Point processes for unsupervised line network extraction in remote sensing

Abstract

This paper addresses the problem of unsupervised extraction of line networks (for example, road or hydrographic networks) from remotely sensed images. We model the target line network by an object process, where the objects correspond to interacting line segments. The prior model, called "Quality Candy," is designed to exploit as fully as possible the topological properties of the network under consideration, while the radiometric properties of the network are modeled using a data term based on statistical tests. Two techniques are used to compute this term: one is more accurate, the other more efficient. A calibration technique is used to choose the model parameters. Optimization is done via simulated annealing using a Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. We accelerate convergence of the algorithm by using appropriate proposal kernels. The results obtained on satellite and aerial images are quantitatively evaluated with respect to manual extractions. A comparison with the results obtained using a previous model, called the "Candy" model, shows the interest of adding quality coefficients with respect to interactions in the prior density. The relevance of using an offline computation of the data potential is shown, in particular, when a proposal kernel based on this computation is added in the RJMCMC algorithm.

Full text

Point Processes for Unsupervised Line Network
Extraction in Remote Sensing
Caroline Lacoste, Xavier Descombes, and Josiane Zerubia, Fellow, IEEE
Abstract—This paper addresses the problem of unsupervised extraction of line networks (for example, road or hydrographic
networks) from remotely sensed images. We model the target line network by an object process, where the objects correspond to
interacting line segments. The prior model, called “Quality Candy,” is designed to exploit as fully as possible the topological properties
of the network under consideration, while the radiometric properties of the network are modeled using a data term based on statistical
tests. Two techniques are used to compute this term: one is more accurate, the other more efficient. A calibration technique is used to
choose the model parameters. Optimization is done via simulated annealing using a Reversible Jump Markov Chain Monte Carlo
(RJMCMC) algorithm. We accelerate convergence of the algorithm by using appropriate proposal kernels. The results obtained on
satellite and aerial images are quantitatively evaluated with respect to manual extractions. A comparison with the results obtained
using a previous model, called the “Candy” model, shows the interest of adding quality coefficients with respect to interactions in the
prior density. The relevance of using an offline computation of the data potential is shown, in particular, when a proposal kernel based
on this computation is added in the RJMCMC algorithm.
Index Terms—Stochastic processes, Monte Carlo, simulated annealing, edge and feature detection, remote sensing.
æ
1INTRODUCTION
T
HIS paper tackles the problem of line network extraction
from satellite or aerial images, the final application
being either the production or the updating of maps. Many
methods have been—and will be—developed to answer this
difficult problem, in particular, for road network extraction.
One possibility is to consider a semiautomatic approach:
an operator gives a starting point and a direction that
initialize a tracking algorithm [1], [2], some endpoints that
may be linked by an algorithm based on dynamic program-
ming [3], [4], or some checking points that initialize an edge
extraction algorithm based on deformable contour models
[5], on dynamic programming [6], or on profile analysis [7].
These approaches usually allow a fast and accurate extrac-
tion. Nevertheless, the productivity gain of such approaches
is weak with respect to the extraction done by an expert.
A second pos sibility is to consider a fully-automatic
approach. The extraction is then an ill-posed problem in
which it is difficult to find a good compromise between
exhaustivity and specificity. Most automatic methods pub-
lished in the literature rely on a local optimization process
based, for example, on morphological operators [8], on
operators dedicated to road extraction [9], on operators based
on texture [10], or on neural networks [11]. The major
drawback of these low-level techniques is their sensitivity
to noise, particularly for high resolution images in which a
noise inherent to the observed scene is added (for example,
trees shadows on the roads). To reduce this sensitivity to
noise, some authors propose to combine different operators
[3], [12]. Although they often provide a coarse detection, such
techniques are widely used to initialize a network reconstruc-
tion procedure. Indeed, they allow the finding of road seeds
for the initialization of semiautomatic algorithms [13], [14], to
construct a graph on which a Markov random field can be
defined [15], or to initialize a self-organizing map algorithm
[16]. These two-step approaches are, however, strongly
sensitive to the predetection. For the extraction of thick
networks from high resolution images, multiscale ap-
proaches are proposed to reduce the effect of noise while
providing an accurate extraction. In [17], the extraction of the
central axis of the roads from an image of reduced resolution
is used to initialize a snake-based algorithm for the extraction
of road edges in the original high resolution image. In [18],
hypotheses of road segment are generated using the detection
of edges at high resolution and the detection of lines at low
resolution. Then, a grouping process is performed and gaps
are bridged using a contextual information.
We aim to develop an unsupervised technique, which is
not based on a combination of processings of the image. The
framework of our study is stochastic, which allows us to
benefit from the robustness with respect to noise and from
the tools associated with this type of method: estimators,
algorithms for exploration of the state space, which are
useful if the space is large, etc. Moreover, these models
avoid the sensitivity to noise of the usual pixel oriented
approaches. We model the line network by a marked point
process, that is, a random set of objects—each described by
a point and some marks—whose number of objects is a
random variable. One such model, called the “Candy”
model, was proposed in [19] for road network extraction.
The objects of this process are segments which interact to
allow the manipulation of strong geometrical constraints.
In this paper, we develop an extension of this first model,
called the “Quality Candy” model , which uses quality
1568 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005
. C. Lacoste is with CREATIS, INSA, 7 rue Jean Capelle, bat. Blaise Pascal,
F-69621 Villeurbanne Cedex, France.
E-mail: caroline.lacoste@creatis.insa-lyon.fr.
. X. Descombes and J. Zerubia are with INRIA, 2004 route des Lucioles, BP
93, 06902, Sophia Antipolis Cedex, France.
E-mail: {Xavier.Descombes, Josiane.Zerubia}@inria.fr.
Manuscript received 12 Aug. 2003; revised 1 Sept. 2004; accepted 31 Dec.
2004; published online 11 Aug. 2005.
Recommended for acceptance by C. Schmid.
For information on obtaining reprints of this article, please send e-mail to:
tpami@computer.org, and reference IEEECS Log Number TPAMI-0226-0803.
0162-8828/05/$20.00 ß 2005 IEEE Published by the IEEE Computer Society

coefficients with respect to interactions between segments to
better model the curvature, the junctions, and the intersec-
tions of the network. Moreover, we construct a new data term
that incorporates data properties through statistical measures
of the local homogeneity and the contrast with the back-
ground near the line network. Two methods implementing
this data term are developed: one is more accurate, the other is
more efficient. A calibration technique is proposed for
choosing the model parameters so that the extracted line
network possesses good properties (no free segments, no
redundancy, no gaps, etc.). The optimization is done via
simulated annealing using a Reversible Jump Markov Chain
Monte Carlo (RJMCMC) algorithm [20], [21]. This algorithm
allows line network extraction without any specific initializa-
tion: the initial state can be the empty state (no segment). The
performance of such an algorithm strongly depends on the
construction of the perturbation proposal kernel. To accel-
erate its convergence, we use relevant perturbations, such as a
segment birth in the neighborhood of a segment and a
segment birth based on data. The extraction algorithm is
tested on satellite and aerial images with each prior model
and with each data term implementation. The results are
evaluated quantitatively with respect to a manual extraction.
This paper is organized as follows: First, Section 2 recalls
the key-points about spatial processes for the understanding
of marked point processes. The “Quality Candy” model is
presented in Section 3 after a brief overview of the “Candy”
model. Section 4 is devoted to the construction of the data
term. Section 5 describes the optimization algorithm.
Section 6 addresses the problem of parameter choice. Finally,
Section 7 presents the results of line network extraction.
2GENERAL FRAMEWORK
Point processes provide a rigorous framework based on
measure theory [22] to describe a scene by an unordered set
of points in a compact F  IR
d
. For n 2 IN , let 
n
be the set
of configurations fx
1
; ...;x
n
g that consist of n unordered
points of F .Apoint process on F is a mapping X from a
probability space to the set configurations  ¼
S
1
n¼0

