dimensionality was at least 256 (16*16). 
Still the discriminatory power of the 
transformed space was better or the same 
than by the five features of Haralick. 
The same applies for the power spectrum 
method compared to the descriptors of /Das- 
Jer84/. This is only true for the k-NN 
and ALSM classifiers, but not for the ML- 
classifier, showing again the problems 
involved in the ML-classif ication. In 
that case the performance of the classifier 
distorted the results so, that correct 
conclusion could not be made. 
| Descriptor 
! 
Classifier 
ALSM k-NN 
ML 
| Variance 
73/78 
77/78 
65/68 
| Cooccurence 
97/98 
98/98 
76/75 
| Fourier Spectrum 
93/98 
94/96 
75/77 
| Fractal-dimension 
76/89 
75/90 
69/80 
| Fractal-signature 
76/88 
76/90 
69/74 
1 AVHR 
94/96 
91/95 
77/78 
Table 1. Summary of the results in case of 1:15000 
aerial imagery. Precentage of correct 
classifications, without/with spectral 
features. 
| Descriptor 
1 
| Classifier 
| ALSM k-NN 
ML 
| Variance 
| 59/82 
59/82 
1 
55/61 
| Cooccurence 
| 86/97 
87/98 
69/82 
1 Fourier Spectrum 
| 74/94 
74/93 
65/77 
j Fractal-dimension 
| 71/94 
71/95 
69/81 
j Fractal-signature 
j 70/95 
71/94 
63/74 
1 AVHR 
1 80/93 
81/93 
70/74 
Table 2. Summary of the results in case of the SPOT 
image 1 (rural). Precentage of correct 
classifications, without/with spectral 
features. 
| Descriptor 
Classifier 
ALSM k-NN 
ML 
| Variance 
62/81 
62/82 
59/69 
j Cooccurence 
87/96 
87/97 
70/86 
| Fourier Spectrum 
71/92 
73/92 
65/82 
| Fractal-dimension 
71/94 
71/95 
69/81 
j Fractal-signature 
70/95 
70/94 
63/80 
| AVHR 
80/93 
81/93 
70/74 
Table 3. Summary of the results in case of the SPOT 
image 2 (urban). Precentage of correct 
classifications, without/with spectral 
features. 
Comparison of the descriptors 
Tables 1-3 summarize all the results. As 
can be seen no clear distinction can be 
made, but usually the cooccurrence statis 
tics yield the best results, achieving a 
very low error rate of 2-4%. As could be 
predicted, the larger scale imagery favors 
the more complex descriptors. At smaller 
scale images, also the very simple fractal 
descriptor produces good results (error 
rate of 7%) and it clearly competes the 
other simple descriptor, namely the varian 
ce . 
Against the expectations, the fractal sig 
nature does not bring more information as 
compared to the fractal dimension. This 
might be caused by the relatively small 
window size, together with the method of 
estimating the fractal signature. 
Contradictionary to the conclusion drawn 
in /ZhuDun90/, the AVHR seems to own a 
little bit higher error rate than the cooc 
currence statistics. 
In the SPOT images, it seems clear, that 
the textural descriptors alone cannot bring 
satisfactory results. 
Comparison of the classifiers 
As could be expected the ML-classifier 
behaves worst. No separation between the 
performance of the k-NN and ALSM-classi- 
fiers can be seen. 
5. CONCLUDING REMARKS 
The results indicated very clearly that 
the choice of a classifier is utmost impor 
tant, when texture classification is per 
formed. Both non-parametric classifiers 
used (k-NN and ALSM) can be highly recom 
mended in this context. The usage of a 
ML-classifiers should be avoided. 
For larger scale imagery some more complex 
measures are asked for, but in case of 
smaller case images, the simple descriptors 
based on computed fractal dimension in four 
main directions of a local window seem to 
work nicely and are computationally light. 
In the case of satellite images, the spect 
ral channels should be combined to the 
texture descriptors before reasonable 
results can be expected. 
The reason for these relatively optimistic 
results (error rates in the order of 5%) 
comes partly from the test data. Only 
ideal windows were used. In practical 
applications, the boarder areas of the tex 
ture areas cause some troubles and this 
test should be carried out also by using 
such indistinct areas. 
Although the result show promising out, 
one should not forget, that the methods 
applied, are all rather heuristic in natu 
re. The best way for texture analysis 
should be to model the whole sampling pro 
cess, e.g. with the help of stochastic 2D 
processes. We hope that in the future 
the algorithms and hardware implementa 
tions are powerful enough to utilize these 
more complete and more formal models. 
6. REFERENCES 
/Bajcsy73/ Bajcsy, R.: 
Computer Description of Textured 
Surfaces. 3rd International Joint 
Conference on Artificial Intelli 
gence, 1973, Stanford, pp. 572-579. 
/ConHar80/ Conners, R.W., Harlow, C.A.: 
A Theoretical Comparision of Textu 
re Algorithms. IEEE Transactions 
on Pattern Analysis and Machine 
Intelligence, Vol 2, No 3, 1980, 
pp. 204-222. 
/CovHar67/ Cover, T.M., Hart, P.E.: 
Nearest Neighbour Pattern Classifi 
cation. IEEE Transactions of In- 
338