hat the axes 
rface types 
e separated 
avoided by 
nsupervised 
'ad of using 
l. 
rom human 
igure 4): 
number of 
t guess clas- 
ams of early 
sulting class 
by the cor- 
  
  
Flight 1 Flight 2 Flight 3 Flight 4 
4:30 MET| | 8:30 MET| | 11:30 MET| | 12:30 MET 
  
  
  
  
  
  
  
  
  
Registration 
  
4 channel 
temperature picture 
   
  
   
   
  
    
    
  
  
  
correlation with 
auss-function 
   
    
k-means 
classification 
  
  
  
  
———r classmap 
  
  
  
  
vegetation non vegetation 
  
  
  
  
  
  
  
  
Figure 4: Algorithm used to calculate vegetation maps by us- 
ing remotely sensed thermal data recorded at different times 
responding calculated mean value and standard devia- 
tion: if the correlation values are smaller than certain 
thresholds (we found the values of 0.8 for morning and 
0.95 for noon temperature histograms to be appropri- 
ate), divide this data subset by a new unsupervised 
classification into two subsets, if the number of pixels 
in each subset exceeds a certain threshold (e.g. 1 per- 
cent of whole image size) 
(The cross correlation Cx y between two sample pop- 
ulations X and Y is defined as: 
ON, (=i — 2) (vi — 9) 
JIE e - o] [zs - 0| 
  
Cxv — 
  
with N: number of samples, æ;: j-th element of X, 
y;: j-th element of Y.) 
3. repeat step 2 until the classmap is constant (a max- 
imum number of iterations should be provided, be- 
cause man-made surfaces cannot be assumed to have 
a Gaussian distribution; in our examinations 3 iteration 
steps yielded sufficiently good results) 
In all cases the initial seeds are calculated as random numbers. 
Of course correlation of a histogram with a Gaussian density 
function is not an adequate test for the hypothesis of normal- 
ity, but for our purposes it provides an appropriate measure of 
similarity and a feasible deduction of the required thresholds. 
The resulting classmap represents a division of the underly- 
ing scene in small subsets (10 to 20 classes in our test scene, 
depending on starting parameters), which can be assumed to 
have very similar heating behaviour. To separate the found 
classes into vegetation and non vegetation we took into ac- 
count the correlation value described above and the noon 
temperature's standard deviation of the underlying regions. 
For all classes representing vegetational regions the following 
observations hold: 
e the correlation value calculated from noon tempera- 
tures is greater than 0.9 
e the noon temperature's standard deviation lies between 
2.0? C and 3.5?C 
Through the correlation value threshold we can exclude 
classes consisting of small artificial areas with slightly dif- 
ferent heating behaviour which have too few pixels to form a 
class of them own (as it is always the case for several roofs). 
The histogram of noon temperatures of such a class consists 
of several peaks representing the areas and therefore yields 
small correlation values. 
The second observation concerns the inhomogeneity of vege- 
“tational surfaces. Man-made surfaces tend to have very small 
temperature ranges because of their homogeneity. Vegeta- 
tional surfaces have much broader temperature distributions 
because of shadow and the contribution of the underlying 
surface (bare soil in most cases), which can be related to the 
Leaf Area Index (LAI) (Smith & Choudhury 1991). Standard 
deviations greater than 3.5°C indicate a class representing 
various small man-made surfaces. 
We found that for classes representing non-vegetational areas 
either one or both of these observations do not hold, provid- 
ing us with a method to calculate a vegetation map of the 
underlying scene. 
5 RESULTS 
A one-time classification of the described scene does not 
yield a separation into appropriate classes. E.g. in many 
attempts light concrete and sparsely vegetated grassland fall 
into one class (as one would expect from the temperature 
curves shown in Figure 2). Here a subdivision of the re- 
sulting classmap according to the method described above 
always yields a more sophisticated classification of the under- 
lying scene. 
The effect of subdivision is shown in Figure 5. After an initial 
unsupervised classification with six classes, trees and a metal 
roof where mixed up in one class. Because of the correlation 
values being less than the threshold value a second unsuper- 
vised classification was performed that provided the division 
of vegetation and the metal roof. 
To test the robustness of the algorithm we classified the air- 
port scene a hundred times using random seeds and performed 
a pixel-by-pixel comparison of the resulting vegetation maps 
Intemational Archives of Photogrammetry and Remote Sensing. Vol. XXXII, Part 7, Budapest, 1998 23]