n
,
such that, for all bounded Borel sets A  F , the number of
points N
X
ðAÞ falling in A is a finite random variable.
The canonical “completely random” point process is the
uniform Poisson point process. X is a uniform Poisson
process on IR
d
if:
1. for all bounded Borel sets A  IR
d
, N
X
ðAÞ has a
Poisson distribution with mean jAj, where >0 is
the intensity;
2. if A
1
; ...;A
k
are disjoint bounded sets, then
N
X
ðA
1
Þ; ...;N
X
ðA
k
Þ are independent.
This definition induces the following conditional property:
Given N
X
ðAÞ¼n, the n points falling in A are independently
and uniformly distributed in A. The law of a Poisson process
of intensity  on an observed frame F  IR
d
is thus defined by
the following probability measure on ð; BÞ:
1
ðBÞ¼
X
1
n¼0

n
e
jFj
n!
Z
F
n
1
B
ðfx
1
; ...;x
n
gÞ dx
1
...dx
n
: ð1Þ
Although, in most applications, it is not realistic to assume
points are scattered randomly, Poisson processes are useful
to build more complex models. Indeed, interactions can be
introduced by specifying a density with respect to the
reference measure . Let h be a nonnegative function on .
Then, the measure  having a density h with respect to  is
defined by:
ðBÞ¼
Z
B
hðXÞðdXÞ: ð2Þ
If 0 <ðBÞ < 1, then  can be normalized to make a
probability measure  defined by: ðBÞ=ðÞ. Interaction
models are usually specified by an unnormalized Gibbs
density given by:
hðXÞ¼exp UðXÞðÞ; ð3Þ
where UðXÞ is the energy of the system. For instance, let us
assume that:
UðXÞ¼vn
I
ðXÞ; ð4Þ
where n
I
ðXÞ is the number of pairs of points in interaction.
Two points interact if the distance between these two points
is lower than a threshold D. Different types of models
derive from (4):
. If v>0, the process, called Strauss process, induces
a repulsion between points.
. If v ¼1, the process, called “hard core” process,
forbids any interaction.
. If v<0, the process induces an attraction between
points, but is not well-defined since
Z
hðXÞ ðdXÞ¼1:
To model the observed scene by a set of objects, we can
augment a point process by adding extra information (i.e.,
object parameters) to each point. Such a process is called a
marked point process or an object process. A marked point
process on F, with marks in a space M, is a point process on
F  M such that NðA  MÞ < 1 almost surely for any
compact A  F . In this context, the uniform Poisson process
is a marked point process where points are distributed
according to a uniform Poisson point process, and marks
associated to each point are uniformly distributed in M.
3PRIOR MODELS FOR LINE NETWORK
EXTRACTION
A line network is generally characterized by several strong
constraints, among them: continuity of the network and
small curvature, especially for road network extraction. If a
line network is considered as a set of segments, these
constraints can be thought of as interactions between
segments which can either penalize or favor some particular
configurations through potentials in the process density.
For the “Candy” model, briefly presented in Section 3.2, all
these potentials are constant. To improve this model, we
propose here to introduce potential functions measuring the
quality of each interaction. Our prior model is presented in
Section 3.3.
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1569
1. B is the smallest -algebra such that, for all Borel sets A  F ,the
mapping fx
1
; ...;x
n
g7!N
X
ðAÞ is measurable.

3.1 Reference Process
The two prior models presented in the following sections are
specified by a density with respect to a uniform Poisson
marked point process. Each object (i.e., marked point) of this
reference process is a segment s described by its midpoint
p 2 F ¼ 0;X
max
½0;Y
max
½, its length L 2 L
min
;L
max
½, and
its orientation  2 0;½.
3.2 “Candy” Model
The “Candy” model, proposed in [23], is based on
three possible relations between segments: the connection
R
c
and two relations of bad orientation, R
io
(internal bad
orientation) and R
eo
(external bad orientation).
Two segments are said to be connected if two of their
extremities are closer than a constant . Indeed, under the
Poisson process, no exact connection between pairs of
segments occurs almost surely. This relation (connection)
defines several types of segments as shown in Fig. 1. Free
segments are those which are not connected, single ones are
those with only one of their endpoints connected to other
segments, and double segments have their two endpoints
connected. In the density, free and single segments are
penalized by positive and constant potentials !
2
and !
3
in
order to avoid breaks in the network and false alarms. The
internal bad orientation, R
io
, is defined to avoid super-
position of line segments or pairs of segments crossing at
too sharp an angle. Two segments s
i
¼ðp
i
;L
i
;
i
Þ and s
j
¼
ðp
j
;L
j
;
j
Þ are concerned by R
io
if:
. ðC
1
Þ: kp
i
 p
j
kmaxfL
i
;L
j
g=2.
. ðC
2
Þ: 
ij
¼ 
ij
 =2 >
min
,where
ij
¼ minfj
1


2
j;j
1
 
2
jg denotes the absolute difference of
orientation between s
i
and s
j
(modulo =2).
Fig. 2 illustrates this definition. A positive and constant
potential !
3
is assigned to pairs that verify R
io
.
The last relation R
eo
has been introduced to control the
curvature of the line network. An influence zone ZðsÞ is
defined for each segment s ¼ðp; L; Þ as the two discs of
radius L=4 whose centers are the two endpoints of p.
Two segments s
i
and s
j
are concerned by R
io
if:
. ðC
4
Þ: either exactly one extremity of s
i
is in Zðs
j
Þ or
exactly one extremity of s
j
is in Zðs
i
Þ.
. ðC
5
Þ: kp
i
 p
j
k > maxfL
i
;L
j
g=2 (i.e., s
i
and s
j
do not
hold ðC
2
Þ).
. ðC
6
Þ: 
ij
¼ minfj
1
 
2
j;j
1
 
2
jg >
max
.
Fig. 3 illustrates this definition. A positive and constant
potential !
4
is assigned to pairs that verify R
io
.
The “Candy” model is then specified by the prior density
h
p
given by:
h
p
ðSÞ/exp  !
0
n þ !
1
n
f
þ !
2
n
s
þ !
3
n
io
þ !
4
n
eo

; ð5Þ
where !
0
is a constant weight, the !
i; i¼1;...;4
are positive and
constant weights, n denotes the total number of segments in
the configuration S, n
f
the number of free segments, n
s
the
number of single segments, n
io
the number of pairs of
segments with respect to R
io
, and n
eo
the number of pairs of
segments with respect to R
eo
. This density specifies a well-
defined marked point process, as the Ruelle’s stability
condition [24] is verified. This condition and the stronger
condition of local stability are proven in [25].
Neverthel ess, the density takes the same value for
configurations which do not have the same quality, as we
can see in Fig. 4. Thus, we can obtain a line network with
little breaks between connected extremities and not as
smooth as possible. That is the reason why we have
introduced quality coefficients to smooth the solution in the
following model, called “Quality Candy.”
3.3 “Quality Candy” Model
Considering the “Candy” model as a good starting point,
we have chosen to keep its general structure, replacing
constant potentials of interactions by variable functions g
r
for different relations between segments. The prior density
is now given by the following formula:
h
p
ðSÞ/expðU
p
ðSÞÞ ð6Þ
with U
p
ðSÞ¼!
0
n þ !
1
n
f
þ !
2
n
s
ð7Þ
þ
X
r2R
!
r
X
<s;s
0
>
r
g
r
ðs; s
0
Þ; ð8Þ
1570 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005
Fig. 1. Segment types of the “Candy” model defined with respect to R
c
.
Fig. 2. Internal bad orientation R
io
. fs
1
;s
2
g and fs
1
;s
3
g hold ðC
1
Þ as p
2
and p
3
are in the circle of center p
1
and radius L
1
=2. The pair fs
1
;s
2
g is
concerned by R
io
, while fs
1
;s
3
g is not.
Fig. 3. External bad orientation R
eo
. s
2
, s
3
, and s
3
have an extremity in
the influence zone Zðs
1
Þ (two small circles). So, fs
1
;s
2
g, fs
1
;s
3
g, and
fs
1
;s
4
g hold ðC
4
Þ. The pair fs
1
;s
2
g does not hold ðC
5
Þ; fs
1
;s
3
g does not
hold ðC
6
Þ; only fs
1
;s
3
g is concerned by R
eo
.

