COMBINING SHAPE DESCRIPTORS AND COMPONENT-TREE

FOR RECOGNITION OF ANCIENT GRAPHICAL DROP CAPS

Benoˆıt Naegel and Laurent Wendling

LORIA UMR 7503, Nancy University, 54506 Vandœuvre-l`es-Nancy, France

Keywords:

Component-tree, Segmentation, Classiﬁcation, Mathematical morphology, Ancient graphical drop caps.

Abstract:

The component-tree structure allows to analyse the connected components of the threshold sets of an image

by means of various criteria. In this paper we propose to extend the component-tree structure by associating

robust shape-descriptors to its nodes. This allows an efﬁcient shape based classiﬁcation of the image connected

components. Based on this strategy, an original and generic methodology for object recognition is presented.

This methodology has been applied to segment and recognize ancient graphical drop caps.

1 INTRODUCTION

Many pattern recognition tasks rely on thresholding

techniques,which can be very efﬁcient to performtwo

class classiﬁcation between object and background

pixels (Weszka, 1978; Fu and Mui, 1981; Sahoo

et al., 1988; Trier and Jain, 1995; Trier and Taxt,

1995a; Sezgin and Sankur, 2004). However these

methods all rely on the choice of a threshold, either

global or local. Therefore, to avoid the threshold

computation, one strategy could consist to consider

the connected-components of all the image threshold

sets. These connected-components can be organized

in a tree called “component-tree”. Component-trees

(also called max-tree (Salembier et al., 1998), den-

drone (Chen et al., 2000), conﬁnement-tree (Mattes

and Demongeot, 2000)) have been involved in many

image processing tasks, such as image simpliﬁca-

tion (Salembier et al., 1998), object detection (Jones,

1999; Naegel et al., 2007), image retrieval (Mosorov,

2005), caption text detection (Le´on et al., 2005).

The component-tree has been used in mathematical

morphology to perform attribute ﬁltering (Breen and

Jones, 1996), by storing an attribute into each node

of the tree. The notion of shape-based attributes has

been considered only recently (Urbach and Wilkin-

son, 2002; Urbach, 2005; Urbach, 2007) and this con-

cept has been applied to ﬁlament extraction in MR an-

giograms (Urbach and Wilkinson, 2002) and classiﬁ-

cation of diatoms (Urbach, 2007). For both segmenta-

tion and detection purposes, shape-descriptors can be

used to perform efﬁcient shape-based classiﬁcation of

the nodes. In this paper we expose a method allow-

ing to perform both object segmentation and recogni-

tion based on the component-tree structure. Such an

approach has been experimented to perform ancient

drop cap recognition.

2 COMPONENT-TREE FOR

OBJECT RECOGNITION

2.1 Component-tree Deﬁnition

An attributed component-tree is deﬁned as a triple

G = (V ,E ,δ), where V represents the set of nodes,

E is the set of edges and δ a function that assigns to

each node u ∈ V a set of attributes δ(u). A grey-level

image is deﬁned as a function F : E → T, where E is

the domain of deﬁnition (E ⊆ Z

) and T ⊆ Z is the set

of values. As we consider only discreteimages having

discrete values, we set T = [0,M]. The i-th connected

component of the superior threshold sets X

(F) =

{p ∈ E | F(p) ≥ t} is denoted C

(F) (in the sequel

we write C

for designing such a component). The set

of all connected components of all superior threshold

sets is denoted C C (F) = {C

(F) | t ∈ T,i ∈ I} (this

set is denoted C C in the sequel). Inferior threshold

sets X

(F) = {p ∈ E | F(p) ≤ u} can be considered

as well, leading to the dual component-tree represen-

tation. The component-tree is constructed as follows.

A map m : V 7→ C C is deﬁned between the set of ver-

tices and the set of components. For each C

∈ C C ,

297

Naegel B. and Wendling L.

COMBINING SHAPE DESCRIPTORS AND COMPONENT-TREE FOR RECOGNITION OF ANCIENT GRAPHICAL DROP CAPS.

