COMPARISON OF TWO METHODS FOR DERIVING SKELETON LINES OF TERRAIN 
T. Gökgöz, F. Gülgen 
Yildiz Technical University, Dept. of Geodesy and Photogrammetry Engineering, 34349 Besiktas Istanbul, Turkey 
(gokgoz, fgulgen)@yildiz.edu.tr 
KEY WORDS: Cartography, Comparison, Algorithms, Reliability, Method 
ABSTRACT: 
Skeleton lines of terrain, i.e. ridge and valley lines are essential features on topographic maps. A skeleton line is the one with 
minimum slope among the slope lines. Slope lines are the lines of the steepest slope. Skeleton lines are used for a wide range of 
aims, e.g. emphasizing land forms, generation of high fidelity digital terrain models, terrain generalization, determining 
characteristic points of contours, etc. There are several methods for derivation of skeleton lines from contours and digital elevation 
models (DEMs). The primary objective of this study is to compare the results obtained by two different methods. Firstly, the 
skeleton lines are derived with respect to the algorithm developed by Aumann et al. (1991) using the contours generated from the 
height points of the DEM in addition to the characteristic points of the terrain. After that, the algorithm developed by Chang et al. 
(1998) for derivation of the skeleton lines from only the height points of the DEM is used. The results are compared with the 
skeleton lines of the terrain drawn by the operator in the stereo models of the area. For comparison, some cartographic and 
geomorphologic properties of contours and skeleton lines (i.e. numbers, locations and lengths of skeleton lines, and relationships 
between the contours and the skeleton lines) are used as the measurements. As a result, the skeleton lines derived from contours are 
more satisfactory than that are derived from DEM. 
1. INTRODUCTION the rain water collectors, i.e. the lines connecting the lowest 
points of the valleys, and the ridge lines are the rain water 
Contours are the most important tools for representing relief separators, i.e. the lines connecting the highest points of the 
forms on topographic maps with their geometries, i.e. locations ridges, in cartography literatures. From the aspect of 
and heights. They are defined as the intersections between the cartography, the coherent relationships between the contours 
terrain surface and the leveling surfaces. A leveling surface and the skeleton lines could be expressed that they cross each 
contains the points of which heights are the same. other at right angle. 
Skeleton lines of terrain, i.e. ridge and valley lines could be Skeleton lines are used for (1) emphasizing the land forms such 
defined as the common paths of the steepest slope lines. In as ridge, valley, and pass represented by contours, (2) giving 
other words, they are specific steepest slope lines. A steepest some specific information to the users, e.g. mountain climbers 
slope line means the path traced along the steepest slope use ridge lines as the paths with minimum slope leading to the 
directions (Figure 1). tops of hills, (3) determining the borders between light and 
shadow in a hill-shading process, (4) deciding the political 
borders, (5) generation of high fidelity digital terrain models, 
(6) terrain generalization, (7) determining characteristic points 
of contours, etc. (Gókgóz, 1999). 
  
Actually, skeleton lines (especially ridge lines) are usually not 
contained in topographic maps explicitly. Nevertheless, certain 
land forms such as ridges and valleys find their expression in 
contours and digital elevation models, and the skeleton lines 
can be derived. 
N ré dius 2. DERIVATION OF SKELETON LINES FROM 
; x p CONTOURS USING STEEPEST SLOPE VECTORS 
    
  
  
Rem -p-—-—- 
  
In the first section, skeleton lines are defined as the common 
paths of the steepest slope lines. According to this definition, it 
is possible to trace enough number of steepest slope lines all 
over the area, and their common paths are determined as the 
skeleton lines, but a lot of time is required for this process. 
However, regions of the skeleton lines are already most 
probably known, i.e. there are their clues. Therefore, there is no 
need to trace too many steepest slope lines all over the area in 
fact. Skeleton lines, each of them is also a steepest slope line, 
Figure 1. Contours (solid and long dashed lines) and the 
steepest slope lines (short dashed lines) 
Aumann et al. (1991) describes the skeleton lines with the 
steepest slope lines as "... the skeleton line is the one with 
minimum slope among the steepest slope lines in the 
surrounding, thus also the longest one..." According to 
Finsterwalder (1986), it is mentioned that the valley lines are 
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