= [) are known we 
AP by applying equa- 
ven if M and J are 
ly the MAP as given 
jblem some alternat- 
Dubes & Jain, 1989]. 
ve simulated anneal- 
which find MAP es- 
As the computational 
erable there are two 
s to the MAP estim- 
' conditional modes) 
r of posterior margin- 
\ethods can be found 
therein. We will cen- 
[Besag, 1986] which 
ent trade-off between 
ion and the required 
rrection using a MRF 
correction methods. 
ed-probability models 
ession given in equa- 
, the contextual cor- 
of the MAP expres- 
ditional independence 
n a spatial neighbor- 
¢ et al., 1985]: a) the 
ind b) the Owen and 
| models in this work. 
the classifications ob- 
cribed in section 2.1, 
lassifications for each 
f the classifiers are two 
3reenland, Denmark! . 
SS image of the lga- 
SAT-5 TM image of 
e 512 x 512 pixels in 
cted by expert geolo- 
ir spectral distribution 
criminate, the training 
s a slight overlapping 
| training samples. In 
iscriminate, the train- 
there is a high over- 
the training samples. 
details. 
t sample estimation to 
ions. The training set, 
(learning set) and 7" 
ng randomly 2/3 of the 
der are placed into 7 '. 
e classifier and the test 
show the learning and 
iversity of Technology, Lyn- 
mages used in this work. 
ina 1996 
   
    
   
  
   
   
   
   
    
  
   
    
   
   
   
    
    
    
   
   
    
   
  
  
  
  
   
   
   
    
   
   
   
   
  
  
   
    
   
   
   
    
   
    
  
   
    
   
    
    
   
  
  
T class quem TTE Sun 
  
  
1 3806 1919 5725 
2 1542 3830 |. 11372 
3 5463 2768 8231 
4 2796 1395 4101 
5 8834 4443 | 13277 
  
  
  
  
  
  
  
  
  
[| Total | 28441 | 14355 | 42796 | 
  
  
Table 1: Learning and test set size. Igaliko. 
  
  
I Class | 9g FT | Sum || 
if 2464 | 1234 3698 
  
  
2 843 392 1235 
3 413 194 6071 
4 196 83 279 
5 480 234 714 
6 476 233 709 
7 178 77 255 
8 344 149 493 
9 52 21 73 
10 187 79 266 
11 94 33 127 
12 656 313 969 
13 144 64 208 
14 369 167 536 
15 227 96 323 
16 192 81 273 
17 274 119 393 
18 453 220 673 
19 271 118 389 
20 247 107 354 
[ Total | 8560 | 4014 | 12574 
  
  
  
  
  
  
  
  
  
  
Table 2: Learning and test set size. Ymer @. 
4 EXPERIMENTAL RESULTS 
In table 3 we show the accuracy of the classifications per- 
formed on the Igaliko image and in table 4 we show the ac- 
curacy of the classifications performed on the Ymer D image. 
We show in the first column the name of the spectral classifier 
used to get the initial map, and the accuracy of that classifica- 
tion, in the second column. The remainder columns show the 
accuracies of the contextual corrections made over the initial 
map by using the three models adopted in this paper. 
5 DISCUSSION AND CONCLUDING REMARKS 
From tables 3 and 4 we must note that the accuracy 
of the spectral classifications can be improved -sometimes 
drastically- if they are used as input to a contextual classifier 
independently of the nature of the spectral classifier. This is 
true for the three contextual classifiers tested in this work. 
We can conclude that among the contextual classifiers ICM 
gives the best results and we must note that the required 
computational effort is lower than the others. As the ICM 
computational effort is identical for every initial classification, 
the global computational cost is determined by the spectral 
classification cost. 
We must note that in both problems the accuracies got with 
the combinations: 
  
  
Spectral Classifier || Orig. | IC™ | Welch | Owen | 
  
  
  
  
  
  
  
  
  
  
  
ML 7351 [9133 | 79.93 | 9021 
RDA 78.97 || 89.37 | 85.46 | 85.68 
CART 80.66 || 92.30 | 86.66 | 86.55 
1-NN (7) 74.61 | 86.94 | 85.87 | 85.70 
1-NN (7m) 77.76 || 83.02 | 84.63 | 84.66 
1-NN (Tmc) 77.08 || 82.83 | 84.83 | 84.85 
1-NN (Tpsm) 77.50 || 85.32 | 84.12 | 84.52 
1-NN (71vo-1) 79.07 | 90.80 | 86.42 | 86.44 
  
  
Table 3: Accuracy of the classifications. Igaliko. 
  
  
|| Spectral Classifier Il Orig. I ICM | Welch | Owen || 
  
  
  
  
  
  
  
  
  
  
ML 61.92 11 91.37 | 85.11 | 85,33 
RDA 64.29 | 85.55 | 69.36 | 69.57 
CART 62.35 || 95.58 | 86.73 | 87.16 
1-NN (7) 78.50 || 97.98 | 86.50 | 87.08 
1-NN (73) 65.67 || 90.07 | 82.96 | 83.60 
1-NN (7uc) 6323 81.09 | 70.12 | 70:35 
1-NN (7psm) 64.55 || 80.97 | 72.66 | 73.22 
1-NN (7rvQ-1) 68.18 | 93.64 | 85.55 | 86.41 
  
  
  
  
Table 4: Accuracy of the classifications. Ymer @. 
a) CART + ICM, and 
b) 1-NN (T1491) + ICM 
are very high. The computational effort associated to CART 
is mainly influenced by the learning step (a function of the 
training set size) but we must note that it is a relatively low 
cost step. LVQ-1 learning is a quick process and as a addi- 
tional advantage we can select the training set size and the 
parameters involved [Kohonen, 1990]. As an additional ad- 
vantage the values of the parameters involved in the LVQ-1 
learning have been automatically estimated by using two al- 
gorithms proposed by the authors. 
These combinations have also been tested on synthetic very- 
high-spectral images [Cortijo, 1995] and the results obtained 
do extend these shown here. 
REFERENCES 
[Besag, 1986] Besag, J., 1986. On the Statistical Analysis of 
Dirty Pictures. Journal of the Royal Statistical Society. Ser. 
B, 48(3), pp. 259-302. 
[Breiman et al., 1984] Breiman, L., Friedman, J., Olshen, R. 
and Stone, C., 1984. Classification and Regresion Trees. 
Wadsworth International Group. 
[Conradsen et al., 1987] Conradsen, K., Nielsen, A.A. 
Nielsen, B.K., Pedersen, J.L. and Thyrsted, T., 1987. The 
Use of Structural and Spectral Enhancement of Remote 
Sensing Data in Ore Prospecting - East Greenland Case 
Study. Technical Report, IMM, The Technical University 
of Denmark, Lyngby, Denmark. 
[Cortijo et al., 1995] Cortijo, F.J., Pérez de la Blanca, N., 
Molina, R. and Abad, J., 1995. On the combination of non- 
parametric nearest neighbor classification and contextual 
correction. In: Pattern Recognition and Image Analysis, 
123 
International Archives of Photogrammetry and Remote Sensing. Vol. XXXI, Part B3. Vienna 1996 
V crm cts 
MEC 
pS t