SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING
The Renewal of an Old Approach for Information Extraction from Images
Aline Deruyver
1
and Yann Hod
´
e
2
1
LSIIT, UMR 7005 CNRS-ULP, 67 000 Strasbourg, France
2
G08 CH Rouffach, 68250 Rouffach, France
Keywords:
Arc consistency, Image interpretation, Graph, Spatial relationships, Constraints satisfaction.
Abstract:
The aim of this paper is to show that symbolic computation based on constraint satisfaction can be useful for
information extraction from images. It presents how some limitations of this approach have been overcome
by the development of new conceptual tools: arc-consistency with bilevel constraints, weak arc-consistency,
a system of complex qualitative spatial relations. The application of these tools to images of various domains
(medical images, high resolution satellite images) shows its effectivity.
1 INTRODUCTION
Animals are able to perform complex visual discrim-
ination tasks and decision making. It means that pro-
cessing visual input does not require a high degree
of symbolic reasoning. The good results obtained by
many computer vision algorithms based on statisti-
cal/physical models tend to prove it. On the other
hand, it is difficult to believe that image understand-
ing will never draw benefit from symbolic reasoning
which is a so powerful tool for human intelligence.
Now, if we want to translate this human specific abil-
ity in a computer algorithm, how to do it? Graph for-
malism has long been used in the field of artificial in-
telligence to represent the conceptual knowledge (on-
tologies, semantic graphs) because it is a convenient
way to represent logical constraints between differ-
ent concepts (textual or visual). These graphs can be
used to solve Constraint Satisfaction Problem (CSP).
The resolution of such problems consists in check-
ing the consistency of a graph. Values are assigned
to a set of variables (which are represented by nodes
of the graph and can be seen as a way of symboliz-
ing concepts) constrained by binary relations (repre-
sented by the arcs of the graph). This kind of prob-
lem is NP-complete. To get a solution in a reasonable
amount of time, fast algorithms of arc-consistency
checking have been proposed (Waltz, 1975), (Mohr
and Henderson, 1986), (Mackworth, 1977),(Mack-
worth and Freuder, 1985), (Hentenryck et al., 1992),
(Freuder and Wallace, 1992), (Bessi
`
ere, 1994). Even
if some authors have proposed applications of con-
straint satisfaction checking on images (Benmouffek
et al., 1991), (Mahonney and Fromherz, 2002), (Nem-
pont et al., 2008), these approaches have been little
used so far in image interpretation.
However, converting an image interpretation
problem into a problem of constraint satisfaction is
fairly easy: the nodes of the graph correspond to ob-
jects or part of objects that we look for in the image
and the arcs symbolize the spatial constraints between
objects. Then, the image interpretation consists in
finding regions of the image that can be assigned to
each node in the graph and that satisfy the spatial con-
straints imposed by the graph.
The two limiting factors of these approaches are:
Classical arc-consistency checking algorithms as-
sume that with one node of the graph is associ-
ated only one value (a node of the graph is asso-
ciated with only one region of the image). It is
a great limitation because images are in practice
often over-segmented.
The local constraints are often too general to de-
scribe many objects made up of over-segmented
regions in unpredictable ways.
Our work sought to overcome these limitations. We
created the concept of arc-consistency checking with
two levels of constraints. This allows to associate sev-
eral regions of the image with a node in the graph
model (for example, several nodes in the adjacency
graph representing the segmented image). With this
multivalent graph-matching by constraint satisfac-
tion checking, it becomes possible to interpret over-
515
Deruyver A. and Hodé Y..
SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING - The Renewal of an Old Approach for Information Extraction from Images.
DOI: 10.5220/0003692105070514
In Proceedings of the International Conference on Knowledge Discovery and Information Retrieval (KDIR-2011), pages 507-514
ISBN: 978-989-8425-79-9
Copyright
c
2011 SCITEPRESS (Science and Technology Publications, Lda.)
segmented images and then to apply the principle of
arc-consistency in common situations. We then devel-
oped various tools to build a more powerful constraint
language:
A richer lexicon of constraints (mainly spatial
constraints).