DOI: 10.5220/0001775502970302

In Proceedings of the Fourth International Conference on Computer Vision Theory and Applications (VISIGRAPP 2009), page

ISBN: 978-989-8111-69-2

a node u ∈ V associated to this component is cre-

ated. An edge is created between each pair of vertices

(u,v) ∈ V × V if and only if:

• (i) u = m

−1

),v = m

−1

t+k

)(t,k ≥ 0);

• (ii) C

t+k

( C

;

• (iii) ∀l ≥ 0,C

t+l

( C

⇒ C

t+l

( C

t+k

and u is the father of v. The root of the tree is denoted

by the node r = m

−1

). An example of component-

tree constructed from a 1D image is provided in Fig-

ure 1.

Figure 1: a) Component-tree of a 1D image. Empty circles

denote nodes that do not meet a criterion, b) Tree pruning.

In the reconstructed image (using direct decision), all irrel-

evant components C

have been removed.

2.2 Node Classiﬁcation

Given a criterion D that accepts or rejects a node de-

pending on its attribute values, an attribute ﬁlter φ can

be deﬁned by acting separately on the component-tree

nodes. Pruning the tree according to this classiﬁcation

decision and constructingthe image obtainedfrom the

pruned tree allows to remove all the irrelevant con-

nected components of the threshold sets of an image.

This is the principle of attribute ﬁlters (Breen and

Jones, 1996; Jones, 1999). Pruning the component-

tree with respect to non-increasing criterion can lead

to remove nodes which have ancestors or descen-

dants that are not removed, which is problematic to

reconstruct an image. Therefore, various strategies

have been deﬁned to reconstruct an image from a tree

pruning based on non-increasing criterion: min, max,

direct, subtractive (Salembier et al., 1998; Urbach,

2007). In an object detection purpose, image recon-

struction can be based on the direct decision (Salem-

bier et al., 1998), which is equivalent to keep only the

relevant connected components of the image (see Fig-

ure 1): φ(F)(x) = max{t | x ∈ C

,D(m(C

)) = true}.

2.3 Attributes

A set of attributes δ(u) is associated to each node

u ∈ V . For efﬁciency reasons, these attributes should

be computed incrementally: for each node, the com-

putation result of child attributes is used to compute

the current ones.

2.3.1 Scalar Attributes

Scalar attributes of various kinds can be associated

to nodes. Many attributes have been used in the lit-

erature such as component area, length of the short-

est path to a leaf node, cumulated sum of area of

all descendant nodes. Pruning the tree according to

criteria based on these attributes led respectively to

the area ﬁlter (Vincent, 1992; Vincent, 1993), the h-

min ﬁlter (Grimaud, 1992; Soille, 2003), and volu-

mic ﬁlter (Vachier, 1998), well known in mathemati-

cal morphology. Combination of scalar attributes can

also be used, leading to vectorial attributes (Urbach,

2005; Urbach, 2007; Naegel et al., 2007). However

these kinds of quantitative attributes are not descrip-

tive enough to perform a robust shape-based classiﬁ-

cation of nodes.

2.3.2 Shape Descriptors

To use the component-tree for pattern recognition,

shape descriptors can be associated to nodes. In-

deed, shape descriptors allow compact description of

a shape, while being robust against noise and pose

variations. There is a large choice of shape descrip-

tors available in the literature (see (Zhang and Lu,

2004) for a survey). In this paper, we compare the

performance of two descriptors, chosen for their ro-

bustness and their performance in content-based im-

age retrievalsystems: the R-transform and the generic

Fourier descriptor (GFD).

R-Transform. The R-transform (Tabbone et al.,

2006) is a shape descriptor based on the Radon trans-

form. The Radon transform of an image f (x,y) is de-

ﬁned by:

(ρ,θ) =

∞

−∞

∞

−∞

f(x, y)δ(xcosθ+ysinθ−ρ)dxdy,

where δ is the Dirac delta-function (δ(x) = 1 if x = 0

and δ(x) = 0 elsewhere), θ ∈ [0, π[ and ρ ∈] − ∞,∞[.

