The International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences. Vol. XXXVII. Part Bl. Beijing 2008 
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Fig.5 IHS Transform Fusion Image based on Fig.l and 
Fig.3 
Fig.6 IHS Transform Fusion Image based on Fig.l and Fig.4 
Principal Components Analysis (PCA) Fusion 
Principal components analysis is a method in which original 
data is transformed into a new set of data which may better 
capture the essential information. Often some variables are 
highly correlated such that the information contained in one 
variable is largely a duplication of the information contained in 
another variable. Instead of throwing away the redundant data 
principal components analysis condenses the information in 
inter-correlated variables into a few variables, called principal 
components. Principal components analysis is a special case of 
transforming the original data into a new coordinate system. If 
the original data involves n different variables then each 
observation may be considered a point in an n-dimensional 
vector space. The change of coordinate system for a two 
dimensional space is shown below. 
Principal component analysis is a method that integrates multi 
variables into few variable. In terms of mathematic, it belongs 
to the technology of dimensional reduction. 
observation number. In some conditions, the total variable 
number is quite numerous and it’s not convenient for 
researcher to deal with the problem. In this condition, less but 
integrated variables are used to replace the original variables. 
For the integrated variables, the most information of the 
original variables should be reflected. 
During the fusion between LIDAR points and Ortho 
photomaps, there’re over 3 variables to indicate the pixel 
information including 
Coordinate Z , Intensity , R , G , B information. So the PCA 
algorithm can be used to built new variables for dimension 
reduction. 
Here, we consider R, G, B, Z and Intensity values as the 
original components. Since the resolution of image is quite 
huge, 1,000 pixels are selected as sample points to conduct the 
PCA. The eigenvalue and the contribution ratio is listed in the 
following table. 
inde 
X 
Eigenvalue 
s 
Contribution 
Ratio 
Cumulated 
Contribution 
Ratio 
1 
3.5693 
71.39% 
71.39% 
2 
1.0764 
21.53% 
92.92% 
3 
0.2941 
5.88% 
98.80% 
4 
0.0522 
1.04% 
99.84% 
5 
0.0080 
0.16% 
100% 
Table. 1 Eigenvalues and Contribution Ratio 
We use L to denote principal components load matrix which 
can also be get from PCA process. In this experiment, L = 
0.9372 0.9495 0.9446 0.6146 0.7207 
0.3198 0.2974 0.2711 -0.7035 -0.5632 
0.0350 0.0480 -0.0070 0.3569 -0.4039 
-0.1233 -0.0529 0.1842 0.0051 -0.0157 
0.0539 -0.0695 0.0159 0.0026 -0.0016 
Usually, we choose Eigenvalues that it’s corresponding 
cumulative contribution ratio is above 95% as new principal 
components. In this condition, new principal components, 
R\ ,G\, 51, are built as follows: 
p?l = 0.9372x R + 0.3198x G+0.0350x B - 0.1233x Z + 0.0539x Intensity (1) 
G\ = 0.9495x R + 0.2974x G + 0.0480x B - 0.0529x Z- 0.0695x Intensity 
[fll = 0.9446x R + 0.271 lx G- 0.0070x B + 0.1842x Z + 0.0159x Intensity 
Use the R\, Gl, B1 as the new RGB values of the fusion 
image. The fusion result are shown as the Fig.7. 
Assume the original data is given in the form of Z~ where the 
index i stands for the variable number and j for the 
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