The possibility of combining these constraints
with logical expressions, which requires the intro-
duction of the notion of weak arc consistency. We
will see the algorithmic solutions to implement
this concept.
The aim of this article is to show that symbolic ap-
proach based on the notion of constraint satisfaction
can bring interesting solutions to image interpreta-
tion problem. This article presents the basic concepts
of this work and describes briefly the different tools
developed in this framework. Some applications in
medical images and high resolution satellite images
are described.
2 SEMANTIC GRAPHS AND ARC
CONSISTENCY CHECKING
In a semantic graph, the binary constraints repre-
sented by the arcs and the unary constraints associ-
ated with the nodes are supposed to be known at the
beginning of the matching process. The hypothesis is
that some specific constraints exist in the image and
the aim is to find the set of regions satisfying these
constraints.
2.1 Problem with Two Levels of
Constraint
We can say that solving an image interpretation prob-
lem is similar to solving a constraint satisfaction prob-
lem. To define such a problem we use the following
conventions:
Variables are represented by the natural numbers
1, ...n. Each variable i has an associated domain
D
i
. We use D to denote the union of all domains
and d the size of the largest domain.
All constraints are binary and relate two distinct
variables. A constraint relating two variables i and
j is denoted by C
i j
. C
i j
(v, w) is the Boolean value
obtained when variables i and j are replaced by
values v and w respectively. Let Rc be the set of
these constraining relations.
A Finite-Domain Constraint Satisfaction Problem
(FDCSP) consists of finding all the sets of values
Figure 1: Structure of a node used to manage the arc-
consistency checking with bilevel constraints. In this ex-
ample the node i of the semantic graph is constrained by the
nodes j, k and l and it constrains the node m. The rectangles
inside the node i represent the sets ”interface”.
{a
1
, ..., a
n
}, a
1
x ... x a
n
D
1
x ... x D
n
, for(1, ...,
n) satisfying all relations belonging to Rc.
A graph G is associated with a constraint satisfac-
tion problem as follows: G has a node i for each vari-
able i. One oriented arc (i, j) is associated with each
constraint C
i j
. Arc(G) is the set of arcs of G and e is
the number of arcs in G. Node(G) is the set of nodes
of G and n is the number of nodes in G.
In this classical definition of FDCSP, one variable
is associated with one value. This assumption cannot
hold for some classes of problems where we need to
associate a variable with a set of linked values as de-
scribed in (Deruyver and Hod
´
e, 1997) and (Deruyver
and Hod
´
e, 2009b). It is the case when several seg-
mented regions have to be associated with a node of
the semantic graph.
To cope with this difficulty, the structure of the
nodes is modified. A node becomes a multi-set made
up of a kernel and several interfaces (each interface is
associated with each arc leaving the considered node,
see Figure 1). Moreover, two levels of constraint
are introduced: The first one, called inter-node, links
two interfaces of two different nodes. (it is similar
to the previous constraint C
i j
between two nodes i
and j but in our case it is reduced to a part of each
node). The checking of constraints on sub-sets of val-
ues associated with each node generates a constraint
relaxation between the nodes and can produce a dra-
matic increase of the number of solutions. This draw-
back can be removed if the intra-node constraint is
efficient enough to balance the inter-node relaxation.
However, additional computation may increase the
time complexity of the constraint satisfaction check-
ing. Then this checking has to be possible in practice
in term of time complexity of the algorithms.
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
516
We propose to use two types of intra-node con-
straint. The first type corresponds to global con-
straints Cmpg
i
linking a set of values of the node i.
The second type corresponds to constraints linking
two values of a node with a compatibility constraint
Cmp
i
associated with each variable i (spatial relations
between sub-parts of an object associated with a node
of the graph). Then, the notion of constraint satisfac-
tion problem with two levels of constraint (FDCSP
BC
)
can be defined as follows:
Definition 1.
