In: Paparoditis N., Pieirot-Deseilligny M.. Mallet C.. Tournaire O. (Eds). IAPRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3, 2010 
1 
PARAMETER ESTIMATION FOR A MARKED POINT PROCESS WITHIN A 
FRAMEWORK OF MULTIDIMENSIONAL SHAPE EXTRACTION FROM REMOTE 
SENSING IMAGES 
Saima Ben Hadj, Florent Châtelain, Xavier Descombes and Josiane Zerubia 
Ariana Research Group CNRS/1NRIA/UNSA 
2004, route des Lucioles - BP 93 - 06902 Sophia Antipolis Cedex - FRANCE 
saima.benhadj@sophia.inria.fr. florent.chatelain@gipsa-lab.inpg.fr, xavier.descombes@sophia.inria.fr, josiane.zerubia@sophia.inria.fr 
http ://www.inria.fr/ariana 
Commission III, WG III/4 
KEY WORDS: shape extraction, marked point process. RJMCMC. simulated annealing, SEM. 
ABSTRACT: 
Previously, an estimation method based on the Stochastic Expectation-Maximization algorithm was studied and proved its relevance 
for estimating the parameters of a marked point process model in order to achieve unsupervised feature extraction from remote sensing 
images. This method was only applied to a simple model of a marked point process of circles. In this paper, we extend the proposed 
estimation method to multidimensional shapes such as ellipses and rectangles. Different types of objects have been extracted: flamingos, 
tree crowns, boats, and building footprints. Furthermore, some prior constraints corresponding to the alignment of boats as well as the 
alignment of buildings are introduced. 
1 INTRODUCTION 
The problem of feature extraction from remote sensing images 
has been addressed in several scopes, namely, environment, civil 
ian and military. As the resolution of the provided aerial and 
satellite images is very high, a smart technique of analysis of such 
data needs to be developed. In this context, a model of marked 
point process (Geyer and Moller, 1994. Moller and Waagepetersen, 
2004) was previously introduced and proved its suitability to such 
a problem. It is basically a stochastic model that involves some 
information about the geometry of the objects present in the im 
age. Certain parameters incorporated in this model must be ad 
justed automatically, according to the processed image. In this 
prospect, a study of estimation methods of these parameters proved 
that a method based on the Stochastic Expectation-Maximization 
(SEM) algorithm (Celeux et al., 1996) was very relevant. It was 
firstly validated on a marked point process of circles (Chatelain et 
al., 2009a. Chatelain et al., 2009b). The aim of this paper is thus 
to extend this estimation procedure to more general geometrical 
shapes such as ellipses and rectangles. Several applications will 
be addressed, namely pink flamingo detection, tree crown extrac 
tion, boat detection as well as building outline extraction. 
The paper is organized as follows: in the second section, we 
propose to review the family of marked point processes which 
has been used to extract surface networks. We then explicit the 
parameters of our model and describe the proposed estimation 
method. In the third section, we present the model of an ellipse 
process. Different tests using the associated estimation proce 
dure have been performed. We discuss the obtained results and 
we modify the energy model spatially for boat detection. In fact, 
boats in a seaport are very close and aligned, which makes their 
discrimination difficult using the model proposed in (Chatelain et 
al., 2009b). In the following section, we look for the extraction 
of building outlines which can be represented by a network of 
rectangles. We therefore expose the adopted rectangle process. 
Moreover, we propose to append an energy component favor 
ing aligned frames owing that buildings of large cities are usu 
ally very organized. Finally we conclude this work by proposing 
some perspectives. 
2 PROPOSED MODEL FOR OBJECT EXTRACTION 
AND PARAMETER ESTIMATION 
2.1 Proposed model for object extraction 
In a marked point process framework (Mpller and Waagepetersen, 
2004), image features are viewed as a set of objects identified 
jointly by their position in the image and their geometrical char 
acteristics. Let W — V x M be the object space. Typically W is 
a bounded set of M, where V is the space of the object position 
while Ai is the space of marks describing the object geometry. 
A configuration x of objects belonging to W is an unordered set 
of objects x = {¡ri,..., x n } G fi n , x r £ W, i = 1 ,...,n. A 
point process X living in W is a random variable whose realiza 
tions are random configurations of objects in Q = U In our 
77. 
work, we focus on a particular family of marked point processes, 
namely the familly of Gibbs processes. One major interest of 
these processes consists in their ability to model the interactions 
between objects. Denoting by y the observed image, the density 
of the considered marked point process is actually: 
p-Uff(x.y) 
MX = xlv) = ^m~ 0) 
where c(0\y) is the normalizing function written in the following 
form f Q e~ Uti( ‘ x,v) y.(dx) (where //(.) is the intensity measure of 
the reference Poisson process). 0 is a parameter vector, allowing 
the flexibility of our model and its suitability to several types of 
images. It hence must be adjusted according to the given image. 
The process energy Ue{x,y) is divided into the two types of en 
ergies: the external energy, Ug(x, y) which quantifies the fit be 
tween the configuration x and the data y and the internal energy, 
Uq(x) which reflects our prior knowledge about the interactions 
between objects. Thus, the most likely configuration which al 
lows object extraction corresponds to the global minimum of the 
total energy: 
x = argmax f e (X = x\y) = argmin [Ufi(x, y) + U$(x)\ 
(2)