where n, n
f
, and n
s
are defined as before, the !
i
are
positive (except !
0
which can be negative) and constant
weights, R denotes the set of possible relations between
segments, <; >
r
is a pair of interacting segments with
respect to the relation r, and g
r
ð:; :Þ is the potential function
with respect to r. One can notice that, if we take the
two relations of bad orientation of the first model and a
potential function equal to 1 in any case, we obtain the
“Candy” model. Thus, the “Quality Candy” model can be
seen as a generalization of the “Candy” model.
First of all, we have chosen to redefine the relation of
connection adding a constraint to accelerate the optimiza-
tion algorithm. From now on, two segments are said to be
connected if the corresponding angle is not sharp. For
example, in Fig. 5, s
1
and s
3
are not connected. Moreover, in
order to promote small curvature and continuity of the line
network, the quality of each connection is introduced in the
density via a potential function. This potential function,
denoted g
R
c
, is defined for each pair of connected segments
<s
i
;s
j
>
R
c
as the average of g

which depends on the
absolute difference of orientation 
ij
(modulo =2) between
s
i
and s
j
and g

which depends on the distance d
ij
between
two connected extremities of s
i
and s
j
:
g
R
c
ðs
i
;s
j
Þ¼
g

ð
ij
Þþg

ðd
ij
Þ
2
with
g

ð
ij
Þ¼
ð
ij
;
max
Þ if 
ij
<
max
2 if not

g

ðd
ij
Þ¼ðd
ij
;Þ:
8
<
:
ð9Þ
Here, g

gives an attractive ( negative) weight to pairs of
segments ðs
i
;s
j
Þ whose absolute difference of orientation 
ij
is lower than a threshold  (such as ðs
1
;s
2
Þ in Fig. 5), and a
repulsive ( positive) one in the other case (such as ðs
1
;s
4
Þ
in Fig. 5). g

is attractive in any case. The attractive terms of
these two functions are given by the quality function 
below:
ð:; MÞ : ½0;M!½0; 1
x 7! ðx; MÞ¼
1
M
2
1 þ M
2
1 þ x
2
 1

:
ð10Þ
This is a decreasing and positive function on ½0;M. The
quality value is thus maximal (equal to one) for a difference
of orientation or a distance equal to 0.
This new potential allows us to work without the relation
of external bad orientation R
eo
, as the repulsive part of the
connection potential concerns the same type of interaction.
Then, we keep exactly the same relation for internal bad
orientation, but redefine the potential function. Pairs of
segments forming a too sharp angle are forbidden for
stability reasons. So, an infinite weight is given to them (i.e.,
“hard-core” potential). For the other pairs in internal bad
orientation, we use the same quality function  to define a
repulsive weight based on the difference of orientation
between the two segments. So, for each pair <s
i
;s
j
>
R
io
,
the formula is the following:
g
R
io
ðs
i
;s
j
Þ¼
1 if 
ij
<c
1  ð
ij
;=2  
min
Þ if not ;

ð11Þ
where 
min
is the minimal difference with respect to the
right angle from which two segments are considered as
disoriented, and c is a positive constant close to zero that
corresponds to the minimal difference of orientation which
is allowed for two close segments (i.e., segments that hold
ðC
1
Þ).
Finally, (7) becomes:
U
p
ðSÞ¼!
0
n þ !
1
n
f
þ !
2
n
s
þ !
3
X
<s
i
;s
j
>
R
c
g
R
c
ðs
i
;s
j
Þ
þ !
4
X
<s
i
;s
j
>
R
io
g
R
io
ðs
i
;s
j
Þ:
ð12Þ
This model is locally stable which guarantees the ergodic
convergence o f the RJMCMC algorithm described in
Section 5.2. The stability proof is given in [26].
4DATA MODELING
4.1 Construction of the Data Term
In order to extract line networks from any remotely sensed
image, we need a realistic and robust modeling of the data.
This section describes the construction of the data term. It is
based on the following assumptions:
. H
1
: The gray level variation between a road and the
background is large.
. H
2
: The local average of the road gray level is
homogeneous.
In order to check that a segment s
i
is well-fitted to the
data, we consider the set of pixels V
i
corresponding to the
object s
i
in the image—which is composed of a fixed
number n
b
of strips according to the supposed constant
width of the line network—and two adjacent strips
corresponding to the nearby background. These two strips
are positioned at a distance d from V
i
in order to allow a
range of widths as illustrated in Fig. 6. Considering the
pixel values in each region x as a sample of a population
composed of n
x
independent values, a Student’s t-test is
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1571
Fig. 4. A drawback of the “Candy” model.
Fig. 5. Different types of connection. fs
1
;s
2
g: attractive connection.
fs
1
;s
3
g: not considered as a connection. fs
1
;s
4
g: repulsive connection
with respect to the orientation.

used to determine if the averages of the two samples are
significantly different. This statistical test is adapted to
inference based on small samples as in our case. The
formula for the t-test is a ratio between the absolute value of
the difference of the two sample means and a measure of
the variability of the sample. Here is the t-test expression for
two samples x and y:
t  testðx; yÞ¼
jx  yj
ffiffiffiffiffiffiffiffiffiffiffiffiffi
e
2
x
n
x
þ
e
2
y
n
y
r
; ð13Þ
where
x, e
x
, and n
x
respectively refer to the sample mean,
the sample standard deviation, and the number o f
observations corresponding to the sample x. Above some
critical value, we can consider that the two samples x and y
come from two populations with different means. The
statistical value we consider for mean difference hypothesis
H
1
is the minimum of the test value between V
i
and a
border region:
T
H
1
ðs
i
Þ¼ min
l2f1;2g
t  testðR
i
l
;V
i
Þ

and the statistical value for homogeneity hypothesis H
2
is
the maximal t-test between two inside strips (if n
b
> 1):
T
H
2
ðs
i
Þ¼ max
j;k2f1;::;n
b
g;j6¼k
t  testðb
j
;b
k
Þ

