The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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vertical edges and that of the shadow edges of vertical 
buildings. 
2.4 Assessment on the Shadow Division Threshold 
After tracking out the shadow edge of the vertical buildings 
using the operator of “the straight edge track under constraints”, 
the shadow division threshold is assessed. This procedure is 
composed of two steps which are eliminated the pseudo 
shadow edges and statistically calculating the grey pixels along 
the shadow edge. 
(1) Elimination of the pseudo shadow edge. 
The line edges at the vertical building extracted out in the 
above procedure are not all the shadow edges in fact which 
maybe roads at this direction, or the building edge. To assess 
the shadow separation threshold accurately, pseudo shadow 
edges must be eliminated out. Four constraints are combined to 
eliminate pseudo shadow edges and keep real ones. 
The first constraint is that great difference should exist between 
grey values of pixels at two sides along the shadow edges. In 
the experiment the threshold for the pixel grey value difference 
is set to be one half the image grey variance. The edges with 
similar grey pixel at two sides will be eliminated out using the 
constraint, for example, the linear road. 
The second constraint deems that the length of the shadow 
edge should not be too large whose threshold value is set to be 
the ratio between the real distance in the field and size of 
image pixel. Through this constraint too long linear roads and 
railroads will be excluded out. 
The third constraint supposes that the shadow edges, especially 
that of tall buildings will not be too over-dense. In the 
experiment it is deemed that there will not exist more than two 
edges in the certain distance at the direction right to the shadow 
direction. Over dense edges, such as roads and railroads in the 
high resolution image can be excluded out through this 
approach. 
The fourth constraint is the context information, which assumes 
the building vertical edges exist near the anti-sun side of the 
shadow edges, especially for the tall buildings. This constraint 
can be used as auxiliary rule to exclude pseudo shadow edge 
which is most advantageous for tall buildings. Moreover the 
grey constraint that the grey pixel value near the shadow edge 
at the anti-sun side is generally larger than that of the shadow 
can also be used to exclude pseudo shadow edge. 
These four constraints mainly consider the grey constraint, the 
geometrical constraint and context constraint. 
(2) Statistical calculation of pixel grey values at one side of the 
shadow edge. 
After exclusion of pseudo shadow edges, the remained edges 
are mostly that of shadow, which are called the supposed edges. 
Statistical calculation is reformed on the pixels with smaller 
grey values in the certain width along the supposed edge. The 
width is related to the size of the pixel. Try to find out the peak 
grey level g max in the histogram, and calculate the total grey 
variance <J Q . Then treat the pixels whose grey values are 
smaller than g max + k^(J 0 (k x =1.5 in the experiment) as 
samples and do further calculation of the average value and 
the variance CJ on these samples. In this approach, the false 
shadow pixels along the edge will be excluded out and only the 
true shadow pixels are remained for statistical calculation. 
Finally the grey threshold for the shadow separation is decided 
as JU + k(7 (k ] — 1.6 in the experiment). 
2.5 Verification of Shadow Extraction Results 
Binary separation is performed area based on the above 
assessed grey threshold. But perhaps the separated interested 
area is composed of not only the shadows but also the water 
areas and vegetations with smaller grey. Therefore false 
shadow areas need to be further excluded out through the 
verification of the extraction results. After validation, only real 
shadow areas will be kept. Before validation, speckle reduction 
and region division will be carried out firstly in the AOI (Area 
of interesting). Theoretically, region division can be carried out 
from any point in the adjacent area to the shadow and towards 
any direction. But it is difficult to realize in algorithm. In the 
experiment, region division mainly starts from the direction of 
sunlight (in Figure 2). Then region marking is done to find the 
belonging of the pixels and give the peculiar sign of the region. 
The 8-neighbourhood region marking algorithm is taken. 
Finally the contour of the region is extracted out. 
There are three rules for judging whether the region belongs to 
the shadow area. The first rule is that the area of the region is 
not too large and the length of the region along the sunlit 
direction is too long. The threshold of the area is decided upon 
the image resolution. The threshold of the length takes the 
pixels length corresponding to room in the field. The second 
rule is that certain boundaries of the region accord with the 
sunlit direction and there exists extracted building vertical 
edges in the anti-sunlit side near the region. The 3rd rule is that 
the average grey value of certain pixels in the anti-sunlit side 
near the region is obviously larger than the average grey value 
of the shadow. 
Figure 2. Division for the adjacent areas of shadow