In: Wagner W., Szgkely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010,1 APRS, Vol. XXXVIII, Part 7B 
3.3 Particularization of the classification model 
FMC models may be built using any t-norm and s-norm 
composition. We favor the max-product composition, since it 
leads to a simple multitemporal classification model with an 
intuitive interpretation,. Thus Equation (1) takes the form: 
,+1 p ; . = max{'a,.T, y } (11) 
for i,j = 1 
The defuzzyfication step is carried out by a hardening function 
H that selects the fuzzy set with the highest membership grade, 
formally: 
\w h ...,w n ] =w= H(p)= H([p/,..., p„]), where 
lforp,. = max{p 1 ,...,p„} (12) 
0 otherwise 
The aggregation function F is the product of corresponding 
elements of the input fuzzy vectors. Thus, 
,+ V =F(' +/ a, <+/ p)= [ ,+ V + %-, ,+k a n ,+/ p„] (13) 
Putting it all together, the multitemporal classifier assigns the 
image object to the class co, e il at time t+1, for which 
"V- = m fx{' +1 a, maxf'a^j} = max{'a,T tt ' +1 a t } (14) 
holds. 
3.4 Estimating transition possibilities 
The estimation of transition possibilities basically selects the set 
of possibility values that maximizes the classification accuracy 
computed upon a given training set. 
The estimation procedure consists of finding the set of 
transition possibility values T={iy} that maximizes the selected 
accuracy function G, for the selected image objects S of image 
objects at the later date (the training set) and for the selected 
monotemporal classifiers. This is formally expressed by: 
T = argmax{G(s, £ C/-C,f)} (15) 
f 
The computation of transition possibilities defined in Equation 
(17) involves an optimization procedure. The classification 
model introduced in the previous sections is actually not bound 
to any particular parameter optimization technique. In this 
work, the average class accuracy was used as accuracy function, 
and a Genetic Algorithm was the optimization technique used to 
estimate transition possibilities (Schmiedle et al., 2002). 
4. EXPERIMENTS 
The experiments described in the following sections were 
designed to evaluate the proposed method over a set of high 
resolution IKONOS II images. The experiments aimed at 
comparing the outcome of the multitemporal classification with 
that of the monotemporal classification of the later image. We 
also investigated the performance of the method tuning the 
performance of the earlier monotemporal classifier, as described 
in Section 4.4. The idea was to investigate how the method 
behaves with different (increasing) performances of the earlier 
monotemporal classifier. 
The data set used in all experiments is described in the next 
section. Afterward, the design of the particular monotemporal 
classifier that composes the multitemporal scheme in the 
experiments is presented. The following two sections describe 
respectively the monotemporal classifier design and the 
optimization technique used to estimate transition possibilities. 
4.1 Description of the data set 
The test site corresponds to a 14.4 km 2 area, situated on the 
north face of the Tijuca National Park, within the city of Rio de 
Janeiro, an important Atlantic Forest reminiscent. The test-site 
is a subset of the area of interest of the PIMAR Project (Remote 
Environmental Monitoring Program), which aims at monitoring 
the suppression of rainforest on conservation units inside the 
municipality of Rio de Janeiro through high resolution optical 
remote sensing images (PIMAR, 2010). 
This area was selected as test-site because of the noticeable 
sprawl of informal dwellings over legally protected natural 
areas. Moreover, the area contents various instances of all land 
cover classes considered by the PIMAR Project. 
Two pan-shaped, orthorectified IKONOS II images were used 
in the experiments. The images actually take part of two stereo 
pairs, each pair acquired on the same orbit, with different 
elevation angles. The orthorectification was performed using 
digital elevation models derived from each stereo pair. For each 
year the image with the highest elevation angle was chosen and 
submitted to orthorectification. 
It is important to note that because of the time of the year the 
images were acquired - March 2008 (late summer) and June 
2009 (late autumn) respectively -, they present quite different 
illumination conditions, with an important presence of clouds in 
the 2009 image. No radiometric correction or equalization was 
performed over the orthorectfied images. 
Figure 2. Area of the test-site in Rio de Janeiro municipality. 
The orthorectified IKONOS II images were segmented using 
the multiresolution segmentation algorithm proposed by Baaz 
and Shape (2000), through the Definiens Developer 7 software. 
The parameters chosen for the segmentation procedure were