Let Cmp
i
be a compatibility constraint such that
(a, b) satisfies Cmp
i
a and b are compatible,
where a D
i
and b D
i
.
Let Cmpg
i
be a global compatibility constraint on
a set of values S
i
D
i
such that S
i
satisfies Cmpg
i
.
Let C
i j
be a constraint between i and j.
Let S
i
and S
j
be a pair such that S
i
D
i
and
S
j
D
j
, S
i
, S
j
|= C
i j
means that (S
i
, S
j
) satisfies
the oriented constraint C
i j
.
S
i
, S
j
|= C
i j
a
i
S
i
, (a
0
i
, a
j
) S
i
× S
j
, such
that (a
i
, a
0
i
) satisfies Cmp
i
and (a
0
i
, a
j
) satisfies C
i j
.
Definition 2. Sets {S
1
...S
n
} satisfy FDCSP
BC
C
i j
, S
i
, S
j
|= C
i j
and S
i
satisfies Cmpg
i
and S
j
satis-
fies Cmpg
j
.
2.2 Arc Consistency Checking Problem
with Bilevel Constraints
Solving the constraint satisfaction problem with
bilevel constraints with the arc consistency check-
ing implies to define a class of problems called arc
consistency checking problem with bilevel constraints
(AC
BC
). Solving this type of problems allows to solve
a multivalent matching problem. This is what we
want to do when we want to match an adjacency graph
and a semantic graph. This class of problem is associ-
ated with FDCSP
BC
. Let P(D
i
) be the set of sub parts
of the domain D
i
.
Definition 3. Let (i, j) arc(G). Arc(i,j) is arc
consistent with respect to P(D
i
) and P(D
j
)
S
i
P(D
i
), S
j
P(D
j
) such that v S
i
t S
i
,
w S
j
, Cmp
i
(v,t) and C
i j
(t, w) and Cmpg
i
(S
i
) and
Cmpg
j
(S
j
) (v and t could be identical).
Definition 4. Let P= P(D
1
) × ... × P(D
n
). A graph
G is arc consistent with respect to P (i, j)
arc(G) : (i, j) is arc consistent with respect to P(D
i
)
and P(D
j
).
The purpose of an arc-consistency algorithm with
bilevel constraints is, given a graph G and a set P,
to compute P’, the largest arc consistent domain with
bilevel constraints for G in P.
3 A SYSTEM OF QUALITATIVE
SPATIAL RELATIONS: THE
CONNECTIVITY-DIRECTION-
METRIC FORMALISM
(CDMF)
In order to better describe complex spatial relations
between two objects made up of several segmented
regions, we developed a system of topological and
directional relations (Deruyver and Hod
´
e, 2009c).
Some of these relations are calculated thanks to the
well known notion of minimum bounding box of a
region and to the notion of minimum bounding boxes
of border interfaces between two regions.
3.1 Minimum Bounding Boxes of
Border Interfaces between Two
Regions
The notion of minimum bounding box of border in-
terfaces is introduced to improve the description of
distance relationship between two objects. We mean
by border interface the border part of a region which,
given a cardinal direction, is in front of another region
(Cf. Fig. 2).
Figure 2: a) In this case the two regions are not overlapped
but their minimum bounding boxes are overlapped. The
analysis of the spatial relation between these two regions
is not possible by using minimum bounding boxes. b) mbb-
biw is the minimum bounding box of the border interface
which is on the left of region A. mbbbie is the minimum
bounding box of the border interface which is on the right
of region B.
