on-line handwritten digit recognition based on trajectory...

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Pattern Recognition Letters 29 (2008) 580–594

On-line handwritten digit recognition based on trajectoryand velocity modeling

Monji Kherallah a,*, Lobna Haddad a, Adel M. Alimi a, Amar Mitiche b,1

a Research Group on Intelligent Machines (REGIM), University of Sfax, ENIS, BP W – 3038, Sfax, Tunisiab Telecommunications (INRS), University of Quebec, 800, de la Gauchetiere Ouest, Suite 6900, Montreal, Quebec, Canada H5A 1K6

Received 11 February 2007; received in revised form 19 September 2007Available online 8 December 2007

Communicated by L. Heutte

Abstract

The handwriting is one of the most familiar communication media. Pen based interface combined with automatic handwriting rec-ognition offers a very easy and natural input method. The handwritten signal is on-line collected via a digitizing device, and it is classifiedas one pre-specified set of characters. The main techniques applied in our work include two fields of research. The first one consists of themodeling system of handwriting. In this area, we developed a novel method of the handwritten trajectory modeling based on elliptic andBeta representation. The second part of our work shows the implementation of a classifier consisting of the Multi-Layers Perception ofNeural Networks (MLPNN) developed in a fuzzy concept. The training process of the recognition system is based on an association ofthe Self Organization Maps (SOM) with Fuzzy K-Nearest Neighbor Algorithms (FKNNA). To test the performance of our system webuild 30,000 Arabic digits. The global recognition rate obtained by our recognition system is about 95.08%.� 2007 Elsevier B.V. All rights reserved.

Keywords: Handwriting modeling; Stroke overlapping; Elliptic trajectory modeling; Beta velocity modeling; Digit recognition

1. Introduction

The automatic recognition of handwritten characters isof paramount importance in applications where handwrit-ing is the desirable input channel, such as in form filling.This importance presents a technological revolution inman–machine interfaces (keyboard, mouse, etc.). The fieldof handwriting recognition can be split into two differentapproaches. The first one deals with the recognition ofhandwriting in the form of an image and it is termed off-line. In this instance, only the completed character or wordis available. The second approach called on-line, concen-

0167-8655/$ - see front matter � 2007 Elsevier B.V. All rights reserved.

doi:10.1016/j.patrec.2007.11.011

* Corresponding author. Tel.: +216 74 274 088; fax: +216 74 275 595.E-mail addresses: [email protected] (M. Kherallah),

[email protected] (L. Haddad), [email protected](A.M. Alimi), [email protected] (A. Mitiche).

1 Tel.: +1 514 875 1266 Poste 2010; fax: +1 514 875 0344.

trates on the recognition of handwriting captured by a tab-let or similar touch-sensitive device, and uses the digitizedtrace of the pen to recognize the symbol. In this area, therecognizer will have access to the x and y coordinates asa function of time which has temporal information abouthow the symbol was formed. It is the on-line approach thathas been taken into account in this work.

In most handwriting recognition systems existing inPDA (personal digital assistant), the processing steps ofsegmentation, recognition, decision-making and post pro-cessing are serially taken.

These systems usually use the resources exhaustively ineach stage of the serial engine. Every stage is tuned tomaximize global performance. Pre-processing is primarilyrelated to character processing operations such as nor-malization to remove irregularities of handwriting.Recognition is the application of classification algo-rithms. Independent contextual information is used as a

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M. Kherallah et al. / Pattern Recognition Letters 29 (2008) 580–594 581

post-processing step to recognize and enhance the hand-written words.

Most architectures of handwriting recognition systemare monotonically linear and based on stochastic modelslike Hidden Markov models (Bellegarda et al., 1994; BenAmara and Belaid, 1996; Cho and Kim, 2004; Hafsaet al., 2004). These models are probabilistic and need pow-erful calculators and a considerable calculation time. How-ever, in the structural method, a set of basic strokes areusually selected as primitives (El-Sheik and El-Taweel,1990; Hafsa et al., 2004; Heutte et al., 1998; Kherallahet al., 2002, 2004; Morasso et al., 1993; Simard et al.,1993), and stroke recognition is based on the use of certaingeometrical features like line segment directions, strokeslength, strokes order, strokes number, strokes relation,etc. These are also found to be useful for character recog-nition. Several properties of human handwriting move-ments were taken. Size and speed can be involuntarilyvaried without changing the shape of the velocity profileof the handwritten script (Uno et al., 1989; Viviani andSchneider, 1991).

The originality of this paper deals with two fields ofresearch. The first one presents a novel approach of thehandwriting modeling system based on Beta–ellipticapproach. The second topic of our contribution deals witha hierarchical recognition system of digits based on anassociation of SOM, FKNN and MLPNN.

The Beta–elliptic representation is consisting of a combi-nation between geometry and kinematics in handwritinggeneration movements (Bezine et al., 2003b; Kherallahet al., 2002, 2004; Viviani and Schneider, 1991). Accordingto this method of modeling, the number of features percharacter can reach 63 – dimensional feature vector. Itdepends on stroke number of trajectory. For such highdimensionality, pattern recognition techniques suffer from

SOM

FKNN

MLPNN

Knowndigit

Training data Testing data

DigitalTablet

Acquisitionand pre-

processing

Beta-Ellipticmodel

Database

« digits »

Fig. 1. A diagram bloc of the proposed system.

the well-known curse of dimensionality phenomenon. Thisproblem is resulting from the fact that the required numberof labeled samples for supervised classification increasesdramatically as a function of dimensionality (Kiviluoto,1996).