The R-transform is deﬁned by:

(θ) =

∞

−∞

(ρ,θ)dρ

The R-transform is invariant under translation and

scaling if the transform is normalized by a scaling

factor (the area of the R-transform). However the R-

transform is not invariant under rotation (a rotation of

the shape implies a translation of the transform).

Generic Fourier Descriptor. Generic Fourier de-

scriptors (GFD)(Zhang and Lu, 2002) belong to stan-

dard MPEG-7. They are deﬁned from polar discrete

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

298

transform. It is similar to Fourier transform, but con-

sidering the polar image in a polar space as a rectan-

gular image in a Cartesian space:

PF(ρ, φ) =

∑

f(x, y).e

2jπ



r(x,y)

ρ+v(x,y)φ

i

The GFD is deﬁned as follows:

GFD =

|PF(0,0)|

|PF(0,1)|

|PF(0,0)|

,.. .

|PF(m,n)|

|PF(0,0)|

GFD is invariant to rotation and translation by deﬁ-

nition. Invariance to scale factor is ensured by divid-

ing the ﬁrst term by area value M

and the others by

|PF(0, 0)|.

Incremental Computation. Computing shape de-

scriptors for all the threshold components leads to a

high computational burden. In order to compute efﬁ-

ciently GFD or R-transform for each node, it is desir-

able to ﬁnd an incremental scheme allowing to use the

results of the child nodes to compute the result of the

current node. This can be done by using accumulator

arrays. The computation of the GFD was based on

an incremental scheme, by taking as origin the image

barycenter for all the nodes.

3 RECOGNITION OF ANCIENT

GRAPHICAL DROP CAPS

In recent years, large digitalization campaigns of an-

cient printed document collections led to recurrent

problems such as data archiving, classiﬁcation and

efﬁcient retrieval. Due to the handwritten nature of

ancient books, recognition of ancient characters can-

not be easily achieved by using modern optical char-

acter recognition (OCR) systems. Ancient graphical

drop caps segmentation has been addressed by Ut-

tama (Uttama et al., 2005), where the image is sepa-

rated into its textural and homogeneous parts. How-

ever the problem of drop cap recognition has not been

addressed due to the difﬁculty of extracting the drop

cap’s uppercase.

3.1 Data

The Madonne database OLDB (Ornamentals Letters

DataBase) consists of graphical decorative initials ex-

tracted from archival documents

. This corpus is part

We would like to thank the “Centre d’´etudes

Sup´erieures de la Renaissance” for the permission to use

their archival documents.

of a study performed by French research teams

historical documents. The database is composed of

more than 6000 drop caps. To conduct our experi-

ments, we have selected from this database a subset

of 200 images representing 20 different uppercases.

The test set has been constructed to be representative

of the various styles of drop caps (see examples on

Figure 2). Drop cap images are grey-scale, composed

of the letter (uppercase) part and texture part. Size of

images is between 150 × 150 and 750× 750. Due to

the digitalization process, the letter is approximately

centered and vertical. Drop cap images are noisy and

contain artifacts such as superimposed text, coming

from following book pages.

Figure 2: Drop cap samples of a subset of the OLDB (Or-

namentals Letters DataBase) database.

3.2 Image Processing

Using the methodology exposed in Section 2 for drop

cap recognition requires to make the assumption that

at least one connected component C

of the supe-

rior threshold sets X

(F) corresponds to the uppercase

part. By making this assumption, the letter part of the

drop cap must appear white on dark background. This

assumption does not always hold, since drop caps up-

percases can also appear black on a white background

(see Figure 2). It is hence necessary to consider not

only the connectedcomponentsof the superior thresh-

old sets, but also those of the inferior threshold sets.

To this aim, the dual component-tree (the component-

tree of the inferior level sets) is computedfor each im-

age. It is obtained by computing the component-tree

of the negative image. In the test set, many drop caps

contain a distinct component corresponding to the let-

ter part. However in some cases the letter part is con-

nected to other image parts (texture or background).

