The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3b. Beijing 2008 
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2. THE BUILDING SHADOW EXTRACTION UNDER 
MULTI-CONSTRAINTS 
2.1 Two Directions Determination 
image, the range of “b” is easily drawn, “ b min < b < b max ”, 
but “b” is treated as an integer during real track. The detailed 
track procedures are listed as follows. 
Two directions determination means deciding the direction of 
the building vertical edges and that of the shadow edges of 
vertical buildings by the auxiliary information. 
(1) For a given “ b ” and slanting ratio “ k Q ”, a “ y ” value can 
be calculated from the equation “y = k Q X + b”. During the 
In projective geometry, parallel lines in real scene converge to 
one point in image, which is called vanishing-point. Since all 
vertical edges of the building are parallel, they must have the 
intersection point in the image. In the frame image, the 
direction of the building vertical edge can be decided through 
the image nadir, whose coordinates can be calculated through 
the image’s exterior elements. For the other types of images, 
the determination of the building vertical edge is relatively 
more complex. Take the IKONOS image for example, while 
approximately vertical photography is done, the direction of 
the vertical edge can be approximately decided by the center 
point of each scan line. Other conditions, the direction of the 
vertical edge can be approximately decided by the angle 
elements of exterior orientation. 
Major buildings’ shadows, especially the vertical building’s 
shadows have the same direction in the image, which is also 
just the direction of sunlight. In other words, the direction of 
the shadow edges of vertical buildings accord with the sunlight 
direction. So the edge of shadow at the sunlight direction can 
be extracted first, and then building shadow can be extracted 
by calculating grey pixels along the structure line statically. 
Most satellite remote sensing data provide sun azimuth and 
zenith angle in the header file. For the aero remote sensing 
image, the direction of sunlight can be decided by the imaging 
time and the position of the imaged area. 
2.2 Edge Detection by Canny Operation 
After the direction of the building vertical edges and that of the 
shadow edges of vertical buildings are decided, useful edge 
detectors can be utilized to detect edges along these two 
directions. 
The canny operator is set up upon the optimal detection rule, 
the optimal detection rule and the mono-response rule. It can 
achieve good balance between noise restrain and edge 
detection and is the optimal choice for step edge under white 
noise contamination (J F Canny, 1986). 
first iteration, “ b ” is set to be “ b min Make ajudgement on 
the calculated value “(x,y)” to see whether the point “(x,y)” is 
the feature point. If it is the feature point, note the value as the 
first value and the current tracking point, else abandon it and 
increase the number of “x” by one, until find the first feature 
point. 
(2) Increase the “x” by one, you can get another point “(x,y)”. 
Under if the circumstance that the newly tracking point is 
known, the distance “Dl” between point “(x,y)” and the newly 
tracking point is larger than the threshold value “dl” and the 
distance “D2” between the first tracking point and the newly 
tracking point is larger than the threshold value “d2”, the line 
between the first tracking point and the current tracking point is 
traced out and is saved. If “D2” is no larger than threshold “d2”, 
abandon the line. As long as “Dl” is larger than the threshold 
value “dl”, set the marking “flag=l” and be prepared to trace 
another line. Make adjudgment on the point (x,y) and its eight 
neighbourhood points to see if they are feature points. As long 
as one of these nine points is the feature point, take it as the 
current tracking point. Moreover, if “flag=l” is satisfied at the 
same time, set this new feature point as the starting point of the 
new line and make “flag=0”. 
y I 
Figure 1. Straight edge track under constraints 
To avoid interruption from unnecessary edges and facilitate the 
subsequent edge extraction, the Canny operator is applied at 
not the all direction but only the direction of the building 
vertical edges and that of the shadow edges of vertical 
buildings. 
2.3 Straight Edge Track under Constraints 
Since the Canny operator has detected edges along these two 
critical directions, the subsequent work is to track and extract 
these detected edges using the straight edge track algorithm. 
For example, if the edge has “ 0 ” angle to the positive 
direction of the “x” axis, the slanting ratio of the edge line can 
be deduced from “ 0 ”. Supposing the line equation is 
“ y — k 0 X + b ”, then “ b = y — k Q X ”. For any given 
(3) Continue step (2) until the value of “x” equals to the width 
of the image. Trace out all the lines (“ k — k Q , b — b ”) 
whose length are greater than the threshold value “d2”. 
(4) Increment b by one, and repeat step (1), (2) and (3) to trace 
out all the lines with “ k = k Q ” whose length are greater than 
the threshold “d2”. 
(5) Repeat step (4) until il b = ¿ max ”. Trace out all the lines 
with “ k = k Q ” whose length are greater than the threshold 
“d2”. 
All the edges can be successfully traced out, whose length are 
great the threshold value along the direction of the building