International Archives of Photogrammetry and Remote Sensing, Vol. 32, Part 7-4-3 W6, Valladolid, Spain, 3-4 June, 1999 
INTEGRATION OF DTMS USING WAVELETS 
M. Hahn ', F. Samadzadegan 2 
Department of Surveying and Geoinformatics, University of Applied Sciences Stuttgart, Schellingstr. 24, D-70174 Stuttgart, 
Germany, m.hahn.fbv@fht-stuttgart.de 
2 Faculty of Engineering, University of Tehran, P.O.Box 11365-4563 Tehran, Iran 
KEYWORDS: Wavelet Analysis, DTM Integration, Fusion, Multiscale Processing, Filtering 
ABSTRACT 
The number of sensors and techniques for the acquisition of Digital Terrain Models (DTMs) and the variety of applications based on 
DTMs have grown significantly during the last decade. As a result of that, DTMs exist with different spatial resolution and accuracy. 
For some areas, quite a number of DTMs is available or there is the task to update existing DTMs with new measurements, e.g. of 
higher accuracy. For merging given DTMs of a certain area, different possibilities exist, even though from a theoretical point of view 
not much attention has been paid to this topic so far. Probably the simplest procedure is to introduce the raster points of different 
DTMs jointly as observations into an interpolation process. 
In this paper, we present a new concept for the integration of DTMs based on wavelets. Wavelets can contribute to tasks for which 
multiscale aspects are essential. The concept considers two or more DTMs which may differ in resolution and accuracy. The three 
most important components of our DTM integration approach are the following: by wavelet decomposition and multiscale processing 
a DTM and its accuracy can be represented in a series of scales. Merging of two DTMs takes place on the same scale level, e.g. by a 
least squares fit. Finally, an integrated high resolution DTM is obtained by a wavelet reconstruction process. First experiments have 
been carried out to illustrate the procedure and gain insight into the achieved accuracy improvements of integrated DTMs. 
1. INTRODUCTION 
In recent years, wavelets have taken over a leading role in 
analysis and synthesis of signals. The wavelet transform is 
widely applied, e.g. in image processing for data compression, 
data de-noising and feature extraction but also in many other 
areas. 
Wavelet-based approaches show some favourable properties 
compared to the Fourier transform. The Fourier transform uses a 
complex exponential function to transform a signal into the 
frequency domain. The plane waves oscillate infinitely with the 
same period and do not allow localisation. Changing a signal in 
just one data point results in a change of the whole spectrum of 
this signal without a possibility to estimate the location of the 
change in the signal from the spectrum. A wavelet can be 
interpreted as a "small wave” or a generalised oscillation. In the 
wavelet transform, a shifted and dilated wavelet is used to 
analyse the signals. Thus, the wavelet transformation can be 
interpreted as a convolution or correlation of the signal with 
scaled versions of the wavelet. The degree of similarity between 
a part of the signal at a certain location and the scaled version of 
the wavelet gives the key input for feature extraction. Threshold 
strategies for the wavelet coefficients with small absolute values 
lead to efficient data compression with high compression rates, 
as well as to noise reduction schemes. For examples, please cf. 
Thierschmann, et al., 1997 and Pan and Schaffrin, 1999. 
Another important issue for the integration of DTMs are the 
conceptual developments in the area of data integration or data 
fusion. It is helpful to have an understanding of the methods 
and goals of integration or fusion. The following table is a 
shortened excerpt taken from Abidi and Gonzalez (1992): 
Signal/Pixel 
Feature level 
Symbol 
level 
level 
Methods 
estimation / 
correspondence, 
logical / 
combination 
attribute 
statistical 
combination 
inference 
Improve- 
of expected 
increased feature 
increase in 
ment 
variance, 
measurement, 
truth or in 
increase quality, 
value of addi- 
probability 
performance 
tional features 
values 
Table 1. Data fusion (adopted from Abidi and Gonzalez, 
1992, p. 37). 
On the feature level, the goal of fusion is to increase the feature 
measurement with regard to quantity or diversity. The symbol 
level pursues decision-related goals by aiming at an 
improvement of probabilistic decisions based on inference 
techniques. The situation on the signal level can be 
characterised by a wide range of estimation techniques which 
typically aim at improving the accuracy or more generally the 
quality of a state. 
The integration of DTMs falls under the category of fusion on 
the signal level. Our integration method consists of multiscale 
signal processing based on wavelets. Localisation provides the 
theoretical background that DTM information of multiple scales 
is combined according to its local spectral property. The goal is