The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
use least-square method. The fit-line slope is parameter B. With 
formula 2, he fractal dimension D, can be calculated out. 
According to the characters of fractal curved surface, the bigger 
the step for calculating the area of curved surface, the smaller 
the area of the curved surface. So the slope value of fitting 
curve is a negative number and the fractal dimension, parameter 
D, is between 2.0 and 3.0. This is accorded with fractal theory. 
The principle of triangular method is shown as Fig.3 (Zheng, 
2005). 
Fig.3 the principal of triangular method 
A grid formed by E, F, G and H, and their grey-level are named 
as P A P B P c , and P D . The grey-level of the grid central 
is Pq . It can be calculated by the formula (3). 
Po = № + P B + + ( 3 ) 
The curved surface area ABCDO is worked out by triangular 
formula. Then, a series of areas are calculated with specified 
steps. Selecting the step values as 1, 2, 4, 8 (The integer 
power of 2) in turn, we can get the 3D areas. With least-square 
method, double logarithm-fitting and formula (2) can to work 
out the fractal dimension of the remote sensing image. 
Fig.4 improved triangular method for edge detection of 
terrestrial LiDAR data 
In Fig. 3, points of E, F, G and H are the four comer of a raster 
grid, with grey value of the points formed their new position, 
points of A, B, C and D. As to terrestrial LiDAR data, the points 
of A, B, C and D in Fig. 4 are real 3D vectors. So it has 
coordinates system. Its original point is the basic point of the 
scanworld of LiDAR data. And formula (3) should be modified 
as formula (4) for one grid may contain a number of points. 
Po = (Pa+Pb + Pc + Pd + + P n )l n ( 4 ) 
n stands for the number of points in the grid. Then it 
calculates the fractal dimension values of grids. There are some 
basic rules for automatic judgments. 
• If the fractal dimension values of adjacent grids are close, 
then there are no edges contained in the grids. 
• If the fractal dimension value of one grid is different from 
one of adjacent grids, it or the adjacent grid contains edge. 
• If the target grid has two adjacent grids with different 
fractal dimension value, and the two adjacent grids are not 
opposite side, there is comer point in one of the grid. 
Comer grid 
Adjacent grid 
Comer grid 
Adjacent grid 
Target grid 
Adjacent grid 
Comer grid 
Adjacent grid 
Comer grid 
Fig.5 target grid and adjacent grids 
Then how to determine which point in which grid lie on the 
edge is a problem. It can be solved by quad tree methods. It 
means to divide related grid by quad tree and go back to carry 
out procedure from the beginning until it can’t be divided and 
found the edge points. 
After we obtain edge points, it links the neighbor points. Then 
calculate the slope of the line. If the slope of the line has distinct 
changed, the last point should be comer point. The thresholds of 
this judgment and that of different fractal dimension value rely 
on experience. The calculation can be easily conducted by 
Matlab. 
4. PROCEDURE OF LINEAR FEATURE EXTRACTION 
Before edge detection of terrestrial LiDAR data, some 
pre-processing measures should be carried out. 
• First, interference should be segmented from target data. 
Main interferences are trees and cars in front of building. 
As mentioned above, Fractal dimension theory provided 
effective way to distinguish man-made objects from 
nature ones. Here the research can use it to fulfill the task. 
• Second is to determine the size of grid. If grid size is very 
small, it will increase the computing volume. On the other 
hand, if the size is very big, this may make it easy to miss 
real edges because large sum of points in grid may make 
the fractal dimension values much closer, which would 
cause incorrect judgments. 
• Third is to obtain reasonable thresholds for edge detection 
and comer point’s judgment. And when the raw terrestrial 
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