odes. 
e of 
final 
are 
, are 
; for 
hbour 
with 
X are 
g the 
using 
same 
rmed. 
ler. 
s not 
ample 
arzen 
sdure 
1able 
rithm 
with 
are 
um ds 
/ious 
and 
"ded. 
le at 
)jokup 
ature 
it in 
are 
) the 
° the 
BI 
curs 
js in 
is to 
id be 
t be 
ther 
all, 
les. 
near 
be a 
ipal 
) or 
ireat 
hree 
lity 
b)), 
The 
the 
ates 
tion 
| can 
data 
ipal 
able 
this 
lled 
few 
thod 
hich 
of a 
e is 
» It 
is a space saving information about some small 
area of feature space which cover the sample set 
Sq. Every part of the table corresponds to the 
three-dimensional array again. But the range in 
every dimension is much smaller. During the 
classification of certain sample the appropriate 
terminal node is found and the key is computed. But 
this key serves as an entry to the "local" lookup 
table. It is necessary to estimate the average 
space needed for every part of main lookup table. 
This space can be estimated after the creation of a 
tree structure. All training samples from the 
corresponding terminal node are used and the range 
in every principal component is determined. 
4. CONCLUSION 
The methods described have been succesfully applied 
at the Earth Remote Sensing Centre (Institut of 
Surveying and Mapping) in Prague, especially for 
the classification of TM data. Several thematic 
maps from the Northeast Bohemia and Prague region 
have been produced. 
The CPU times requirements depend on the number of 
spectral classes as well as on the number of the 
training samples. In fact, the performance of the 
proposed algorithms depends upon the spatial 
configuration of the data set in the feature space. 
The influence of the number of classified pixels 
can be substantially reduced when using the method 
described in 3.5. 
The average number of pixels was approximately 400 
for every Tlanduse cathegory in Prague region. The 
number of spectral cathegories was 12. Then the 
time requirements on IBM PC 386 personal computer 
for 106 pixels when using the 6 TM bands (the 
thermal band has not been included) were: 
- nearest neighbour (1-NN) classification - 15 min. 
- 5 - nearest neighbours classification - 60 min. 
(both nearest neigbours classifiers were 
implemented according to the part 3.4) 
- Bayesian nonparametric classification 
(basic algorithm) - 88 min. 
- Bayesian nonparametric classification 
(algorithm according to the part 3.4.) - 51 min. 
- Bayesian nonparametric classification 
using lookup table - 46 min. 
The probability estimates of correct classification 
were similar for all methods (using the 
resubstitution method) and exceed 90 %. 
In certain situations it is desirable not to 
classify samples which cannot be assigned with 
sufficient certainty. Such samples are marked as 
nonclassified. This "reject option" can be 
implemented with the  classifiers using the 
nonparametric probability estimates easily. If the 
extent of nonclassified areas is too large, it is 
necessary to complete the training sets and to 
repeate the classification process. 
5. REFERENCES 
Cervenka, V., Charvat, K., 1990. Digital processing 
of pictorial image data in remote sensing (in 
Czech). Tech. Rep. No 33/1990, Geodetic and 
cartographic enterprise, Prague - Czechoslovakia. 
Charvat, K., Cervenka, V., 1987a. The Development 
of Classification and Segmentation System (in 
Czech). In: Digital ‘image processing 87, CSVTS 
TESLA A.S.Popova, Prague - Czechoslovakia. 
Charvat, K., Cervenka, V., Soukup, P., 1987b. Using 
Statistical Tests for Computation of the 
Classification Parameters in Remote Sensing of 
Earth (in Czech). In: Application of Artificial 
Intelligence AI '87, UISK, Prague - Czechoslovakia. 
Charvat, Ks Cervenka, V. 1990. Pseudocolor 
photomaps production using neural networks. In: 
International symposium on thematic mapping from 
satellite  imagery., Paris - France, Bulletin of 
French Committee for Cartography, No 127 - 128, pp. 
75-78. 
Cover, T. M., Hart, P. E., 1967. Nearest Neighbour 
Pattern Classification. IEEE Transactions on 
Information Theory, Vol. IT-13, January, pp. 21-27. 
Crist, F. P., Cicone, R. C., 1984a. A Physically 
Based Transformation of TM Data - the Tasseled Cap. 
IEEE Transaction on Geoscience and Remote Sensing, 
No. 3. 
Crist, F. P., Cicone, R. C., 1984b. Comparisons of 
the Dimensionality and Features on Simulated 
LANDSAT 4 MSS and TM Data. Remote Sensing of 
Environment, Vol 15. 
Fahlman, S. E., 1988. An Empirical Study of 
Learning Speed in Back Propagation Networks. tech. 
Rep. CMU-CS-88-162. 
Feiveson, A. H., 1983. Classification by 
thresholding. IEEE Transactions on Pattern Analysis 
and Machine Intelligence, PAMI-5, January, pp. 
48-53. 
Fukunaga, K., Narendra, P.M., 1975. A Branch and 
Bound Algorithm for Computing k-Nearest Neighbours. 
IEEE Transactions, Vol. C-24, July, pp. 751 - 753. 
Hinton, G. E.,; 1987. Connectionist Learning 
Procedures, Tech. Rep., CMU-CS-87-195. 
Parzen, E., 1962. on Estimation of Probability 
Density Function and Mode. Ann. Math. Statist., 
Vol. 33, pp. 1065-1076. 
Skidmore, A. K., Turner, B. J. 1988. Forest Mapping 
Accuracies Are Improved Using a Supervised 
Nonparametric Classifier with SPOT Data. 
Photogrammetric Engineering and Remote Sensing, 
Vol. 54, October, pp. 1415-1421. 
Tomek, I., 1976. A Generalization of the k-NN Rule. 
IEEE Transactions on Systems, Man, and Cybernetics, 
Vol. SMC-6, February, pp. 121-126. 
Wilson, D., 1972. Asymptotic Properties of Nearest 
Neighbour Rules Using Edited Data. IEEE 
Transactions on Systems, Man, and Cybernetics, Vol. 
SMC-2, pp. 408 - 421. 
877