In: Wagner W., Székely, B. (eds.): ISPRS TC VII Symposium - 100 Years ISPRS, Vienna, Austria, July 5-7, 2010, IAPRS, Vol. XXXVIII, Part 7B 
MULTITEMPORAL FUZZY MARKOV CHAIN-BASED CLASSIFICATION 
OF VERY HIGH RESOLUTION IMAGES OF AN URBAN SITE 
G. A. O. P. Costa 2 ' *, R. Q. Feitosa 3 , L. F. G. Rego b 
a Department of Electrical Engineering 
b Department of Geography 
Pontificia Universidade Catolica do Rio de Janeiro Rua Marqués de Säo Vicente 225, Gâvea, Rio de Janeiro, CEP: 
22453-900, RJ, Brasil - (gilson, raul)@ele.puc-rio.br, regoluiz@puc-rio.br 
KEY WORDS: Multitemporal, Interpretation, Fuzzy Logic, High Resolution, Urban, Land Use, Land Cover 
ABSTRACT: 
This work discusses the application of the cascade, multitemporal classification method based on fuzzy Markov chains originally 
introduced in (Feitosa et al. 2009), over a set of IKONOS images of urban areas within the city of Rio de Janeiro, Brazil. The 
method combines the fuzzy, monotemporal, classification of a geographical region in two points in time to provide a single unified 
result. The method does not require knowledge of the true class at the earlier date, but uses instead the attributes of the image object 
being classified at both the later and the earlier date. A transformation law based on class transition possibilities projects the earlier 
classification to the later date before combining both results. While in (Feitosa et al. 2009) the fuzzy Markov chain-based method 
was evaluated over a series of medium resolution, LANDSAT images, in this work very high resolution images were processed. 
Additionally, while the target area of the previous work was characterized predominantly by agricultural use, in this work an urban 
area was the subject of classification. The results showed that the performance of the multitemporal method was consistently superior 
to that of the monotemporal classification of the study area, and confirmed the robustness of the fuzzy Markov chain-based method 
with respect to sensor characteristics and target sites. 
1. INTRODUCTION 
Sequences of Remote Sensing images of the same geographical 
area acquired at different points represent a valuable source of 
information that can be used to improve the accuracy and 
reliability of classification-based image analysis. 
Most traditional multidate image classification methods can be 
regarded as “post-classification” approaches (Weismiller et al., 
1977), which are decisively dependent on the accuracy of the 
initial classifications. More powerful alternatives, called 
“cascade-classification” approaches (Swain, 1978) use all the 
information contained in the image sequence, trying to explore 
the correlation contained in the temporal data sets. 
Feitosa et al. (2009) presented a detailed overview of the most 
relevant efforts towards automatic cascade multitemporal 
schemes found in the literature. These attempts include 
probabilistic methods, methods based on neural networks and 
multi-classifier approaches. 
A first attempt towards a fuzzy cascade classification technique 
can be found in (Mota et al., 2007). That method is restricted to 
applications where the true class of the object being classified at 
an earlier time is known. Feitosa et al. (2009) described a new 
fuzzy cascade multitemporal classification model, explicitly 
based on fuzzy Markov chains, in which object features other 
than the true classification are used as the information from the 
earlier date. In the later method, before the classifications of 
two images at two dates are combined, the fuzzy classification 
at the earlier date undergoes a temporal transformation that 
projects it onto the later date. 
This work discusses the application of the cascade, 
multitemporal classification method introduced in (Feitosa et al. 
2009), originally applied over an agricultural over a set of 
IKONOS II images of urban areas within the city of Rio de 
Janeiro, Brazil. 
2. FUZZY MARKOV CHAINS 
This section describes briefly the concept of Fuzzy Markov 
Chain (FMC). A complete and more general presentation about 
this technique and the related concepts may be found in 
(Avrachenkov and Sanchez, 2002). 
In this work we consider images acquired at dates t 0 +tAt, where 
t 0 is some stipulated initial time, At is a given time interval, and 
t is any integer number. For simplicity the date t 0 +tAt will be 
denoted from this point on as time t, and t 0 +(t+l)At as time t+1, 
forte Z 
Let ft = {co!, co 2 ,•••, co n } be a set of n distinguishable land- 
use/land-cover (LULC). A binary fuzzy relation can be defined 
on the Cartesian product ftxft represented by a nxn transition 
matrix T = {r, ; }. The symbol zy stands for the possibility that an 
image object belongs to the class co,- e ft at time t and to the 
class co ; e ft at time t+1, with 0 < zy < 1, for ij = 1,...,«. 
This can be pictorially described by a class transition diagram 
(Figure 1), a weighted directed graph whose nodes correspond 
to classes and links to plausible class transitions between t and 
t+1. Each link is labeled with the class transition possibility Zy. 
For simplicity links with zy = 0 are not drawn. 
* Corresponding author. 
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