The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B3h. Beijing 2008 
k is decided by the location of P in the aerial image. Connect 
the principal point and one end of line 1 which is nearer to 
principal point. Suppose ¡5 is the angle between this 
connective line and line 1, and calculate the value of)3, which 
can be examined whether line 1 is one of vertical edges. If the 
value of P is smaller than the threshold 8 , then line 1 is 
regarded as one of vertical edges which pass through the 
principal point. Otherwise, line 1 is not vertical edge. In 
conclusion, the vertical edges in image block P should satisfy 
the following conditions: 
X X, 
1) Ctga x <k< Ctga 2 (ctga l = —, ctga 2 = — ) ; 
J', ^2 
2) /3<8. 
3. CHANGE DETECTION FOR BUILDINGS 
The ground coordinates of buildings and their altitudes can be 
calculated according to the location and length of vertical lines. 
Meanwhile, there is some information contained in the three 
dimensional city models. For example, the coordinates of each 
point which is typical structure point composing the building, 
the topological relationship of typical structure points, and the 
relationship of each surface of the building(Zhu and Lin 2004). 
Then, the changes of buildings in this area will be obtained by 
comparing these two kinds of data. 
3.1 Localization of Vertical Edges 
Edge extracting is needed before extracting vertical edges in 
aerial images. There are several operators for edge extracting, 
for example, Laplacian operator, Roberts cross operator, Sobel 
operator, Canny operator and so on. And Canny operator does 
well for enhancing the signal-to-noise ratio and the accuracy of 
localization(Canetti et al. 1999). Hough transform is used to 
detect straight lines after obtaining the edges in images. The 
main idea of Hough transform is detecting straight lines in 
images, taking advantage of the duality for points and lines. 
And the prominent advantage of Hough transform is that there 
is little influence of noise and interrupted curves(Zhang 1999). 
The two vertices of building’s vertical edge correspond to 
building’s base and top separately in the object space. So, it is 
necessary to find out the relationship between the vertices of 
vertical edges and building’s base before calculating their 
coordinates. According to the mode of projection, the vertices 
which is nearer to the principal point is building’s base, and the 
farther one is building’s top. The point of building’s base 
located on the ground, so its coordinate can be calculated using 
the principle of frontage intersection. The point of building’s 
top has the same coordinates as that of building’s base in the 
direction of x and y. And the building’s elevation will be 
calculated by the projection difference which is the length of 
vertical edges as well. 
According to the principle of frontage intersection, a point’s 
homonymy point in the other image must be found before 
calculating its ground coordinates. Usually, image matching is 
an effective method to find the homonymy points rapidly. 
However, there is much difference for building’s texture in left 
image and right image, and it is not able to find the homonymy 
point accurately, using the method of image matching. 
Considering these problem, relative orientation is adopted to 
renew the positional relationship between the left image and 
right image in the photographic instantaneous. Then, a point’s 
homonymy point in the right image can be found according to 
its position in the left image and the element of relative 
orientation. There is a fact, what is worth to be noticed, that the 
position obtained according to the element of relative 
orientation is not the same as the position extracted in image 
directly, and the difference is existent. Therefore, another 
threshold is needed to ensure the computational accuracy of 
the building’s coordinates in the object space. If the difference 
is smaller than 8, , the average values of these two coordinates 
are regarded as the position of homonymy point, and calculate 
the position in the left image inversely corresponding to the 
average values. If the difference is larger than S 2 , this vertical 
line is regarded as an incredible line, and it will not be used for 
later calculation. In this way, not only the homonymy points 
can be found accurately, but also the precision of vertical lines 
extraction can be enhanced after correcting the error. Then, the 
method of frontage intersection is used to calculate a point’s 
ground coordinates, according to its coordinates in images. 
Based on the coordinates of building’s base, only a single 
image is needed to calculate the elevation of the building, 
depending on the projection difference of vertical edges in the 
image. As shown in Figure 2, point S is the perspective center, 
and a is the phantom image of line A which is one of building’s 
vertical edges. Then, the building’s elevation can be calculated 
as follows: 
dH 2 
fD + dH 
(1) 
where f = focal length 
H = flight height 
d = projection difference of building’s vertical lines 
in the image 
D = length between the perspective centre and 
building’s base in the object space 
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