 
and interpolation processes, and it's possible to regularization can be divided in two large classes, 
say that sampling is paramount because there is no which it will be called Type 1 and Type 8 errors. 
way to obtain good results from any interpolation 
method if the samples are of poor quality. 3.1 Type i error 
So, after a series of experiments with linear, cubic This error occurs when the algorithm for sample 
and bicubic  interpolators (Gomes, 1990a), it was selection chooses non-representative data, even 
chosen to make use of (1) linear interpolation for though they exist. The Figure 1 is an example of 
the most part of model generation, (2) cubic this kind of error when the nearest neighbors 
interpolation in the cases where linear interpolator is used for each quadrant . 
interpolation presents difficulties, and (3) bicubic 
interpolation for grid densification. 3.2 Type 2 error 
2. EXISTING METHODS In opposition to the type 1 error, this error isn't 
: caused by the data choice algorithm, been due to the 
Literary review indicates three different approaches not existence of good samples in the regions where 
for modelling: this error can be found. Figure 2 shows an example 
; where equal samples chosen by the nearest neighbors 
1) It's assumed that the relief data are randomly method will be encountered both in area A (peak 
related, and a local sampling Process with region) and area B (valley region), causing both 
interpolation as a function of distance is used Peaks and valleys to become flatten. 
(e.g. Barnes,1964). 
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