Definition 5. Let R be a region (a set of connected
pixels) and let p(x,y) be a pixel of R. E(R)={p(x,y)
R | p(x’,y’) one of the 8 connected neighbors of
p(x,y), p(x’,y’) 6∈ R}. Let A and B be two regions:
The border interface Cw(A,B) is defined by
{p(x,y) E(A) such that p(x’,y) E(B) and
p(x”,y) such that x < x” < x’ p(x”,y) 6∈ A and
p(x”,y) 6∈ B }
The border interface Ce(A,B) is defined by {p(x,
y) E(A) such that p(x’, y) E(B) and p(x”,
y) such that x> x” >x p(x”, y) 6∈ A and p(x”, y) 6∈
B }
The border interface Cn(A,B) is defined by {p(x,
y) E(A) such that p(x ,y’) E(B) and p(x,
SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING
- The Renewal of an Old Approach for Information Extraction from Images
517
y”) such that y< y”<y’ p(x, y”) 6∈ A and p(x, y”)
6∈ B }
The border interface Cs(A,B) is defined by {p(x,
y) E(A) such that p(x ,y’) E(B) and p(x,
y”) such that y> y”>y’ p(x, y”) 6∈ A and p(x, y”)
6∈ B }
Definition 6. The minimum bounding box of a border
interface in the direction d (mbbbid) is defined by
(in f
x
(Cd(A,B)), in f
y
Cd(A,B))), (sup
x
(Cd(A,B)),
sup
y
(Cd(A,B)))
We can see on the example of Figure 2 that the
two mbb of the regions A and B are overlapped. On
the contrary the mbbbiw and the mbbbie are not over-
lapped. Then, thanks to the mbbbi, it is easy to de-
duce, on this example, that the region A is on the left
side of region B.
3.2 Additional Relations between Two
Regions
Minimum bounding boxes of border interface
(mbbbiw, mbbbie, mbbbin, mbbbis) allow to describe
additional relations. The four spatial relations be-
tween A and B linked to the corresponding mbbbid
can be defined as follows:
A Ei B iff sup
x
(Cw(B, A)) 6 in f
x
(Ce(A, B)),
A Wi B iff sup
x
(Cw(A, B)) 6 in f
x
(Ce(B, A)),
A Ni B iff sup
y
(Cn(A, B)) 6 in f
y
(Cs(B, A)),
A Si B iff sup
y
(Cn(B, A)) 6 in f
y
(Cs(A, B)),
All these relations may be associated with the metric
d defined as follows: d(A, B)= in f
z
(A)-sup
z
(B) where
z = y for Ni or Si relationship, and z = x for Ei or Wi
relationship.
3.3 Elementary Relations in CDMF
CDMF allows to define very complex relationships
by a combination of elementary relationships. An el-
ementary relationship is a relation:
(1) of connectivity or non connectivity
(2) of directional constraint between mbb with
none or one metric relation chosen among the
metrics dsi and dgi (i=1 4) described in Figure
3 (with inferior and superior limits). In that case,
we have four directional relationships: N (North),
S (South), W (West) and E (East).
(3) of directional constraint between mbbbi with
one metric relation d defined before (with inferior
and superior limits). In this case, we have four
directional relationships: Ni, Si, Wi and Ei.
A concrete implementation of these relations is
proposed to use it in the context of a constraint sat-
isfaction problem with bilevel constraints. These re-
lations are used as spatial constraints associated with
the arcs of a semantic graph.
Figure 3: The 8 distances that can be defined on minimum
bounding boxes.
3.4 Weak Arc-consistency to Combine
Spatial Relations
To be able to describe more complex relationships be-
tween regions such as ”is surrounded by”, it is neces-
sary to combine relations in a logical expression such
that Ei or Wi or Ni or Si which means that a region
has to be in the neighbourhood of another region in
one of the four directions. To express such combina-
tion we use the notion of quasi-arc consistency de-
scribed in (Deruyver and Hod
´
e, 2009b). The idea
is to associate a number of relaxation with a set of
arcs. For example let a1, ..., an be a set of n arcs.
With the notion of quasi-arc consistency it is possible
to associate with this set, a number r of relaxation.
If r = n 1, then at least one constraint associated
with one of these arcs has to be satisfied. This no-
tion of quasi-arc consistency introduces an operator
or between each constraint associated with the arcs.