;
where b
j
is the jth inside strip. If n
b
equals 1, there is no
homogeneity test and we fix T
H
2
ðs
i
Þ at 1. Then, the statistical
value T
i
corresponding to s
i
is the ratio of these two quantities,
with the additional condition that T
H
2
ðs
i
Þ is lower than 1 in
order to avoid promoting excessively very homogeneous
regions:
T
i
¼
T
H
1
ðs
i
Þ
max 1 ;T
H
2
ðs
i
Þ½
: ð14Þ
Moreover, we proceed to a thresholding and a conversion of
the test values from ½0; 1 to ½1; 2. These two boundaries
were chosen in order to obtain final configurations with the
properties listed in Section 4. Finally, the potential value is
the following:

i
¼
2ifT
i
<t
1
1  2
T
i
t
1
t
2
t
1
if t
1
<T
i
<t
2
1ifT
i
>t
2
;
8
<
:
ð15Þ
where t
1
and t
2
(t
1
<t
2
) are two positive thresholds
emp irically chosen. The potential 
i
associated to the
segment s
i
is a dual potential: it can take attractive
(negative) values, as well as repulsive (positive) values.
The thresholds t
1
and t
2
are robust in the sense that results
are similar if we modify their values a little bit and that we
can use the same thresholds for two different images with
similar radiometric properties. Finally, the data term energy
of a configuration S is defined as the sum of the potentials
associated to the segments belonging to S. The data term is
thus given by:
h
1
d
ðSÞ/exp 
d
X
s
i
2S

i
!
; ð16Þ
where 
d
is a positive and constant weight.
We have built a data term based on realistic and general
hypotheses to represent various types of networks. More-
over, we perform a reliable testing of these hypotheses
thanks to the use of statistical tests particularly well
adapted to small samples.
4.2 Offline Computation
Nevertheless, the online computation of these statistical
tests is time consuming, the RJMCMC algorithm having no
memory and often requiring a few millions of proposals of
new elements. We thus suggest to realize a precalculation of
the data term. We consider segments of minimal length
L
min
, positioned at every pixel of the image lattice, for a
fixed number of orientations N. For every considered
orientation
~

k; k¼1;...;N
, we assign to every pixel p of the
image lattice the value w
k
ðpÞ which minimizes the potential
value given by (15) as follows:
w
k
ðpÞ¼ min
fs
i
=L
i
¼L
min
;
i
¼
~

k
;p2V
i
g

i
: ð17Þ
For a segment s
i
with orientation 
i
, the potential is defined
by the mean of the precomputed values (for the orientation
~

k
of the discrete space which is the closest to 
i
) on the set
of pixels V
i
corresponding to s
i
:
~

i
¼
1
cardðV
i
Þ
X
p2V
i
w
k
ðpÞ ;k¼ arg min
j
j
i

~

j
j: ð18Þ
The expression of the data term is the same as in (6),
replacing 
i
by
~

i
:
h
2
d
ðSÞ/exp 
d
X
s
i
2S
~

i
!
: ð19Þ
Let us note that this term is less precise than the previous
one because a single length of segment is considered for the
statistical tests and because of the orientation discretization.
5OPTIMIZATION
5.1 Simulated Annealing
To extract the line network from an image, we aim to find a
configuration
b
SS which maximizes the unnormalized process
density h given by:
hðSÞ¼h
p
ðSÞ h
d
ðSÞ; ð20Þ
where h
p
is the prior density and h
d
is the data term. This is a
nonconvex problem for which a direct optimization is not
possible given the large size of the state space that is
S
1
n¼0

n
, where 
n
is the set of configurations of n segments.
We propose to estimate this maximum by a simulated
1572 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005
Fig. 6. A mask corresponding to a road segment.

annealing, which consists of successive simulations of the
process distribution 
T
specified by the density h
1=T
, with T
gradually decreasing to 0. A proof of convergence is given in
[27] when the decrease of temperature T is logarithmic. In
practice, temperature decreases geometrically in order to
reduce the computing time.
5.2 Simulation of Spatial Point Processes
The algorithm chosen to simulate the unnormalized
measure 
T
is a Reversible Jump Markov Chain Monte
Carlo (RJMCMC) algorithm with a Metropolis-Hastings-
Green dynamics [20], [21]. It consists in simulating a
discrete Markov chain S
t
which performs small jumps
between the spaces 
i
. The measure of interest occurs as the
stationary measure of the chain. This iterative algorithm
does not depend on the initial state. At each step, a
transition from the current state S to a new state S
0
is
proposed according to a proposal kernel QðS ! :Þ. The
transition is accepted with a probability ðS; S
0
Þ given by
the Green’s ratio. This acceptance ratio is computed so that
the detailed balance condition is verified, condition under
which this algorithm converges to 
T
. This strong condition
is given by:
Z
A
Z
B

T
ðdSÞ P ðS; dS
0
Þ¼
Z
B
Z
A

T
ðdS
0
Þ P ðS
0
;dSÞ; ð21Þ
where A and B are two sets of the tribu associated to  and
P is the transition kernel of the Markov chain S
t
. Supposing
that 
T
ð:Þ QðS ! :Þ has a finite density, D, with respect to a
symmetrical measure on   , (21) is satisfied if:
ðS;S
0
ÞDðS; S
0
Þ¼ðS
0
;SÞDðS
0
;SÞ: ð22Þ
As shown in [28] for the finite space state case, it is optimal
to make the probability  as large as possible to reduce the
autocorrelation of the Markov chain. Thus, we take:
ðS;S
0
Þ¼min 1;RðS; S
0
Þ
fg
; ð23Þ
where R is the Green’s ratio given by:
RðS;S
0
Þ¼
DðS
0
;SÞ
DðS;S
0
Þ
ð24Þ
and (22) is verified.
One interesting point of the Metropolis-Hastings-Green
algorithm is that the proposal kernel Q can be decomposed
into several kernels q
i
, each corresponding to a reversible
move, as it has been proposed in [21]. Although it is
sufficient to define the uniform birth-and-death [20] in
order to simulate a marked point process (theoretically, S
t
should converge to the same measure), it is important to
define relevant moves in order to accelerate the conver-
gence of the Markov chain. For example, a simple move,
such as a translation or a rotation, is more efficient than a
death followed by a birth, leading to the same result.
Furthermore, a birth-and-death within a neighborhood of
an object of the current configuration is often relevant,
especially if objects are supposed to be in interaction.
5.3 Proposal Kernels
In this section, several proposal kernels are described and
the explicit formula of the associated Green’s ratio is given.
5.3.1 Uniform Birth-and-Death (UBD)
It is the simplest proposal kernel which allows to make
small jumps between spaces of different sizes. It consists of
a uniform birth of a segment in F ½L
min
;L
max
½0;—
proposed with a probability p
b
—and a uniform deat h
(inverse proposal) in the set of segments S.
In the case of the birth of a segment s
0
, the Green’s ratio is
given by:
RðS;S [ s
0
Þ¼
h
1
T
ðS [ s
0
Þ
h
1
T
ðSÞ
p
d
p
b
jF j
nðSÞþ1
; ð25Þ
where p
b
(respectively, p
d
¼ 1  p
b
) is the probability of
choosing a birth (respectively, a death) and  is the intensity
of the reference Poisson process. In the case of the death of a
segment s
0
, the Green’s ratio is given by:
RðS;S n s
0
Þ¼
h
1
T
ðS n s
0
Þ
h
1
T
ðSÞ
p
b
p
d
nðSÞ
jFj
: ð26Þ
5.3.2 Simple Moves
The second kind of move usually proposed is the
modification of a randomly chosen object according to a
symmetrical transformation. Let T¼fT
a
: a 2 Eg be a
family of symmetrical transformations parameterized by a
vector a 2 E. If the modification of an object s is done by
applying T
a
where a is uniformly chosen in E,
RðS; ðS n sÞ[s
0
Þ¼
h
1
T
ðS; ðS n sÞ[s
0
Þ
h
1
T
ðSÞ
: ð27Þ
For instance, T can be defined as the family of rotations
defined in ½

; 

. A rotation T
d

consists in changing the
orientation  of the considered segment by adding
d

2½

; 

