851 
4 ERROR INVESTIGATION OF DIFFERENT GENERALIZATIONS OF 
THE THERMAL IMAGE 
In this chapter we want to extent the concept of the 
adequate generalization level from non-spatial feature 
spaces of temperatures and land cover classes to the 
spatial domain of a remote sensing image. We do not 
yet want to classify the image but only do an enhance 
ment by generalization to show the main thermal struc 
tures like heat islands and cool air valleys in the 
temperature field of Klagenfurt. 
For this the original pixels (micropixels) were 
spatially generalized to larger areas by calculating 
the arithmetic mean values of these macropixels. Then 
the new temperature values were classified into six 
temperature classes and the resulting macropixelfields 
were plotted to visualize the result. An example 
of this procedure, which is fully described in Seger 
& Mandl 1985 is shown in Fig. 2. To illustrate the 
differences between the various micro- and macropixel 
radiation temperature fields some statistical parame 
ters shown in table 4 were calculated. There we see 
that the standard deviation decreases with increasing 
macropixelsize, which is due to the calculation of 
mean values. These mean values nearly are the same. 
The small differences can be explained by the increase 
of the standard error with increasing macropixelsize. 
The increasing median and modus values show,that with 
increasing macropixelsize the centre of the distribu 
tion is going towards the higher temperature values 
which is due to the positive skewnesses of all the 
distributions. We can also see that the range of the 
temperature values in the micro- and the macropixel- 
fields varies so that the temperature classes in the 
micro- and macropixelfields have to be changed in order 
not to get empty classes plotted (compare Fig.l and 
Fig.2). 
A variation in the range and the locations of these 
temperature classes can also be used to stress special 
aspects of the image like the heat islands in the 
inner city, when the classes are moved to the upper 
region of the temperature scale and the inner differ 
entiation of the forests and green areas, when the 
classes are shifted to the lower parts of the scale. 
Finally it was analysed which effect has a shifting 
of the macropixelgrid relativ to the original macro- 
pixelgrid when all other parameters (size of the macro 
pixels and temperature classes) are held constant. 
The 50 x 50 macropixelgrid was moved 10, 20 or 30 
micropixels in one direction parellel to the shorter 
side of the image. The structure of the temperature 
field is not changed very much and in table 5 the per 
centages of the macropixels which are classified into 
other temperature classes are listed. We can see that 
in a 30 pixel shifted grid more than 60% of the macro 
pixels fall into the same temperature class they had 
fallen in the original image which is due to the two 
fold generalization. 
All these investigations were done to analyse the 
effects of spatial generalization on the special urban 
temperature field in Klagenfurt. The generalization 
in Fig.2 (50 x 50 pixel macropixelfields, six tempera 
ture classes of this special location in the tempera 
ture scale) describes the desired picture of the town 
best. We see the heat islands (inner city, industrial 
regions, cut fields), the fresh air valleys and areas 
(woods around the built up areas, fields with maize 
crop, green belts around the town) and the mixed areas 
mainly the single-family-houses region which are cha 
racteristic for the town structure of Klagenfurt. 
5 REGIONALISATION OF THE RADIATION TEMPERATURE IMAGE 
USING CLUSTER ANALYSIS 
In chapter 4 spatial and radiometric generalization 
was used as image enhancement method to emphasize the 
thermal structures of the urban area of Klagenfurt. 
The next step of information reduction and generali 
zation is classification. Using an unsupervised clus 
tering' algorithm (SPSS-X procedure Quick Cluster) a 
regionalisation of the temperature field trying to 
Table 4. Statistical parameters of the micro- and macropixelfields 
Pixelfield size 
number of 
rasterfields 
Min. 
Max. 
Range 
Median 
Modus 
arithm. 
mean value 
stand. 
error 
stand. 
devia. 
skewness 
1 x 1 = 
5,4. m 
1 
2,568.797 
1 
256 
255 
100, 3 
93 
107,3 
0,017 
26,8 
1,4 
10x10 = 
538 in 
100 
25.839 
17 
200 
183 
103,7 
95 
105,8 
0,113 
18,1 
0,7 
25x25 = 
3364 in 
625 
4.191 
66 
161 
95 
105,2 
100 
105,6 
0,227 
14,7 
0,3 { 
50x50 = 
1,3456 
2.500 
ha 
1.071 
66 
147 
81 
105,7 
109 
105,4 
0, 397 
13,0 
0,1 
100x100 
5,3824 
= 10.000 
ha 
279 
71 
137 
66 
105,8 
118 
105,1 
0,694 
11,6 
- 0,2 
Table 5. Matrix of the change of 
direction, in % of all macropixel 
temperature classes. 
class membership of the macropixels 
s in the image, macropixelsize 50 x 
after shifting the macropixelgrid in one 
50 pixels, 1071 rasterfields, constant 
Class membership change 
from - to 
classified 
3 2 
temp. classes 
1 
lower 
no change 
1 
temp. 
classified 
2 3 
classes higher 
original 
data 
10 pixel shift 
8,6 
82,8 
8,4 
0,1 
10 pixel 
shift - 
20 pixel shift 
8,4 
83, 1 
8,3 
0, 1 
20 pixel 
shift - 
30 pixel shift 
0,2 
10,0 
81,2 
8,5 
0, 1 
original 
data 
20 pixel shift 
0,8 
13,2 
71,8 
13,5 
0,7 
10 pixel 
shift - 
30 pixel shift 
1,0 
14,5 
70,2 
13,6 
0,7 
original 
data 
30 pixel shift 
0,2 2,2 
17,3 
61,6 
16,9 
1,8 0,1