The Figure 4 shows the structure of a node describ-
ing the logical expression (A or B or C) and (C or
D) and (D or E) and (E or F) where A, B, C, D, F
and G are spatial relations. The quasi-arc consistency
can be defined as follows: Let Γ
i
be the set of the
nodes linked to the node i in the graph G such that:
Γ
i
= { j Node(G), (i, j) Arc(G)}
Figure 4: Node representing the expression (A or B or C)
and (C or D) and (D or E) and (E or F). The relaxation
numbers have the following values: R2=2, R1=1, R3=1,
R4=1.
Let the function Rl(i) be such that it maps to a
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
518
node i the number nb of constraint relaxations in the
graph G and it is such that:
Rl : node(G) N
i 7→ Rl(i) = nb with nb 0
and nb Card(Γ
i
)
This function allows that nb binary constraints asso-
ciated with the node i can be not satisfied. Let Γ
ac
i,l
the
set of the nodes j Γ
i
making arc-consistent arc with
a given node i and a given l D
i
such that:
Γ
ac
i,l
= { j Γ
i
| (i, j) is arc-consistent with respect to
l D
i
and P (D
j
)}
With the function Rl, a new class of problems called
quasi arc-consistency problem can be defined. The
definition of a quasi arc-consistent graph is:
Definition 7. Let P (D
i
) be the set of sub parts of the
domain D
i
. Let P=P (D
1
)× .... ×P (D
n
). A graph G is
quasi arc-consistent with respect to P iff i node(G)
we have
Card(Γ
i
) min
lD
i
(Card(Γ
ac
i,l
)) Rl(i)
4 EXPERIMENTS
We present three applications of image interpretation
using semantic graphs and arc-consistency checking.
The first one concerns the interpretation of anatom-
ical cerebral images. The second one concerns the
analysis of water meter images and the last one con-
cerns the detection of residential areas in high resolu-
tion satellite images.
4.1 Interpretation of Anatomical
Cerebral Images
Experiments have been made on a set of NMR im-
ages obtained on the web site ”BrainWeb” (http://
www.bic.mni.mcgill.ca/brainweb/). This web site
contains a database of simulated images. In these ex-
periments we focus our interest on six internal grey
nuclei (small internal anatomical structures of the
brain). Figure 5 shows the conceptual graph describ-
ing this part of the cerebral anatomy. In this applica-
tion the white and the grey matter are labeled. The in-
terpretation is made on the 10 slices containing these
nuclei (Figure 6 shows 3 slices taken from this set of
images). The semantic analysis is done directly on a
segmentation provided by a watershed algorithm. The
arc-consistency checking algorithm had to deal with a
large number of segmented regions (between 500 and
more than 1000 regions). On each slice, the 6 grey nu-
clei are correctly identified. As we had to work with
Figure 5: Structure of the semantic graph representing the
anatomy of the brain.
a large number of regions, our analysis was applied
to 2D data to avoid some problems of memory space.
However, in this case, the definition of a conceptual
graph in 3 dimensions may be easily achieved from
anatomical book. Such 3D conceptual graph should
lead to better results.
a.
b.
c.
Number of regions in each image before applying the semantic
analysis: 625, 552, 819,
Figure 6: Experiments on a set of NMR images obtain on
the brain web. a) original images, b) segmentation obtained
with a watershed algorithm c) interpreted images: Every
anatomical structure is identified by a color. The 6 grey
nuclei (small internal anatomical structures of the brain) are
correctly identified.
4.2 Analysis of Water Meter Images
In this application, the aim is to localize in the image,
the water meter in order to detect if it is not broken,
to recognize its type (analogical or numerical) and to
SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING
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519
read the numerical value displayed on it if there is
one. These images are very noisy and the grey level
values are not a relevant information to recognize the
frame and the center of the water meter. The only
way to make a correct interpretation is to use the spa-
tial relations and the morphological characteristics of
the object sub-parts. Our approach has been applied
to a set of 26 images to localize the frame and the cen-
ter of the water meter. Among these images, 6 images
do not contain any water meter but an object sharing
some similarities with the water meter. This 6 im-
ages were correctly detected as not containing water
meter. In this case the graph is not consistent. All
the other images were correctly interpreted. Figure 7
presents the 26 test images. The following step will
be to analyse the content of the center of the water
meter. Figure 8 shows that the differences between
the coordinates of the gravity center of the water me-
ter’s center detected manually and automatically re-
main small compared to the size of the water meter’s
centers which varies between 80 and 100 pixels.