In order to ensure that at least one component corre-

sponds to the letter part we process each image us-

ing morphological openings (Soille, 2003), to remove

thin connections between components. Due to the

stack property of morphological operators, applying a

morphological grey-scale opening is equivalent to ap-

plying a binary opening on all of its superior threshold

sets. Therefore, for each drop cap image F, we com-

pute the set:

S(F) = {F,F

,{γ

(F)}

1≤i≤r

max

,{γ

)}

1≤i≤r

max

see http://l3iexp.univ-lr.fr/madonne/

COMBINING SHAPE DESCRIPTORS AND COMPONENT-TREE FOR RECOGNITION OF ANCIENT GRAPHICAL

DROP CAPS

299

where F

is the image complement (negative), γ de-

notes the morphological opening, B

∈ P (E) is the

disk structuring element of radius i, and r

max

is the

maximal value of the radius. For each image F

∈ S is

computed the corresponding component-tree G

From an algorithmic point of view, Salembier’s

algorithm (Salembier et al., 1998) was used to com-

pute efﬁciently the component-tree, using a recursive

scheme

3.3 Training Set

A set of letters has been segmented using interactive

method based on the choice of the most relevant con-

nected component of the threshold sets, using area

and compacity criteria to prune the component-tree.

The GFD signatures associated to the component-

tree nodes have been computed using an efﬁcient in-

cremental method (Section 2). As a consequence, the

GFD signatures are not translation invariant, since the

same origin has been taken for all the components.

Although the uppercases are approximately centered,

slight translation variations can occur between letters

of similar classes. This can be addressed by adding in

the training set translated versions of segmented let-

ters along the x-axis.

We chosed a cluster head for each class and com-

puted two translated images by a vector v = (v

,0),

with v

= {±0.1 dx}, dx denoting the image width.

Each class of the training set is then composed of a

segmented image and its two translations.

3.4 Recognition Process

For each tree node u is retrieved the least Euclidian

distance between the node attributes and the training

set samples attributes. From all these distances, the

k least distances are retained, as well as the k corre-

sponding classes. The recognition is performed by

considering the most represented class from these k

classes (here k = 30).

4 RESULTS

4.1 Validation Protocol

We have compared the following methods. The three

ﬁrst onesrely on the component-treecomputation; the

According to (Najman and Couprie, 2006), Salembier’s

algorithm is quadratic in the worst case; however it is gen-

erally twice as fast as Najman’s one in practical cases when

the image range is [0...255].

fourth is based on global grey-scale GFD computa-

tion. The last one is based on a binarization strategy.

1. CT+scalar. Component-tree based recognition

using scalar attributes. In this method, we con-

sider for each node u ∈ V the set of scalar at-

tributes δ(u) = (a

) with:

• a

= area/(image size) the normalized area of

the component with respect to the image size;

• a

= 4π∗area/perimeter

an attribute related to

the compacity of the component.

2. CT+GFD. Component-tree based recognition us-

ing GFD. The GFD has been computed using

m = 5 radial and n = 5 angular frequencies.

3. CT+RT. Component-tree based recognition using

R-Transform. The R-Transform has been com-

puted using r = 10 radial and t = 10 angular sam-

ples.

For the GFD and the R-Transform, a perfor-

mance evaluation of the shape descriptors follow-

ing different discretization parameters has been

performed. In both cases, increasing the param-

eters beyond the chosen ones did not improve the

results while increasing the processing time. In

the latter methods based on the component-tree,

the maximal radius for the morphological open-

ings has been set to r

max

= 3.

4. Grey-scale GFD. Classiﬁcation based on grey-

scale GFD computation. A training set composed

of one head drop cap for each class has been con-

structed. Each tested image was classiﬁed accord-

ing to the closest training set GFD.

5. Entropy+GFD. Binarization method based on

entropy. A powerful binarization method which

performs a fuzzy partition on a bidimensional his-

togram of the image (Cheng and Chen, 1999)

has been experimented. The partition criteria are

based on the optimization of the fuzzy entropy.

This approach is threshold free and it has been

shown that the results obtained are better than for

the 2D non fuzzy approach. The image is classi-

ﬁed according to the GFD of the remaining con-

nected components, using the same method (train-

ing set and classiﬁcation strategy) than CT+GFD.

