вядемикг 
In: Paparoditis N., Pierrot-Deseilligny M.. Mallet C„ Tournaire O. (Eds). 1APRS. Vol. XXXVIII. Part ЗА - Saint-Mandé, France. September 1-3. 2010 
SEGMENTATION OF NETWORKS FROM VHR REMOTE SENSING IMAGES USING A 
DIRECTED PHASE FIELD HOAC MODEL 
Aymen El Ghoul, Ian H. Jermyn and Josiane Zerubia 
ARIANA - Joint Team-Project INRIA/CNRS/UNSA 
2004 route des Lucioles, BP 93, 06902 Sophia Antipolis Cedex, France 
{aymen. el_ghoul, ian. j ermyn, j osiane. zerubia}®sophia. inria. f r 
Commission III, WG III/4 
KEY WORDS: shape priors, higher order active contours, phase fields, segmentation, road and hydrographic network 
ABSTRACT: 
We propose a new algorithm for network segmentation from very high resolution (VHR) remote sensing images. The algorithm 
performs this task quasi-automatically, that is, with no human intervention except to fix some parameters. The task is made difficult 
by the amount of prior knowledge about network region geometry needed to perform the task, knowledge that is usually provided by 
a human being. To include such prior knowledge, we make use of methodological advances in region modelling: a phase field higher- 
order active contour of directed networks is used as the prior model for region geometry. By adjoining an approximately conserved 
flow to a phase field model encouraging network shapes (i.e. regions composed of branches meeting at junctions), the model favours 
network regions in which different branches may have very different widths, but in which width change along a branch is slow; in which 
branches do not come to an end, hence tending to close gaps in the network; and in which junctions show approximate ‘conservation 
of width’. We also introduce image models for network and background, which are validated using maximum likelihood segmentation 
against other possibilities. We then test the full model on VHR optical and multispectral satellite images. 
1 INTRODUCTION 
In this paper, we address the problem of road and hydrographic 
network segmentation from VHR optical and multispectral im 
ages: given an image 7, we seek the region R in the image do 
main Q that contains the network. We would like to perform this 
task quasi-automatically, that is, with no human intervention ex 
cept to fix some parameters. Such segmentation problems remain 
challenging due to a combination of difficulties. First, the net 
work is usually not distinguishable from the background using 
image measurements alone. Rather, knowledge of the geomet 
ric properties of R (e.g. , that it is composed of branches that 
meet at junctions) is necessary for successful segmentation. Cur 
rently, this knowledge is provided, in one way or another, by a 
human being. Automation of the segmentation process therefore 
requires models that incorporate this knowledge of region geom 
etry. This is a nontrivial matter, particularly since the regions 
corresponding to networks have huge variability in their topol 
ogy as well as their geometry. Second, there is great variability in 
the appearances of network and background from one image to 
another. Third, models incorporating the necessary prior knowl 
edge of region geometry are complex, and this leads to efficiency 
issues when confronted with the large size and number of images 
to be processed. 
The contribution of this paper is a new algorithm for road and hy 
drographic network segmentation from VHR remote sensing im 
ages of rural and non-urban areas which present many occluded 
parts of the network entity to be extracted. Our new algorithm 
uses recent advances in shape modelling allowing the incorpora 
tion of sophisticated prior knowledge about network region ge 
ometry, thereby addressing the first difficulty. A ‘phase field 
higher-order active contour’ (‘phase field HOAC’) model of di 
rected networks (El Ghoul et al., 2009b) is used to favour regions 
composed of branches that meet at junctions. The network con 
tains a ‘flow’, which is approximately conserved. This means that 
the width of each branch changes slowly, while different branches 
can have very different widths; that branches tend not to end; and 
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that, at junctions, there is approximate ‘conservation of width’: 
for example, several small incoming branches combining to form 
a larger outgoing branch. These characteristic geometric prop 
erties are different from those of road networks in VHR images 
of urban areas (Peng et al., 2010), and from those of networks 
in medium resolution images (Rochery et al., 2005); the problem 
therefore requires the use of a new model. 
In (El Ghoul et al., 2009b), the model used here was described, 
but the automatic parameter setting described herein was not used, 
and the model was not applied to or tested on real images. Real 
images generate the second difficulty described above. To ad 
dress it, we also propose generic models for the image in the net 
work region and in the background whose parameters can easily 
be learned from examples of these two classes. We test these 
models on several VHR images. The image models are com 
pared to other possibilities using maximum likelihood (ML) clas 
sifications. They outperform standard indices, which suggests 
that their performance when combined with the region geometry 
model will also be superior. We then test the full model, com 
bining the phase field model of directed networks with the image 
models, on several satellite images. The segmentation problems 
involved are very hard, but the results show that the new algo 
rithm is able to ignore confounding factors in the background 
due to the sophisticated knowledge of region geometry it con 
tains, and is able to complete the network over reasonable gaps. 
Before going on, it is useful to formalize the problem and our ap 
proach to solving it, and to introduce some notation. We seek to 
infer the region R containing the network from the image data I 
and our prior knowledge K, e.g. of image formation, network 
geometry, and so on. In other words, we wish to construct a 
probability distribution P(R\I,K) for the region R containing 
the network, given the current image data I and our knowledge 
K. As usual, this can be written as the product of a likelihood 
P(/|/?, K), which models the images we expect to see given that 
R C il corresponds to a network, that the image is a VHR op 
tical image, etc.; and a prior P(7?|A'), which incorporates our