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FRACTAL_BASED ANALYSIS AND REALISTIC DISPLAY 
THE THEORY AND APPLICATION TO DTM 
Qing Zhu, Remote Sensing and Informatics, WTUSM 39 Luoyu Road,Wuhan 430070,P.R.China 
Commission IV, Working Group 4 
KEYWORDS: DEM/DTM, Analysis, Visualization, Reconstruction, Adaptive Fractal Interpolation, Fractal Features H 
and o. 
ABSTRACT 
3-Dimensional(3-D) surface representation and reconstruction and surface analysis are important problems in variety 
of disciplines including geographic data processing ,computer vision,computer graphics,computer-aided design,and so 
on. The current terrain analysis successively derives contours or slopes and aspects to represent the local details of 
terrain features. However,it is still the most difficult problems to extract the global features of terrain surface such as the 
roughness and terrain types which are more and more necessary and important for creating precise construction 
cost's economic model, land classification and planning,assisting image interpretation of remote sensing etc. After 
introducing the fractal Brownian model (fBm) as a mathematical model for describing real natural surface,the author 
presents two parameters H and c which respectively represents the complexity and global slope of surface. This paper 
also analyzes its physical meanings and introduces the estimating method . The combination of H and o can 
completely represent the global and local features of complex surfaces. 
3-D reconstruction is very important for comprehension of terrain structure and facilitating its automatic manipulation 
and analysis.Because of the irregularity and complexity of natural surface detail,the realistic modelling of earth surface 
is one of the most challenging problems.Since the current methods always omit the details and over smooth the 
natural surface,this paper presents an adaptive local stationary fractal interpolation technique to model the real terrain 
details realistically.Compare with other fractal models,the author's proposal is more complete theoretically and can 
generate more realistic geometric texture. 
The research results achieved in this paper have solved some crucial problems in digital terrain analysis and 3-D 
terrain reconstruction, which have potential applications in 
planning etc. 
1. INTRODUCTION 
3 D surface representation and reconstruction and 
surface analysis are important problems in variety of 
disciplines including geographic data processing, 
computer vision, computer graphics, computer-aided 
design, and so on. To achieve its goal, to describe 
efficiently the shape of a complex surface such as 
irregular natural terrain surface is a key problem. Usually, 
a set of simple shape primitives such as spheres, 
cylinders, cones, and cubes are used to define the shape 
of man-made object. However, such an approach is not 
suitable for describing natural shapes, since it requires a 
huge amount of data and computation to describe them 
in detail, this is too difficult to accomplish. In recent 
years, fractal geometry is considered as a hopeful model 
for this purpose(Yokoya et al.,1989).Specially, the fractal 
‘Brownian function fBf (Pentland,1984),which is a 
mathematical generalization of Brownian motion, is very 
frequently used to describe such kind of complex 
surfaces, and in most cases, fractal dimension(or 
parameter H)is used to characterize the complexity or 
roughness of the shape. In fact, it is impossible to use 
this single fractal value to distinguish different surfaces, 
for example, the fractal dimension of runway at the JFK 
airport may be approximately the same as that of the 
Himalayas(Musgrave et al., 1989). Fortunately, we can 
GIS, surveying, civil engineering,and land classification and 
use another feature of fBf, i.e. the standard deviation o , 
to describe a surface more completely. In this paper, the 
author will develop the physical meaning of o, and 
presents a practical method for estimating H and c of a 
DEM. 
3-D Visualization will be used to enhance the user's 
perception and understanding of the structure and 
relations of spatial data, so many applications of GIS in 
present day need some kind of realistic and accurate 
display of existing landscapes to visualize the spatial 
query and spatial analysis. However, in most practical 
activities, the smallest shapes are always omitted during 
surveying, that means it is not feasible to obtain all the 
necessary data for the generation of realistic and 
accurate display. Moreover, because real terrain surface 
is usually crumpled and crenulated,the realistic modeling 
of earth surface is then one of the most challenging 
problems. Since the current methods always omit the 
details and over smooth the natural surface, this paper 
introduces an adaptive local stationary fractal 
interpolation technique to reconstruct the terrain details 
realistically and accurately. 
2. FRACTAL MODEL AND FRACTAL-BASED 
ANALYSIS 
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International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B4. Vienna 1996