# Full text: Proceedings, XXth congress (Part 7)

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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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