5. EXPERIMENTAL RESULTS AND ANALYSIS 
Two high-resolution urban aerial images from Shanghai are 
employed in this experiment, both true color and color infrared 
aerlal images containing evident building shadows in each 
image. The experiment was done with MATLAB program. In 
order to analyze and get the proper p value of the Minkowski 
norm for aerial image shadow removal, we test different p (from 
1 to 10) on the above two aerial images in the experiment. 
5.1 Shadow removal experiment with true color aerial 
images 
The test image is a true color image, dated Dec. 2008; image 
area is Pudong, Shanghai city, with a resolution of 25cm/pixel 
and an image size of 2340x3624 pixel. In the experiment, the 
original image size was reduced to 585x906pixel; the space 
resolution therefore is 1 m/pixel. 
  
  
  
  
  
(a) (b) (c) p=2 
Figure 2. True color aerial image (a), the shadow detection 
result (b) and the results of shadow removal (c) 
Figure 2 (a) is the original image. Figure 2 (b) is the shadow 
detection result; the black area is shadow region (note a few 
errors at the edge of shadow region). Figure2 (c) is the shadow 
removal image when p is 2. 
  
   
  
    
   
   
   
  
    
   
    
     
    
   
   
   
    
   
   
   
  
  
  
  
   
   
   
   
   
  
  
  
   
  
   
In order to analyze the shadow removal result, the brightness, 
contrast and average gradients of the shadow and non-shadow 
regions are calculated separately in the original image band. 
Then, after shadow removal, the corresponding indices are 
determined likewise in the shadow region. Table 1 is the result. 
The three statistic indexes of shadow region are changed, when 
the value of p is from 1 to 10 in shadow removal processing. 
Figure 3 includes three statistical index trend charts of the 
shadow region. 
From the shadow removal resulting image, Table.l and the 
statistical trend chart (Figure 3), we find: 
(l)Compared with the non-shadow region, the brightness 
decreases more in the shadow region. It decreases sharply 
especially in red band because most light in the shadow region 
is scattered light from the sky, which contains more short-wave 
and less long-wave. The contrast and average gradients in the 
shadow region decreased also, but the degree of decrease in the 
three bands is the same. 
(2)The SoG shadow removal algorithm based on Color 
Constancy can recover the light conditions in shadow regions, 
especially for the red band. After shadow removal with p=2, the 
shadow region brightness in the red band is improved mostly 
from 38.76 to 70, and the contrast is close to the value in non- 
shadow region. Average gradients is improved too, but not 
improved as much as brightness and contrast. 
(3) From Figure 3, the change trend lines show that the 
brightness, contrast, and average gradients of three bands 
increase at first, then decrease slowly when p is a value from 
1-10. They achieve maximum value when p is 2. And when 
p-2, it also makes the shadow contrast and average gradients 
have a good agreement with this in non-shadow region. 
(4) The visual effect shows that the shadow region color is 
similar to non-shadow region and no visible color error exists 
after the shadow removal processing with the SoG algorithm. It 
follows that true color aerial images obtain the best result of 
shadow removal when p equals 2 in this experiment. 
Table 1. The brightness, contrast and average gradients of the true color aerial image before and after shadow removal 
  
brightness contrast 
average gradients 
  
ir g b r 
G b r g b 
  
Shadow region 38.7595 47.7784 |51.6944 |14.8921 |13.8919 [10.7231 |1.0603 [1.1871 11.1193 
  
1 76.1407 [81.1661 [74.9656 [29.2543 [23.5993 [15.5501 [2.0828 [P.0167 11.6231 
  
76.1734 [81.1875 [75.3754 [29.2669 [23.6056 [15.6351 [2.0837 [2.0172 (1.632 
  
73.5785 [80.0854 [75.4451 [28.2699 [23.2851 [15.6496 [2.0127 [1.9898 11.6335 
  
68.6354 [77.6796 [75.0428 6.3707 [22.5856 [15.5662 1.8775 1.93 1.6248 
  
63.2672 [74.2705 [74.059 24.3081 21.5944 |15.3621 11.7307 11.8453 11.6035 
  
53.979 (70.612 72.511 22.6605 20.5307 15.041 11.6134 01.7544 1.57 
  
55.9903 167.3786 [70.6091 (21.5122 |19.5906 [14.6465 [1.5316 [1.6741 1.5288 
  
53.9821 [64.8395 [68.6673 [20.7407 [18.8523 [14.2437 [1.4767 [1.611 1.4868 
  
52.6118 162.9679 166.9317 [20.2142 [18.3081 [13.8837 [1.4392 [1.5645 [1.4492 
  
  
— OQ [RTL] 
© 
51.6335 161.6297 165.5043 [19.8383 |17.9191 13.5876 |1.4124 [1.5313 [1.4183 
  
  
  
  
  
  
non-shadow region [76.1361 [81.1607 [74.9599 [29.3503 [23.6779 [17.4938 [3.4292 [3.2324 2.6647 
  
  
  
  
  
  
  
Figure 
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