:
 ð þ d

Þ½;
where ½: denotes the modulo function. In the same way,
families of translations and dilations are defined.
5.3.3 Improved Simple Moves
The proposal of a move described in the previous section is
not relevant when the considered segment is connected: the
connection often disappears with such a move. That is why
we define a new subkernel which depends on the segment
state with respect to the connection. First, we randomly
choose a segment s in the configuration. If s is free, we
uniformly choose a rotation, a translation, or a dilation,
which are described in Section 5.3.2. If s is single, we
randomly choose between three possible moves:
. Translation of the unconnected extremity e
u
s
:We
uniformly chose a vector ½dx; dy in a given square
½; ½;  and translate e
u
s
by adding the
vector ½dx; dy. If the new length is not in ½L
min
;L
max
,
the operation is iterated.
. Translation of the connected extremity e
c
s
:We
uniformly chose a vector ½dx; dy in a square of side
lower than  and e
c
s
by adding the vector ½dx; dy.If
the new segment is not connected through e
c
s
anymore, the operation is iterated.
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1573

. Translation of a connection: First, we choose a pair of
connected segments to which this segment belongs;
secon d, we uniformly choose a vector ½dx; dy in
½; ½; ; finally, we translate both con-
nected extremities by adding the vector ½dx; dy. If the
new lengths are not in ½L
min
;L
max
, the operation is
iterated.
If s is double, we uniformly choose one of its extremities
and propose one of the two last above-mentioned moves for
a single segment. Note that if there is a change of segment
state, we have to refuse the proposal (because in this case,
the inverse move will never be proposed). The Green’s ratio
is the same as the one given by (27) for simple moves.
5.3.4 Birth-and-Death Based on Data (BDD)
Rather than uniformly proposing a new segment, it would be
relevant to use data information to propose segments that are
well-positioned more often. Following this idea, we use the
offline computation of the statistical values w
k
—presented in
Section4.2—todefine abirth-and-death(BD) kernel. Westore,
for every pixel p
i; i¼1;...;P
and every orientation
~

k; k¼1;...;N
, the
potential 
k
i
—given by (15)— corresponding to the segments
s
k
i
¼ð
^
pp
i
;L
min
;
~

k
Þ whose midpoints
^
pp
i
are positioned in the
square ½p
i
 of F corresponding to p
i
. We then obtain, for every
orientation 
k
, a map C
k
defining an inhomogeneous (i.e.,
nonuniform) birth kernel:
C
k
ðp
i
Þ¼
M  
k
i
P
P
j¼1
ðM  
k
j
Þ
; ð28Þ
where the constant M is chosen so that C
k
defines a strictly
positive probability measure. Here, we choose M ¼ 3. The
weaker the potential associated to a pixel p
i
, the stronger the
probability C
k
ðp
i
Þ of proposing a segment midpoint in ½p
i
.
The procedure is then the following one: Firstly, the length
and the orientation of the new segment are uniformly drawn
in the mark space. Secondly, a pixel p is randomly chosen
according to the map C
k
corresponding to the closest
orientation of the discrete orientation space. Finally, the
segment midpoint is uniformly drawn inside ½p. Then, a
death part is defined in order to obtain a reversible move. It
consists of uniformly removing a segment from the config-
uration. Let us note that this difference between birth and
death treatments is counterbalanced by the Green’s ratio.
In the case of the birth of a segment s
0
, whose midpoint is
in ½p and orientation corresponds to 
k
, in the discrete space
the Green’s ratio is given by:
RðS; S [ s
0
Þ¼
h
1
T
ðS [ s
0
Þ
h
1
T
ðSÞ
p
D
d
p
D
b
j½pj
C
k
ðpÞðnðSÞþ1Þ
; ð29Þ
where p
D
b
and p
D
d
are, respectively, the probability of
choosing a birth and a death based on data. In the death
case, the Green’s ratio is given by:
RðS;S n s
0
Þ¼
h
1
T
ðS n s
0
Þ
h
1
T
ðSÞ
p
I
b
p
I
d
nðSÞ C
k
ðpÞ
jpj
: ð30Þ
5.3.5 Birth-and-Death within a Neighborhood (BDN)
To accelerate the process, it is important to make proposals
which are coherent with the model. Here, the segments are
supposed to be connected. So, proposing a birth near an
extremity of a segment in the current configuration seems to
be relevant. That is the reason why we have introduced a
BD kernel within a neighborhood with respect to the
connection. The birth part consists in uniformly choosing a
segment s
0
in the current configuration S and an endpoint
e
s
0
;i
among the endpoints of s
0
which are inside F (compact
set corresponding to the data image) and then proposing a
new segment from this endpoint. The procedure to compute
this new segment is the following:
. one endpoint is uniformly generated in the ball of
center e
s
0
;i
and radius ;
. the orientation is uniformly selected either in ½0; 2
when the connection only depends on the distance
between segment endpoint (“Candy” model), or in
½  =2;þ =2, when the connection is only
defined for segments forming a large angle (“Quality
Candy” model);
. the length is uniformly drawn in ½L
min
;L
max
.
The death part consists in uniformly choosing a segment s
among connected segments.
The Green’s ratio for the birth of a segment s
0
is then the
following:
RðS; S [ s
0
Þ¼
h
1
T
ðS [ s
0
Þ
h
1
T
ðSÞ
p
N
d
p
N
b

2
nðSÞ
jF j n
s
0
V
ðS [ s
0
Þ n
c
ðS [ s
0
Þ
;
ð31Þ
where p
N
b
and p
N
d
are, respectively, the probabilities of
choosing a birth and a death in a neighborhood, n
s
0
V
ðS [ s
0
Þ
is the number of neighbors of s
0
in the configuration ðS [
s
0
Þ with respect to the connection and  is the ratio
between the Lebesgue measure of the mark space
M ¼½L
min
;L
max
½0;, and the measure of the space
where the length and the orientation of the new segment
are drawn. Thus, when the connection only depends on
endpoint distance, this ratio is equal to 2 and, when the
connection is only defined for a large angle, this ratio is
equal to 1. For the death case, it becomes:
RðS; S n s
0
Þ¼
h
1
T
ðS n s
0
Þ
h
1
T
ðSÞ
p
N
b
p
N
d
jFj n
s
0
V
ðSÞ n
c
ðSÞ

2
nðS n s
0
Þ
: ð32Þ
6PARAMETER CHOICE
This section addresses the problem of parameter choice,
which is a crucial issue given the large number of
parameters involved in the model construction. Indeed,
we distinguish between physical or radiometric parameters
and weight parameters.
The physical parameters are used in the definition of
objects (L
min
, L
max
), in the construction of the mask used to
compute the data term (n
b
, d), and in the definition of
interactions (, 
min
, 
max
). The choice of the physical
parameters is relatively easy. For example, the number of
bands n
b
in the pixel mask directly depends on image
resolution and the type of the line network (river, road,
highway, etc.). The parameter  has to be lower than L
min
=2
for a good definition of the connection. Moreover, it is
important not to take  too small: First, the network
flexibility is reduced for a small ; second, the network
extension is often refused for a small  as the acceptance
1574 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005

