The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
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evolution of the curve can be traced by its evolution time T , 
satisfmg the following function. 
|at|f = 1, (F> 0) 
(1) 
function (1) is one of Eikonal functions. It should be solved 
numerically due to the fact that it is difficult to be solved 
analytically. Rouy et al. proposed a very convenient upwind 
difference method (Rouy et al., 1992), in which solving 
function (1) is equivalent to solving the following quadratic 
function: 
[max(D..T,-D;T,0) 2 + rm\(D;/T,-D + /T,0) 2 ~\ 2 = — ( 2 ) 
where D7 X T = the forward difference of T . along x direction 
D* y T = the forward difference of T i} along y direction 
Dy X T = the backward difference of f . along x direction 
D~ y T = the backward difference of T i . along y direction 
The solving of function (2) not only requires the time f . to be 
known, but also requires the speed function F determined by 
the image features to be monotonely decreasing function 
(Caselles et al., 1997). The time T j} in LS-FM algorithm can be 
updated with the inserting, deleting and sorting operations of 
the minimum heap structure (Sethian, 1996a). 
3. FEATURES EXTRACTION FROM REMOTE 
SENSING IMAGES 
3.1 Features Extraction from Multi-spectral Image 
Both spectral and texture features are extracted from multi- 
spectral image for road detection. To make full use of the 
spectral information of road in multi-spectral remote sensing 
images and removing redundant information, three bands with 
close digital number to road but big digital number to other 
objects were selected to extract road from multi-spectral images 
with the following iterative difference algorithm: 
R n+i =|/?'’-G n | 
G n+ ' =\G n -B n \ 
\ R »+i Cj n+ 1 
S 
n+1 
= (R n+ '+G n+ '+B n+ ')l 3 
(3) 
where n = the iteration times 
Figure 1. Relationship between S and iteration times for three 
bands data of different objects 
Figure 1 shows the summary S of the spectral difference for 
different objects in the three bands after Yl iterations. It can be 
seen that there are obvious difference between road and other 
objects. And the higher the reflectivity of the object is, the 
bigger the S is. Only after 5 times of iteration, S of the object 
with lower reflectivity is going to zero while S of the object 
with higher reflectivity is still greater than zero. Thus, the 
contrast between road and grassland or water is enhanced and 
this presents a convient way to recognize the road from them. 
The texture information of multi-spectral remote sensing image 
is presented with the entropy value calculated from its grey- 
level co-occurrence matrix (Haralick et al., 1973; Anys et 
al., 1994). 
3.2 Features Extraction from Microwave Remote Sensing 
Image 
Spatial auto-correlation scales of microwave radar remote 
sensing image is calculated with the multi-layer and multi-scale 
Getis algorithm (Jin,2005; Yan et al.,2006). The distribution of 
the best spatial scale is used to present the cluster of the pixel 
values. And it is useful for the road extraction from the 
microwave radar remote sensing images due to the fact that the 
road often appears black in the images resulting from its low 
backscattering. 
4. SPEED FUNCTION DEFINITION IN LS-FM 
ALGORITHM 
The speed function in LS-FM algorithm is defined with 
different functions founded with different image features 
extracted above as well as the backscattering feature of 
microwave radar image. As for the spectral feature of multi- 
spectral image, texture and backscattering features of SAR 
image, the following function is used: 
Xj 
X’(i,i) 
#(*,./)“exp(.4-(J!'(i,./))*) 
fa 
(4)