Thë International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part B7. Beijing 2008 
2.4. Decision process 
The statistical tools of least squares adjustments provide the 
mathematical foundation necessary to come with a valid 
analysis of the obtained results and automatically decide 
whether change occurred or not. During the execution of the 
matching loop, several criteria are considered such as Shift dX. 
A threshold of 0.5 pixels is set to classify a matching as 
successful. During the application of the least square matching 
process, a significant amount of visually successful matches 
was not correctly identified, because the value of the shift was 
not close to our threshold. The distinction between a successful 
match and an unsuccessful one is the range of dX. If the 
variation is less than 0.5 pixels, then the match is considered 
successful, otherwise rejected. 
Figure 4: GDs in the case of an edge represented by three levels 
3. RESULT AND DISCUSSION 
When multiple edges exist, they can result from the actual shape 
of the edge or random condition such as noise, shadow, 
different projection, etc. We compensate for theses effects by 
introducing a scaling factor describing the expected geometry of 
the edge. Two new GDs are created on the both side of the 
vector edge. The means of these GDs are assigned the values of 
//* ± dj depend on which side they are (Fig. 5). The standard 
deviation of the expected geometry GDs expresses the 
uncertainty of this information and it is defined as a constant 
based on the distance of each edge to vector edge i/, and d 2 ■ 
The value of standard deviation corresponds to value of d i 13 , 
for a threshold of 99%. The experiments showed that the 
standard deviation should be limited to 40% at the distance of 
standard deviation to compensate random condition. The 
mathematical expression of scaling factor is: 
(x-/j.-d t ) 2 (x-tu+d 2 f 
Kj(x) = Max{e ~ 2a ' ,e ~ 2cT ‘ }, (21) 
(■x-M,) 2 
G,(x) = e ~ 2a ‘ 
The weight distribution P(x) on the axes perpendicular to the 
vector edge is given by the following formula: 
P(x) = Max{K, (x) x G, (x), G 2 (x), K 3 x G 3 (jc)} (22) 
Figure 5: Gaussian distribution in the case of an edge 
represented by four levels 
The developed algorithm in this paper is implemented using 
Microsoft's visual C# Net < Visual Basic 6 and Esri's 
MapObjects ActiveX component. The datasets and assessment 
process is described as follow. The available datasets to test 
change detection algorithm performance is described in table 1. 
datasets 
properties 
Digital image of 
city 
• IslamAbad 
• 1/10000 
• 1988 
• TIFF format 
Digital image of 
city 
• The same 
area(IslamAb 
ad) 
• 1/10000 
• 2002 
• TIFF format 
Vector 
information 
• 1988 
• Esri's 
shapefile 
format 
Table 1: datasets and their characteristics to test proposed 
methodology 
3.1 Evaluation of implemented system 
3.1.1 Accuracy assessment of developed least square 
matching algorithm 
The accuracy of the measurement refers to how close the 
measured value is to the true or accepted value. So, we have 
considered 50 buildings with known information in the test 
area, and compared the implemented system results with 
expected ones, in order to evaluate the accuracy of developed 
building change detection algorithm. The result of this 
evaluation has been shown in table 2. 
Comparison between expected and 
computed result 
Percentage 
(%) 
Buildings that algorithm can 
detect their changes correctly 
Upper 70% 
Buildings have changed but the 
algorithm can not detect their changes 
Under 10% 
Buildings have not changed but the 
algorithm detect changes; 
Approximately 
20% 
Table 2: the accuracy assessment of implemented system