probability of a segment birth within a neighborhood
decreases with  (see (31)). In practice, we take  equal to
2 pixels for low resolution images ( 5 meters) and equal to
5 pixels for high resolution images ( 1 meter).
The radiometric parameters are the thresholding para-
meters t
1
and t
2
used to compute data potential (see (15)).
We choose t
1
and t
2
according to the contrast between the
line network and the nearby background.
The choice of the weight parameters that control the
importance of the various terms in the density is more
delicate. The estimation methods refer to these parameters
(the physical parameters are supposed to be known). In
complete data, the parameters of the “Candy” prior model
are estimated by stochastic gradient in [25]. This algorithm
converges to a local optimum located in the neighborhood
of the initial set of parameters. The interest of the method is
reduced as the line network is supposed to be known. In
incomplete data, the weight parameters have to be
estimated in parall el with the configuration
b
SS which
maximizes the density h. The most well-known estimation
algorithm is the Expectation-Maximization (EM) algorithm.
Nevertheless, the EM algorithm and its variants are not
always adapted and there is no proof of convergence
towar d the max imum likelihood estimation. Here, we
propose to use a “calibration” approach which guarantees
that the configuration
b
SS would have good properties. We
first define constraints on local representative configura-
tions according heuristic considerations on the network
topology. We then translate these constraints into a set of
inequalities between the weight parameters. Note that the
relations derived on the parameters are rather simple since
the energy is a linear function of parameters. Finally, this set
of inequalities provides a set of admissible parameters.
At the end of the simulated annealing, we aim to obtain a
configuration with the following properties:
1. No free segment.
2. No pair of single segments not connected to the rest
of the network.
3. No interruption in the network if the addition of a
segment allows to obtain a branch of small curvature.
4. No branches composed of several consecutive
segments all of which perform badly in the data
statistical tests.
5. No additional segment at the end of a branch which
does not fit the data or which leads t o strong
curvature.
6. No too close segments.
Let us recall that, given (12) and (16), the energy of a
configuration S can be written as:
UðSÞ¼!
0
n þ !
1
n
f
þ !
2
n
s
þ !
3
X
g
R
c
ðs
i
;s
j
Þ
þ !
4
X
g
R
io
ðs
i
;s
j
Þþ
d
X

i
;
ð33Þ
where !
i;i¼1;::4
and 
d
are positive weights. The properties
on the final configuration can be translated by the following
constraints on the weight parameters ð!
i;i¼0;::4
;
d
Þ:
1. The energy of a free segment s
1
is larger than the
energy of the empty configuration. In the worst case,

1
is equal to 1. Then, we get:
!
0
þ !
1
 
d
> 0: ð34Þ
2. The energy of two single segments s
1
and s
2
is larger
than the energy of the empty configuration. Con-
sidering the worst case (
1
, 
2
and g
R
c
ðs
1
;s
2
Þ are
equal to 1), we have:
2!
0
þ 2!
2
 !
3
 2
d
> 0: ð35Þ
3. Theenergymustdecreasebyaddingadouble
segment s
i
linking two single segments such that the
two associated connection potentials are negative.
The worst case is thus reached when 
i
is maximal
(i.e., equal to 2) and when the connection potentials
are zero. The expression of this constraint is then:
2
d
þ !
0
< 2!
2
: ð36Þ
But, we want the energy to be increased when the
connection potentials are equal to 1, so that:
2!
3
þ 2
d
þ !
0
> 2!
2
: ð37Þ
4. The energy must increase by adding two double
segments which do not fit the data (i.e., data potential
equals to 2) linking two single segments (worst case:
all connection potentials are equal to 1):
 3!
3
þ 4
d
þ 2!
0
> 2!
2
: ð38Þ
5. Theenergymustdecreasebyaddingasingle
segment s
i
to another single segment s
j
if g
R
c
ð:Þ <¼
0 and 
i
<¼ 0:
!
0
< 0: ð39Þ
On the contrary, it must increase if 
i
¼ 2
!
0
 !
3
þ 2
d
> 0: ð40Þ
6. The last property (no too close segments) is verified
as soon as !
4
> 0 due to the “hard-core” imposed on
the relation of bad orientation.
Taking 
d
¼ x!
3
, these equations lead to the parameter
tuning rule given in Table 1, where a, b, and c are positive
constants. One example is given with the additional con-
straint that the potential of a free segment is larger (or equal)
than the potential of two single segments in order to widely
accept the birth from a free segment at the beginning of the
algorithm, the initial state being the empty configuration.
7RESULTS
7.1 Quantitative Evaluation with Respect to a
Reference Network
As we aim to compare different models and algorithms, we
need to find criteria of performance that can be obtained by
conducting a quantitative evaluation of the detected line
networks with respect to a reference line network. For each
image for which a reference network is given, segments
provided by our algorithm are matched with the branches
of the reference (supplied in the form of broken lines by a
specialist). A segment is matched with the reference if each
of its extremities is at a distance from the reference network
lower than a threshold fixed by the user (we can take, for
example, a threshold equal to ten pixels). This matching is
illustrated by Fig. 7. It allows the computation of L
0
and L
F
,
the lengths of omitted and overdetected sections, and A, the
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1575

area included between these sections which have been
matched. The three criteria for the evaluation of the
extracted network are:
. F ¼ 100
L
F
L
ref
, the ratio of false alarms with respect to
the reference length L
ref
;
. 0 ¼ 100
L
0
L
ref
, the ratio of omissions with respect to the
reference length;
. D ¼
A
L
ref
L
0
, a geometrical error corresponding to the
distance between matched sections, equal to the area
A included between these sections divided by the
length of the reference sections which have been
matched.
7.2 Comparison of the Prior Models
The performance of the “Candy” model in simulating and
detecting line network was reported in [19]: the results are
encouraging, with relatively few false alarms and omissions
for an automatic method. Nevertheless, the line network is
not as smooth as possible and undesirable interruptions are
observed. Our first o bjective was to determine if the
incorporation of quality measures in the density could
improve the results.
First, Fig. 8 provides one sample from each prior model
obtained using the RJMCMC algorithm described in
Section 5. The initial state is the empty configuration. The
chosen proposition kernel is composed by two equiprobable
kernels: uniform birth-and-death (UBD) and birth-and-
death within a neighborhood (BDN). The sample obtained
for the “Candy” model seems good in the sense that all
segments are connected and form long broken lines.
Nevertheless, the drawback of this model, mentioned in
Section 3.2, is confirmed: We observe small breaks and
points of strong curvature. The consequence of this draw-
back is that we obtain a line network which is not as smooth
as a real road network. The “Quality Candy” model seems
to be more appropriate for road detection as the sample
obtained is clearly smoother than the one obtained with the
“Candy” model.
Second, Fig. 9 provides results of road network extraction
from a satellite SPOT image (Panchro, size: 256  256 pixels,
resolution: 10 m) with the two prior models. The extraction
algorithm is a simulated annealing using an RJMCMC
algorithm whose proposal kernel Q
1
is composed of
three equiprobable kernels: UBD, BDN, and improved
simple moves. The data term used here corresponds to an
online computation: The data term is given by (16) with t
1
¼
4 and t
2
¼ 8. Two rates of temperature decrease are tested.
Globally, the results present less than 10 percent of false
alarms. The geometrical error with respect to the manual
extraction is of subpixel magnitude. Nevertheless, the
percentage of omissions is high: more than 30 percent. These
omissions co rrespond to dirt tracks, which are not as
rectilinear and clearly contrasted with respect to the back-
ground as the main roads. For the “Candy” model, if the
temperature decrease is too fast, the main roads are not
completely detected, as shown in Fig. 9d. Indeed, there is a
critical temperature for which it is important to have a slow
decrease in order to reach the global maximum of the
density. That is why the main roads are well detected in
Fig. 9c, obtained with a slower temperature decrease. This
points out that the algorithm result is very dependent on the
temperature decrease. The “Quality Candy” model provides
a smoother line network. Moreover, there are less omissions
for the same temperature decrease. It appears to be not as
sensitive to the temperature decrease as the “Candy” model.
This implies a possible significant reduction of the comput-
ing time.
7.3 Online Computation of the Data Potential
This section presents extraction results using the “Quality
Candy” model with an online computation of the data term.
As in Section 7.2, the extraction algorithm is a simulated
1576 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005
TABLE 1
Parameter Tuning Following the Constraints on the Final Configuration
Fig. 7. Matching between detected and reference line network.
Fig. 8. Samples of the prior models. (a) “Candy” model and (b) “Quality
Candy” model.