4.2 Results on 8 Classes

In a ﬁrst experiment, we tested the methods on a sub-

set of 80 drop caps divided in 8 classes. The selected

classes correspond to the most frequent letters in the

whole database. Table 1 shows a comparison of the

segmentation and classiﬁcation results between meth-

ods.

VISAPP 2009 - International Conference on Computer Vision Theory and Applications

300

Table 1: Comparison of segmentation, recognition rates

and computational time (in s) of methods on 80 drop caps

from 8 classes.

Method Segmentation Recognition Time

CT+scalar 7.5% 12.5% 52

CT+RT 5% 18.8% 575

CT+GFD 62.5% 76.3% 332

ent.+GFD 38.7% 47.5% 534

gr. GFD - 18.8% 40

The method based on the component-tree and

GFD descriptor outperformed the others, with a

recognition rate of 76.3%. This result is promis-

ing, since the method has not been speciﬁcally tuned

for the drop cap recognition. Component-tree meth-

ods based on other attributes (scalar or R-transform)

performed poorly on the considered dataset. The

method based on entropy binarization gave interest-

ing results; howeverin 25% of the images, the method

chosed a wrong threshold, leading to nearly black

or white images. Moreover this method is slower

than CT+GFD, due to the computation of the opti-

mal threshold. Grey-scale GFD gave poor results,

since the drop caps show many texture and contrast

variations. The confusion matrix obtained with the

CT+GFD method is given in Table 2.

Table 2: Confusion matrix of the classiﬁcation results using

the CT+GFD method on 8 classes.

Uppercase A C E I L P Q S

A 8 1 0 0 0 0 1 0

C 0 8 0 0 0 0 2 0

E 0 0 6 1 1 0 1 1

I 0 0 0 7 1 0 0 2

L 0 1 0 1 7 0 0 1

P 0 0 2 0 2 6 0 0

Q 0 0 0 0 0 0 10 0

S 0 0 0 1 0 0 0 9

In the tree based methods, morphological open-

ing allowed to disconnect the uppercase from texture

parts as illustrated on ﬁgure 3, therefore increasing

the recognition rate.

Figure 3: a) Original drop cap image, b) Segmentation of

(a) (letter recognized as ”S”), c) Opened image (the upper-

case is disconnected from the background), d) Segmenta-

tion of (c) (letter properly recognized).

4.3 Scalability of the Approach

The number of classes has been gradually increased,

by decreasing order of their frequencies in the whole

database. The Figure 4 summarizes the results ob-

tained with the different methods and shows the good

behaviour of the proposed approach.

Figure 4: Recognition percentages of the methods with re-

spect to the number of considered classes.

4.4 Discussion

The method based on entropy binarization and GFD

classiﬁcation is less robust than the method CT+GFD,

due to the inaccurate image binarization in some

cases. These results demonstrate that method based

on the component-tree structure extended with robust

shape-descriptors allows to analyse all the threshold

components, therefore avoiding to chose a speciﬁc

binarization threshold. Hence, the method CT+GFD

reached the best results, achieving a recognition rate

of 63.5% on 20 classes.

5 CONCLUSIONS

In this paper we have proposed to combine the

component-tree representation of an image with ro-

bust shape-descriptors, in order to perform object

recognition. Based on this strategy, we have ex-

posed a methodology for ancient graphical drop cap

recognition. The best recognition rate was 76.3%

on 8 classes and 63.5% on 20 classes. These re-

sults, although perfectibles, are interesting since the

method has not been speciﬁcally tuned for this appli-

cation. Moreover, the computation of the attributed

component-tree could be done ofﬂine, leading to efﬁ-

cient recognition tasks.

In future works we will investigate the clas-

siﬁcation strategies offered by the combination of

component-tree and shape descriptors. More speciﬁ-

cally, we plan to use more deeply the information car-

ried by the component-treestructure to performimage

recognition and spotting.

COMBINING SHAPE DESCRIPTORS AND COMPONENT-TREE FOR RECOGNITION OF ANCIENT GRAPHICAL

DROP CAPS

301

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