4.3 Extraction of Residential Areas in
High Resolution Satellite Images
The obtained segmentation is described by a region
adjacency graph. A graph model describing houses
belonging to a residential areas is build. Then, the
AC
BC
algorithm is applied to detect these houses.
4.3.1 The Model Graph
The model graph is made up of 5 nodes and 18 arcs.
It uses 13 kinds of spatial relation: 4 relations cor-
responding to the four directions (north, south, east
and west) imposing distance constraints, 4 relations
corresponding to the four directions that verify that
there is no region belonging to a given node (ex: the
node associated with the concept of street) between
the two considered regions (To use this relation, no
binary constraint has to be imposed on the considered
node), 4 relations corresponding to the four directions
without any distance constraint and the identity rela-
tion.
A simplified version of the graph can be seen on fig-
ure 9.
4.3.2 Gathering of Houses belonging to
Sub-parts of Residential Areas
Surrounded by a Road
To gather houses belonging to sub-parts of a residen-
tial area surrounded by a road, we use an algorithm
based on a region growing process. We first look for
a.
b.
c.
d.
Figure 7: Interpretation of water meter images. a) original
images, b) segmented images with a watershed algorithm
c) detection of the frame and the center of the water meter
d) images providing a non consistent graph. The object of
these images does not have the morphological characteris-
tics described by the conceptual graph.
region belonging to the node ”houses of a residen-
KDIR 2011 - International Conference on Knowledge Discovery and Information Retrieval
520
x coordinate y coordinate
(unit: pixels) (unit: pixels)
mean 6 3.35
median 5 3.5
standard deviation 4.93 2.64
min 0 0
max 16 9
Figure 8: Statistics concerning the differences between the
coordinates of the gravity center of the water meter’s center
obtained manually and the coordinates of the gravity center
obtained automatically.
Figure 9: The model used to recognize residential areas
tial area”. For each region we look for its supports
belonging to the node ”houses”. If these supports be-
long to the node ”houses of a residential area”, they
are marked and they are enqueued to process them re-
cursively. If they do not belong to this node, these
supports are simply marked in the result image.
4.3.3 Experiments
The experiments were made on images from the
French satellite SPOT 5 representing the urban area
of Strasbourg (France) at different spatial resolutions
and scaling. The result can be seen on the figure 10.
We can see that the approach is general enough to pro-
cess different kind of configuration and different spa-
tial resolutions.
5 DISCUSSION
This paper tries to show that symbolic approach based
on constraints satisfaction is an interesting way to
solve some problems of image interpretation and to
extract information from images. A set of tools has
a.
b.
a. b.
a. b.
a. b.
Figure 10: Test images: a) original images with annotation
b) labelised images. Houses belonging to a same residential
area (set of houses surrounded by a street) have the same
color.
been developed in this framework and the applica-
tions of these tools on images from different domains
shows their effectiveness. In this paper only binary
relations have been used, however it is quite easy to
introduce n-ary relations by using hyper-arc. In this
case, the time-complexity will increase, however, the
algorithm of arc-consistency checking with bilevel
constraint can be parallelized (Deruyver and Hod
´
e,
2009a), and the search domain (segmented regions)
can be reduced by data partitioning. Moreover, it is
possible to assign an order of priority to the arcs such
that less time consuming arcs can be process before
the others. All these points show that this approach is
valuable and can be complementary to numerical or
statistical approaches.
ACKNOWLEDGEMENTS
We thank the company ”V
´
eolia” for having supplied
us the set of images of water meter and the LIVE of
Strasbourg for having supplied us the high resolution
satellite images.
SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING
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521
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