annealing using an RJMCMC algorithm with the proposal
kernel Q
1
(UBD, BDN, and improved simple moves).
First, Fig. 10 gives a result of road extraction from a high
reso lution aerial image provided by the IGN (French
Mapping Institute). The task is not straightforward: Some
trees interfere with good detection of road sections, some
fields have nearly the same grey level as the roads, and field
textures might produce a significant answer to the statistical
tests used to compute the data term. The “Quality Candy”
model is well-adapted to this extraction problem. With an
online computation of the data potential, we obtain about
4 percent of false alarms and 16 percent of omissions, and
the geometrical error D is lower than one pixel. There are no
breaks except in the road crossing where the data potential
is positive. The omissions correspond in majority to
secondary roads which have not been detected due to their
small size and higher curvature than the ones observed for
the main roads.
Second, Fig. 11 presents a result of river extraction from a
satellite image of Guinea provided by the BRGM (French
Geological Survey). Despite the low contrast of the image,
the extraction algorithm provides a line network with few
omissions and overdet ections with respect to reference
network provided by the BRGM. Nevertheless, the detection
is not very accurate due to the sinuosity of this network.
7.4 Offline Computation of the Data Potential
In this section, we evaluate the improvement due to the use
of an offline computation of the data potential. We have
tested two proposal kernels: the proposal kernel Q
1
(UBD,
BDN, improved simple moves) and the kernel Q
2
composed
of three equiprobable kernels: birth-and-death based on
data (BDD), BDN, and improved simple moves.
For the aerial image given in Fig. 10a, the use of an
offline computation of the data potential induces a small
loss of quality (see Table 2). Nevertheless, Table 2 shows
that the use of an offline computation is very efficient in
terms of computing time. Moreover, it shows that it is
relevant to use the BDD kernel as the results obtained using
Q
1
and Q
2
(for the same model) are of equivalent quality.
For the satellite image given in Fig. 11a, the results
obtained with the two methods are of equivalent quality but
the computing time is much lower when we use an offline
computation (see Table 2). This can be explained by the fact
that the average length of a segment is very close to the
minimal length used for the precalculation.
Globally, these results show the relevance of using a
kernel based on data: We obtain nearly the same result with
Q
1
as with Q
2
and the gain in computing time is important
(see Table 2).
8CONCLUSION AND FUTURE WORK
We have proposed in this paper a method for performing
unsupervised line network extraction from remotely sensed
images with medium or high resolution. The “Quality
Candy” prior model is particularly suited to the extraction
of road networks. Indeed, the use of quality coefficients for
the connection relation leads to a continuous line network
with a small curvature. It can be adapted in an encouraging
way to the case of networks which are more sinuous such as
riverine forests. The optimization was performed using
simulated annealing with an RJMCMC algorithm, which is
based on a composed proposal kernel built in order to
accelerate the convergence. The results have shown the
relevance of using an offline computation of the data
potential, in particular, when a proposal kernel based on
this computation is added in the RJMCMC algorithm.
Nevertheless, a small loss in quality can be observed when
an offline computation is performed.
The proposed stochastic model allows us to perform data
fusion in order to benefit from the contribution of several
sources (for instance, multisensor or multitemporal data;
some p reliminary work has been con ducted with radar
images). Moreover, this model could be extended to more
complex objects, such as broken lines, which would adapt
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1577
Fig. 9. Road network extraction from a SPOT image for each prior model
and the same data term: t
1
¼ 4, t
2
¼ 8. (a) Data (256  256 pixels).
(b) Manual extraction. (c) Candy. (d) Candy. (e) Quality Candy.
(f) Quality Candy.

themselves more easily to sinuous networks (this work is
currently in progress). Regarding optimization, as this study
has shown that the optimization algorithm has an influence
not only on the computing time but also on the final result, we
will focus in a near future on the improvement of the
simulated annealing scheme by using an adaptive rule of
temperature decrease or using parallel simulated annealing.
Finally, work remains to be done to provide a product for
updating and creating maps. To make it easier to exploit the
extraction results, it is essential to develop tools for the
evaluation of the extracted network, based on data and
assumptions on the network topology and geometry. Evalua-
tion criteria could be used to indicate the ambiguous parts of
the detected line network to a user. Moreover, postprocessing
based on these criteria could be relevant.
ACKNOWLEDGMENTS
The authors would like to thank the French Mapping
Institute (IGN) for providing an aerial image, the French
Geological Survey (BRGM) for providing data shown in
Fig. 11 and for partial financial support, as well as Nicolas
Baghdadi from the BRGM for several interesting discussions.
This work was conducted while C. Lacoste was a PhD
student with the Ariana research group.
REFERENCES
[1] G. Vosselman and J. de Knecht, “Road Tracing by Profile
Matching and Kalman Filtering,” Automatic Extraction of Man-
Made Objects from Aerial and Space Images, pp. 265-274, Apr. 1995.
[2] D. Geman and B. Jedynak, “An Active Testing Model for Tracking
Roads in Satellite Images,” IEEE Trans. Pattern Analysis and
Machine Intelligence, vol. 18, pp. 1-14, 1996.
[3] M.A. Fischler, J.M. Tenenbaum, and H.C. Wolf, “Detection of
Roads and Linear Structures in Low-Resolution Aerial Imagery
Using a Multisource Knowledge Integration Technique,” Compu-
ter Graphics and Image Processing, vol. 15, pp. 201-223, 1981.
[4] N. Merlet and J. Zerubia, “New Prospects in Line Detection by
Dynamic Programming,” IEEE Trans. Pattern Analysis and Machine
Intelligence, vol. 18, no. 4, pp. 426-431, Apr. 1996.
[5] W.M. Neuenschwander, P. Fua, L. Iverson, G. Sze
´
kely, and O.
Kubler, “Ziplock Snakes,” Int’l J. Computer Vision, vol. 25, no. 3,
pp. 191-201, 1997.
1578 IEEE TRANSACTIONS ON PATTERN ANALYSIS AND MACHINE INTELLIGENCE, VOL. 27, NO. 10, OCTOBER 2005
Fig. 10. Road network extraction from an aerial image (resolution: 50 cm) with an online computation of the data potential. (a) Data (892  652 pixels).
(b) Manual extraction. (c) Extracted line network.
Fig. 11. Hydrographic network extraction from a satellite image (SPOT XS2) with the parameter values given in Table 1 and with t
1
¼ 3 and t
2
¼ 7
and with an online computation of the data potential. (a) Data (682  674 pixels). (b) Manual extraction. (c) Extracted line network.
TABLE 2
Quantitative Comparison between the Online (D
1
) and Offline (D
2
) Computations of the Data Potential

