In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
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such that the resulting segments were small in size, as defined 
by the low scale parameter value, giving priority to color 
homogeneity instead of coherently shaped segments. The idea 
was to absolutely avoid that the segments disrespect the border 
between two different land cover objects. 
Parameter 
Value 
Scale 
30 
Color 
0.9 
Shape 
0.1 
Compactness 
0.5 
Smoothness 
0.5 
Layer weights (bands 1,2,3 and 4) 
1,1,1,1 
4.2 Monotemporal classifier design 
A simple design is adopted in our experiments for the earlier 
('C) and later ( ,+/ C) monotemporal image classifiers. Feature 
vectors x are built for each segment by stacking the attribute 
value of the segments (recorded at a specific date). It is assumed 
that all classes co, can be appropriately modelled by a Gaussian- 
shaped membership function MFJx) given by the formula 
below: 
MF ai {x) = exip 
(x-x«) 7 I^(x-xa*) 
(16) 
Table 1. Segmentation parameters used in the experiments. 
All segments generated from the two images were duly, visually 
classified by specialists. Table 2 describes the land-use classes 
considered. Actually, shadow segments were also classified as 
such, but they were not considered in the experiments. 
After classification, all segments from each class in 2008 were 
merged to the adjacent segments of the same class, generating 
larger area segments. Then, only the segments from 2009 that 
fell completely inside the large 2008 segments (generated from 
the merging procedure) were selected. 
For those selected segments (generated through the 
segmentation of the 2009 image), feature attributes were 
calculated from each of the two images. The feature extraction 
procedure was also implemented on the Definiens Developer 
software. The features extracted for each segment were: mean 
values of the four spectral bands and the textural entropy feature 
(for all bands in all directions). 
The basic idea of the procedure described above was to produce 
a set of segments with class labels for 2008 and 2009, and with 
two sets of attributes, extracted respectively from the 2008 and 
2009 images. Table 3 shows the number of segments assigned 
to each class, in each year and the class transitions observed 
from 2008 to 2009. 
Label 
Class 
Description 
Rock (co/) 
Rock 
Exposed rock (granite) formations. 
Field (co 2 ) 
Grass field 
Grass fields naturally formed over 
thin soil or created by 
anthropogenic activities. 
Urban (co 3 ) 
Urban Area 
Constructed area (buildings, roads, 
etc.) including bare soil areas 
Trees (co 4 ) 
Arboreous 
Individual or clusters of trees 
Vegetation (inside urban areas or not). 
Table 2. LULC classes considered in the esperiments. 
2009 
2008 
Rock 
Field 
Urban 
Trees 
Total 
Rock 
188 
10 
0 
1 
199 
Field 
11 
421 
66 
153 
651 
Urban 
0 
9 
5594 
220 
5823 
Trees 
1 
194 
390 
33947 
34532 
Total 
200 
634 
6050 
34321 
41205 
Table 3. Class transitions from 2008 to 2009. 
for co,- e (rock, field, urban, trees], where and 2^ 
correspond respectively to the mean and to the covariance 
matrix of the class co,-. 
4.3 Optimization procedure 
The transition possibility values were estimated, as mentioned 
in Section 3.4, by a Genetic Algorithm (GA) using as objective 
function the average class accuracy. The genes were the 
transition possibility values. The GA design used in the 
experiments was the same as in (Feitosa et al., 2009). 
4.4 Simulating monotemporal classifiers with tunable 
performance 
The multitemporal classification based on fuzzy Markov chains 
is evaluated for for monotemporal classifiers with varying 
performances. Such evaluation scheme can be done by defining 
a simulated monotemporal classifier l+k C* with tuneable 
performance, that is, for all image objects, we have: 
t+k a* = m l+k W +(l-m) t+k a (17) 
where ' + *W is the true crisp label vector, ,+k a is the fuzzy label 
vector from the monotemporal classifier, and m is a mixture 
factor that takes values in the interval [0,1]. For m = 0, the 
simulated monotemporal classifier is identical to the 
monotemporal classifier described in the previous section; for 
m = 1, it is equal to the ideal classifier. 
The monotemporal classifiers, ,+k C, are replaced in our 
experiments by the simulated monotemporal classifier, l+k C*, 
and a continuous variation of m permits to observe how the 
relative performance of the monotemporal classifiers affects the 
accuracy of the multitemporal model. It is worth anticipating at 
this point the low performance of the real monotemporal 
classifier described in Section 4.2 in comparison to state of the 
art classification approaches (see experiment results in the next 
section). This is convenient in view of the objective of the 
analysis since it permits to assess the multitemporal models for 
a wide range of monotemporal classification performances. 
4.5 Results 
The benchmark for the analysis reported in the subsequent 
sections is the outcome of the monotemporal classifiers that 
take part of the multitemporal scheme. As the object of 
comparison is the crisp classification of the later image 
segments, a defuzzification step was performed over the output 
of the fuzzy monotemporal classifier, simply assigning to each