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