[6] A. Gru
¨
n and H. Li, “Road Extraction from Aerial and Satellite
Images by Dynamic Programming,” ISPRS J. Photogrammetry and
Remote Sensing, vol. 50, no. 4, pp. 11-20, Aug. 1995.
[7] I. Couloigner and T. Ranchin, “Mapping of Urban Areas: A
Multiresolution Modeling Approach for Semi-Automatic Extrac-
tion of Streets,” Photogrammetric Eng. and Remote Sensing, vol. 66,
no. 7, pp. 867-874, July 2000.
[8] M.A. Serendero, “Extrac tion D’informations Symboli ques en
Imagerie SPOT: Re
´
seaux de Communication et Agglome
´
rations,”
PhD Thesis (in French), Univ. of Nice—Sophia Antipolis, 1989.
[9] R. Duda and P. Hart, Pattern Classification and Scene Analysis. New
York: John Wiley & Sons, 1973.
[10] D. Haverkamp, “Extracting Straight Road Structure in Urban
Environments Using IKONOS Satellite Imagery,” Optical Eng.,
vol. 41, no. 9, pp. 2107-2110, Sept. 2002.
[11] U. Bhattacharya and S. Parui, “An Improved Backpropagation
Neural Network for Detection of Road-Like Features in Satellite
Imagery,” Int’l J. Remote Sensing, vol. 18, pp. 3379-3394, Apr. 1997.
[12] D. Wang, D. He, L. Wang, and D. Morin, “Extraction du Re
´
seau
Routier Urbain a
`
l’Aide d’Images SPOT HRV,” Int’l J. Remote
Sensing, vol. 17, no. 4, pp. 827-833, 1996.
[13] A. Zlotnick and P. Carnine, “Finding Road Seeds in Aerial
Images,” Computer Vision, Graphics, and Image Processing, vol. 57,
pp. 243-260, 1993.
[14] M. Barzohar and D.B. Cooper, “Automatic Finding of Main Roads
in Aerial Images by Using Geometric-Stochastic Models and
Estimation,” IEEE Trans. Pattern Analysis and Machine Intelligence,
vol. 18, no. 7, pp. 707-721, July 1996.
[15] F. Tupin, H. Maitre, J.-F. Mangin, J.-M. Nicolas, and E. Pechersky,
“Detection of Linear Features in SAR Images: Application to Road
Network Extraction,” IEEE Trans. Geoscience and Remote Sensing,
vol. 36, no. 2, pp. 434-453, 1998.
[16] P. Doucette, P. Agouris, A. Stefanidis, and M. Musavi, “Self-
Organized Clustering for Road Extraction in Classified Imagery,”
ISPRS J. Photogrammetry and Remote Sensing, vol. 55, pp. 347-358,
2001.
[17] I. Laptev, T. Lindeberg, W. Eckstein, C. Steger, and A. Baumgart-
ner, “Automatic Extraction of Roads from Aerial Images Based on
Scale Space and Snakes,” Machine Vision and Applications, vol. 12,
pp. 23-31, 2000.
[18] A. Baumgartner, C. Steger, H. Mayer, W. Eckstein, and H. Ebner,
“Automatic Road Extraction Based on Multi-Scale, Grouping, and
Context,” Photogrammetric Eng. and Remote Sensing, vol. 65, no. 7,
pp. 777-785, July 1999.
[19] R. Stoica, X. Descombes, and J. Zerubia, “A Gibbs Point Process
for Road Extraction in Remotely Sensed Images,” Int’l J. Computer
Vision, vol. 57, no. 2, pp. 121-136, 2004.
[20] C.J. Geyer and J. Møller, “Simulation and Likelihood Inference for
Spatial Point Process,” Scandinavian J. Statistics, Series B, vol. 21,
pp. 359-373, 1994.
[21] P. Green, “Reversible Jump Markov Chain Monte-Carlo Compu-
tation and Bayesian Model Determination,” Biometrika, vol. 57,
pp. 97-109, 1995.
[22] M. van Lieshout, Markov Point Processes and Their Applications.
Imperial College Press, 2000.
[23] R. Stoica, “Processus Ponctuels pour L’extraction des Re
´
seaux
Line
´
iques dans les Images Satellitaires et Ae
´
riennes,” PhD Thesis
(in French), University of Nice—Sophia Antipolis, Feb. 2001.
[24] D. Ruelle, “Superstable Interactions in Classical Statistical
Mechanics,” Comm. Math. Physics, vol. 18, pp. 127-159, 1970.
[25] M. van Lieshout and R. Stoica, “The Candy Model Revisited:
Markov Properties and Inference,” Research Report PNA-R0115,
CWI, Amsterdam, The Netherlands, 2001.
[26] C. Lacoste, X. Descombes, and J. Zerubia, “A Comparative Study
of Point Processes for Line Network Extraction in Remote
Sensing,” Research Report 4516, INRIA, Sophia Antipolis, France,
July 2002.
[27] M. van Lieshout, “Stochastic Annealing for Nearest-Neighbour
Point Processes with Application to Object Recognition,” Research
Report BS-R9306, CWI, Amsterdam, The Netherlands, 1993.
[28] P.H. Peskun, “Optimum Monte Carlo Sampling Using Markov
Chains,” Biometrika, vol. 60, pp. 607-612, 1973.
Caroline Lacoste received t he engineering
degree in mathemati cal modeling an d the
master of science degree in applied mathe-
matics from the National Institute of Applied
Sciences (INSA) of Toulouse in 2001. She
received the PhD degree in signal and image
processing in 2004 from the University of
Nice—Sophia Antipolis. In 2004, she joined the
INSA of Lyon where she is a teaching fellow at
the “first cycle” department and a research fellow
at the CREATIS laboratory (CNRS/INSERM/INSA/UCBL). Her research
interests include inverse problems, image pr ocessing, stochastic
geometry, and Monte Carlo methods.
Xavier Descombes received the bach elor’s
degree in telecommunications from the Ecole
Nationale Superieure des Telecommunications
(ENST) Paris, France, in 1989, the master of
science in mathematics from the University of
Paris VI in 1990, the PhD degree in signal and
image processing from the ENST in 1993, and
the “habilitation” in 2004 from the University of
Nice—Sophia Antipolis. He has been a posdoc-
toral researcher at ENST in 1994, at the
Katoliek e Universitat Leuven in 1995, at the Institut National de
Recherche en Informatique et en Automatique (INRIA) in 1996, and a
visiting scientist in the Max Planck Institute of Leipzig in 1997. He is
currently a permanent researcher at INRIA. His research interests
include Markov Random Fields, stochastic geometry, and stochastic
modeling in image processing.
Josiane Zerubia received the MSc degree from
the Department of Electrical Engineering at
ENSIEG, Grenoble, France in 1981, the doctor
engineer degree in 1986, a PhD in 1988, and an
“Habilitation” in 1994, all from the University of
Nice—Sophia Antipolis, France. She has been a
permanent research scientist at INRIA since
1989 and the director of research since July
1995. She was head of a remote sensin g
laboratory (PASTIS, INRIA Sophia Antipolis)
from mid-1995 to 1997. Since January 1998, she has been in charge
of a new research group working on remote sensing (ARIANA, INRIA-
CNRS-University of Nice). She has been adjunct professor at Sup’Aero
(ENSAE) in Toulouse since 1999. Before, she was with the Signal and
Image Processing Institute of the University of Southern California
(USC) in Los Angeles as a postdoctoral researcher. She also worked as
a researcher for the LASSY (University of Nice and CNRS) from 1984 to
1988 and in the research lab of Hewlett Packard in France and in Palo
Alto, California from 1982 to 1984. She was part of the IEEE IMDSP
Technical Committee (SP Society) from 1997 to 2003 and associate
editor of the IEEE Transactions on Image Processing from 1998 to
2002. She has been member-at-large of the board of governors of the
IEEE SP Society since 2002, area editor of IEEE Transactions on Image
Processing since 2003 and, guest coeditor of a special issue of IEEE
Transactions on Pattern Analysis and Machine Intelligence in 2003. She
has also been a member of the editorial board of the French Society for
Photogrammetry and Remote Sensing (SFPT) since 1998. She has
been cochair of two workshops on Energy Minimization Methods in
Computer Vision and Pattern Recognition (EMMCVPR ’01, Sophia
Antipolis, France, and EMMCVPR ’03, Lisbon, Portugal), cochair of a
workshop on Image Processing and Related Mathematical Fields (IPRM
’02, Moscow, Russia), and chair of a workshop on Photogrammetry and
Remote Sensing for Urban Areas, Marne La Vallee, France, 2003. Her
current research interest is image processing using probabilistic models
or variational methods. She also works on parameter estimation and
optimization techniques. She is a fellow of the IEEE.
. For more information on this or any other computing topic,
please visit our Digital Library at www.computer.org/publications/dlib.
LACOSTE ET AL.: POINT PROCESSES FOR UNSUPERVISED LINE NETWORK EXTRACTION IN REMOTE SENSING 1579