Stefan Diener 
  
a) CIEXYZ (linear transformation, [Fairchild98]) 
b) CIE Lab (non-linear, [Fairchild98]) 
c) CIELuv (non-linear, [Fairchild98]) 
d) HL (linear, [Kao97]) 
e). HSI (non-linear, [Kender76]) 
D YCC; (linear, [Bourgin95]) 
We produced a couple of colour composites for test purposes. From a high resolution colour image we created a low 
resolution colour image (1/4 of width and height) and a high resolution panchromatic image to meet the requirements of 
the colour composite generation as described in section 3.1. We used the original image as a loss less reference for later 
comparisons. 
At first human observers took a look at the computed composite images. The results from the CIE XYZ transformation 
were a disappointment, because especially the green channel of the composites showed a big difference to the original 
image. This is only a consequence of the back transformation from CIE XYZ to RGB: 
R 19104. —0,5333 — 0,2891 |[ X 
G|=|-0,9844 1,9985 —0,0279 |! Y (3.1) 
B 00333  —01187 0,9017 \Z 
with X and Z as the colour valences and Y as the exchanged luminance. 
One can see that a change in Y is always doubled in the green channel of the composite. So this colour space 
transformation is not stable for variations in the high resolution panchromatic image. 
With this fact in mind it is surprising that the derived colour spaces CIE Lab and CIE Luv produce much less visible 
adulterations. This is caused by the additional non-linear transformation steps. CIE Lab and CIE Luv are quite stable 
and the resulting composites show a very good quality. 
The three other colour space transformations are stable too, but especially HSI showed noticeable differences in some 
cases. All computed colour composites were viewed by several observers but an objective comparison is needed. 
For a mathematical approach we computed the difference images between the composites and the original images. Then 
we calculated the RMSE for each colour channel from the difference images. As expected the RMSE produced by CIE 
XYZ was very high compared to the other transformations and CIE Lab and CIE Luv are very close to each other. 
Figure 3 shows the computed RMSE's relative to CIE Lab for all investigated colour space transformations. 
  
  
  
  
  
  
  
  
  
channel CIE XYZ CIE Luv CIE Lab lilola HSI YO,C; 
red 5.541 1.027 1.000 1.153 1.148 1.074 
green 7.058 1.004 1.000 1.382 1.446 1.040 
blue 2.939 1.062 1.000 1.188 1.124 1.119 
  
  
  
Figure 3. Mean above all sample images of the RMSE of the differences 
between original images and computed colour composites. All values are relative to CIE Lab. 
One might choose CIE Lab as the favourite transformation because it causes the smallest errors and the composite 
images look very well. But another important item is the achievable matching accuracy. 
The matching on colour images does not use all colour channels. Most applications pick a single channel, preferable the 
green one. We applied an affine transformation to the extracted green channel of the original images. The least squares 
matching algorithm had to match these images against the green channel from all the colour composites. The resulting 
affine transformation parameters were used to do the inverse transformation of the modified green channel of the 
original images. To compare the quality the difference between the back-transformed results and the original images 
were computed and afterwards the RMSE. The RMSE relative to the mean occurred error is shown is figure 4. 
  
86 International Archives of Photogrammetry and Remote Sensing. Vol. XXXIII, Part B1. Amsterdam 2000. 
  
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