SEMANTIC GRAPHS AND ARC CONSISTENCY CHECKING

The Renewal of an Old Approach for Information Extraction from Images

Aline Deruyver

and Yann Hod

LSIIT, UMR 7005 CNRS-ULP, 67 000 Strasbourg, France

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

 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

. 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

}, a

x ... x a

∈ D

x ... x D

, 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

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

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

)

can be deﬁned as follows:

Deﬁnition 1.

• Let Cmp

be a compatibility constraint such that

(a, b) satisﬁes Cmp

⇔ a and b are compatible,

where a ∈ D

and b ∈ D

• Let Cmpg

be a global compatibility constraint on

a set of values S

⊂ D

such that S

satisﬁes Cmpg

• Let C

i j

be a constraint between i and j.

• Let S

and S

be a pair such that S

⊂ D

and

⊂ D

, S

|= C

i j

means that (S

, S

) satisﬁes

the oriented constraint C

i j

, S

|= C

i j

⇔ ∀a

∈ S

, ∃(a

, a

) ∈ S

× S

, such

that (a

, a

) satisﬁes Cmp

and (a

, a

) satisﬁes C

i j

Deﬁnition 2. Sets {S

...S

} satisfy FDCSP

⇔

∀C

i j

, S

|= C

i j

and S

satisﬁes Cmpg

and S

satis-

ﬁes Cmpg

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

). 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

. Let P(D

) be the set of sub parts

of the domain D

Deﬁnition 3. Let (i, j) ∈ arc(G). Arc(i,j) is arc

consistent with respect to P(D

) and P(D

) ⇔

∀S

∈ P(D

), ∃S

∈ P(D

) such that ∀v ∈ S

∃t ∈ S

∃w ∈ S

, Cmp

(v,t) and C

i j

(t, w) and Cmpg

) and

Cmpg

) (v and t could be identical).

Deﬁnition 4. Let P= P(D

) × ... × P(D

). A graph

G is arc consistent with respect to P ⇔ ∀(i, j) ∈

arc(G) : (i, j) is arc consistent with respect to P(D

)

and P(D

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

(Cd(A,B)), in f

Cd(A,B))), (sup

(Cd(A,B)),

sup

(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

(Cw(B, A)) 6 in f

(Ce(A, B)),

• A Wi B iff sup

(Cw(A, B)) 6 in f

(Ce(B, A)),

• A Ni B iff sup

(Cn(A, B)) 6 in f

(Cs(B, A)),

• A Si B iff sup

(Cn(B, A)) 6 in f

(Cs(A, B)),

All these relations may be associated with the metric

d deﬁned as follows: d(A, B)= in f

(A)-sup

(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

be the set of the

nodes linked to the node i in the graph G such that:

= { 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

)

This function allows that nb binary constraints asso-

ciated with the node i can be not satisﬁed. Let Γ

i,l

the

set of the nodes j ∈ Γ

making arc-consistent arc with

a given node i and a given l ∈ D

such that:

i,l

= { j ∈ Γ

| (i, j) is arc-consistent with respect to

l ∈ D

and P (D

)}

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

) be the set of sub parts of the

domain D

. Let P=P (D

)× .... ×P (D

). A graph G is

quasi arc-consistent with respect to P iff ∀i ∈ node(G)

we have

Card(Γ

) − min

∀l∈D

(Card(Γ

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.

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

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

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-

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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.

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

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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