International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences, Vol XXXV, Part B7. Istanbul 2004 
imageries that show the blueness of sky for all images. We call 
this index as Sky Index. 
Sky Index = (DNpje — DNgea) / (DNpjye + DNgea) (1) 
where DNgıue = digital number of blue channel 
DNgeq = digital number of red channel 
Here, we examined the relationship between the indexes and 
sampling pixels in various areas in order to refer the value of 
the boundary with blue sky and clouds (Table 1) 
Table 1. Sky Indexes at sampling pixels 
  
  
  
  
  
  
  
  
  
  
Sampling area / Colors |DN (Red) |DN (Blue) |Sky Index 
Clear sky / Blue 26 123 0.65 
2003/2/1 |Clear sky / Light blue 42 134 0.52 
at 9:48 |Stratocumulus / Grey 93 131 0.17 
Cirrus / Light grey 140 189 0.15 
Clear sky / Light blue 45 120 0.46 
2003/2/1 Clear sky / Light blue 60 127 0.36 
at 12:21 Cirrus / grey 83 116 0.17 
Cumulus / grey 79 111 0.17 
Cumulus /White 176 211 0.09 
Clear sky / Light blue 58 134 0.40 
2003/2/1 |Cumulus / Dark grey 64 95 0.20 
at14:00 Cumulus / Dark grey 81 113 0.17 
Cumulus / Light grey 169 207 0.10 
Cirrus / Light grey 157 192 0.10 
  
According to Table 1, the Sky Indexes of clear sky area show 
high values almost more than 0.3, on the other hand, cloud 
areas have low index values less than around 0.2. The value of 
the boundary is supposed to be between 0.2 and 0.3. 
3.2 Cloud distribution in hemisphere coordinates 
On the assumption that the fisheye lens dose not have any 
distortions, the relationship between the image coordinates 
(Xi,Yi) taken by Equidistant Projection and the hemisphere 
coordinates consists of zenith angle and direction (0, ¢) is 
expressed by following equations. 
Xi = (R-1)+R*sin(¢-180) *6/90 
Yi = (R-1)+R*cos(¢-180) *6/90 
@) 
0 = ((Xi - (R-1))?+ (Vi-(R-1)}*) *90/R 
when 0°<=d <180°, 
à = 180 - acos ((Yi-(R-1)) / R*(90/0)) /n*180 
when  1809?«- $ «360^, 
à = 180 + acos ((Yi-(R-1)) / R*(90/0)) /n*180 
(3) 
where 60; Zenith angle, $ ; Direction angle (units; degrees) 
( 09«- 0 «— 90°, 0°<= $ «—360? ) 
R; the radius of circle filled with hemisphere area 
(Xi; Yi: Pixel Line of one specified image 
coordinates 
when the origin is the upper left of the image shown in 
fig.3(middle). 
  
The grid surfaces which are allocated by Zenith and Direction 
angles using equations (2) and (3) are generated. In this way, it 
is possible to understand cloud distribution viewed from the 
observation point by overlaying the grid surfaces of 
hemispherical coordinates to the clouds detection images. 
3.3 Procedure of cloud cover estimation 
Used fisheye lens has the equidistant projection, so that the 
numbers of pixels dose not correspond to the area which we can 
see in hemisphere from the observed point. Therefore, the 
cosine correction of zenith angles must be done for each pixel 
to estimate cloud cover. The procedure to calculate the ratio of 
the detected clouds to the whole sky area describes as follows: 
1) Generating grid allocated the value of cosine zenith angle 
2) Summation of values of cosine zenith angle corresponded 
to all pixels in the masking image in fig.3 (right) 
3) Summation of values of cosine zenith angle corresponded 
to pixels which is detected as cloud area 
4) Calculating the ratio of 3) to 2) as cloud cover 
4. RESULTS AND DISCUSSION 
4.1 Clouds detection 
Figure 4 shows the original RGB images and the Sky Index 
images, which are illustrated with the contours of 0.1 intervals 
Sky Index. 
Eg--0 
(71023 - 025 
[71025 - 03 
2 [03-04 
E304 -05 
, EEO05-06 
2% M06-1 
- Contours of 
/ Sky index 
(0.1int.) 
Figure 4. Comparison with RGB (left) and Sky Index (right) 
images taken at two different times on 7" February, 2003 
These two samples are taken at 12:23 (uppers) and 8:56 
(lowers) on 7^ of February 2003. Two Sky Index images (fig.4 
right) are classified to ten classes by considering Table 1. As for 
between 0.2 and 0.3 of Sky Index, three classes are set as 0.2- 
0.23, 0.23-0.25 and 0.25-0.3 (see the legend in fig.4). By visual 
interpretation, it is seemed that the boundaries of the blue sky 
and clouds are shown around between 0.2 and 0.25. These 
trends are looked in the others of Sky Index images. Therefore, 
we define the value of boundary as 0.23, and then apply the 
other images to detect cloud areas in this case. 
Figure 5 shows the comparison with the hemisphere RGB 
image, its Sky Index and clouds detection images as one 
example taken at 12:53 on 1* of February, 2003. 
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