The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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The conversion assumes equal-interval mapping of elevation 
parameter to grey scale, as showed by the formula (1). The 
variance of grey pixels actually reflects the up and downs of 
terrain surface. PFF can be implemented directly based on the 
pixels’ grey scale value, if the mapping isn’t greatly smoothing 
the elevation information. 
h..-h 
G = — —-255 
IJ h - h- 
(1) 
where hy = current point’s elevation value 
h max , h mm = area’s largest and least elevation value 
Gy = current point’s corresponding grey scale 
From the counterpart aspect, the equal-interval conversion also 
has the effect of noise-filtering for elevation-measurement data, 
which reduces the influence of earth surface’s fine fluctuations, 
such as little potholes, low shrubs and etc. 
2.1.2 Edge extraction 
Edge extraction is the key circle for automatic determination of 
rivers’ location and distribution. Simultaneously it establishes 
the bridge between LiDAR data and RS images embodying the 
terrain objects’ spectral information. 
Adaptive wavelet transform-based edge extraction methods 
give solutions for river edges’ acquiring. LiDAR images are 
duller compared with optical images, because pixel element 
reflects ranging and suffers less disruption factors. The relative 
process of de-noising is less complex. So edge extraction is 
usually based on Prewitt operator applicable of lower frequency 
(Hong, 2006). 
The concrete parameters are achieved as the first derivative of 
the smoothness function, and the two elements of 2-dimensional 
2-grade wavelet transform is equivalent to the two elements of 
signal’s gradient vector after smoothness, as formula (2). 
r W x S(2 i ,x,yj' 
K W y S(2 J ,x,y) > 
(d - \ 
-(S*0j)(x,y) 
jr(S*0)(x,y) 
= 2 j V(S*0j)(x,y) 
(2) 
MS(2 J ,x,y) 
= yj\w x S(2 J ,x,y)\ 2 +\w y S(2 J ,x,y)\ 2 
(3) 
where 0(x, y) = smoothness function 
(W*. W) = 2-dimensional 2-grade wavelet transform 
S(x, y) = signal deployment 
MS(2 i , x, y) = maximum value function 
V(S*9j)(x, y) = gradient vector 
The value of gradient vector keeps direct ratio with the 
parameter MS. From equation (3) multi-scale edge detection 
using 2-grade wavelet transform at last lies in the local 
maximum value’s calculation. 
But edge extraction can’t identify similar terrain characteristics, 
which means that the recognition function should be enhanced. 
Natural rivers and artificial rivers have the similar edge results. 
And simple utilization of the elevation information is also not 
promising. On the surface with some extent of slope, the water 
surface of upstream probably is higher than the road surface of 
downstream. And this embarrassment enhances the necessity of 
automatic recognition factor’s introduction, such as profile. 
2.1.3 Skeleton generation 
Skeleton generation supplies the reference for following profile 
factor functions’ implementation. Edge detection of a channel 
will generate two anti-parallel edges from either side of it. 
Nevatia and Babu (Nevatia, 1980) describe an algorithm to 
associate edges together. After parallel edges’ association, the 
skeleton can be determined. 
As we know, the regions between two borders are generally 
highway surface or water surface, which are relatively flat. And 
the median regions can be considered as element sets with 
equivalent characteristic amplitude. So the traditional but stable 
Hilditch algorithm (Lam, 1992; Abe, 1994; Jonathan, 2007) 
suitable for binary image can be improved for skeleton 
generation in this pre-process. 
Simple Hiditch algorithm possibly adds false thinning sections, 
and its skeleton results sometimes are not in coincidence with 
the real centrelines. The improvements assume horizontal and 
vertical average individually as formula (4). Then the averaged 
point sets are used to modify the skeleton from the traditional 
Hiditch algorithm. 
f 
\ 
.It 1 1 \ 
i,—\m\ +n\ 
2 l ^.m* 255 1/5,„*255) 
P im<l< „* 255 
V 
=255&/5„ +1 =255 j 
where (i,j) = river’s median point’s horizontal location 
Pij = relating pixel’s grey scale value 
After the skeletons have been got, the equal-division points for 
given number of sections can be calculated. Then the cross- 
lines of the skeleton through the above segmentation points can 
be achieved. Then PFF can be carried out on the cross lines 
within the range of rivers’ average length. 
2.2 Profile statistics 
Automatic recognition based on profile factor still arises from 
the problems left by pre-process operations, as the traditional 
methods can detect grey-scales’ difference but can’t distinguish 
roads, natural rivers and artificial canals. Considering that 
LiDAR data is composed of ranging information, profile factor 
is one good choice to represent and determinate different terrain 
topographical categories. 
In river’s identification, after edge extraction operation there 
are commonly three types of terrain distribution with the similar 
features, namely artificial rivers, natural rivers and highways, 
whose shapes are generally in long strip. Experience knowledge 
tells us that their profiles are in different shapes, and the 
following statistical analysis of profile shape from real LiDAR 
data is conducted, as shown in Figure 1, 2 and 3.