For reducing the problem of dimensionality, we proposea hierarchical neural network representation for the on-linerecognition of handwritten digits. The training system isbased on a fuzzy concept. In fact, because individual stagesusually do not have all the information, we propose anassociation between the SOM and the FKNNA. The resultobtained by the last classifiers will be used in the trainingprocess of MLPNN (see Fig. 1).

This paper is organized as follows: Next section explainsthe details of the Beta–elliptic representation. Section 3 isdevoted to the recognition system architecture. Experimen-tal results and the comparison of our method with the avail-able methods in the literature are discussed in Section 4.

2. Trajectory modeling by Beta–elliptical representation

The basic role of the trajectory modeling is to boost thecomprehension of handwriting generation and improve on-line recognition system.

In literature, the study of hand movements was based onproposed models. Two general methodologies of handwrit-ing modeling become apparent from the review of litera-ture. The first methodology takes into consideration thecomputational models, which are based on using some fea-tures of Human handwriting movements such as velocityprofiles and some relations between different aspects ofthe dynamic movement; such as curvilinear velocity, accel-eration, strokes length, etc. Such methodology includesoscillators models (Heutte et al., 1998; Ruiz-pinals andLecolinet, 2000), which combine various velocity sinusoidsto yield different movement shapes. The second methodol-ogy of the handwriting modeling is based on staticapproach such as geometric forms: curvature, direction,circular, etc. (Chan and Yeung, 1999; Connel and Jain,2001; Flash and Hogan, 1985; Ruiz-pinals and Lecolinet,2000; Sung and Wolfgang, 2001). The oscillation modelof Hollerbach (1981) and the Hollerbach and Flash(1982) uses kinematic parameters such as velocities andamplitude of motion to represent the handwriting move-ment. Denier Vander Gon simulated the production of gra-phic patterns, representing different letters of alphabet bythe timing of acceleration and deceleration of two orthog-onal motor systems, the first is responsible for the excur-sions of writing trace parallel to the writing line (X axis),and the second is responsible for the excursions orthogonalto the first ones (Y axis) (Denier and Thuring, 1965). Opti-mization models refer also to such methodology (Chenet al., 1997; Flash and Hogan, 1985; Saltzman and Kelso,1987; Sung and Wolfgang, 2001; Van Galen and Weber,1998). Plamondon and Guerfali presented a handwritingmodel, which refers to the first methodology as mentionedpreviously (Guerfali and Plamondon, 1995; Guerfali and

582 M. Kherallah et al. / Pattern Recognition Letters 29 (2008) 580–594

Plamondon, 1994; Plamondon, 1991; Plamondon, 1995;Plamondon et al., 1993; Plamondon and Alimi, 1997;Uno et al., 1989). Their model uses the ‘‘delta-lognormalsynergies”. This name refers to the authors’ definition ofthe velocity of a muscle synergy as a Gaussian functionof the movement parameters that vary logarithmically withtime. They have been interested in the kinematic propertiesof handwriting generation process and omitted the rela-tionship between kinematics and the involved handwritingtrajectory. Plamondon and Guerfali (1998) suggest thatstrokes timing is considered as the solely crucial factor indetermining the trajectory shape. Using real handwritingdata, it is obvious that some models perform better thanothers. Therefore, the decision of manipulating a propermodel depends on the goal of the research.

The trajectory/velocity modeling techniques were manyyears ago applied in the handwriting modeling field (Alimiand Plamondon, 1994; Alimi, 1997, 2002, 2003; Morassoet al., 1993; Plamondon, 1995; Plamondon et al., 1993;Plamondon and Alimi, 1997; Uno et al., 1989). Previously,modeling systems were mainly based on either trajectory orvelocity features.

Kherallah et al. (2002, 2004) present the first idea ofcombining the kinematics and geometry in the trajectory

Fig. 2. Curvilinear velocity and accele

modeling. These studies considered neither the overlap ofBeta signal nor the inflexion points which present a key rolefor the strokes number determination. The strokes numberwas based only on velocity signal extremum. Local extre-mum were not considered in (Bezine et al., 2003b and Khe-rallah et al., 2002, 2004); consequently, the weakness of thisapproach is that it cannot detect the smallest handwrittentrajectory curvature or the catastrophe variability of thehandwritten trajectory caused by involuntary psychologi-cal behavior of the writer. However, in this paper we pro-ceed to locate the inflexion points of the handwrittentrajectory. For each inflexion point of trajectory we attrib-uted one Beta to the velocity signal (see Figs. 2 and 3). Wealso take into account the variability of the handwrittentrajectory curvature.

In (Kherallah et al., 2002) the modeling system wasbased on Beta-circular approach. The circular strokes aresuperposed but there are not of overlapping shapes andcannot perfectly reconstruct the handwritten trajectory.While, in our work the modeling system is based onBeta–elliptical approach in which the overlapping of Betasignal is taken into consideration.

The novelty of our modeling approach is the combina-tion of trajectory-based features (elliptic parameters) and

ration signal of handwritten digit.

Fig. 3. Beta modeling of the velocity trajectory.

Fig. 4a. Beta signal of one stroke.


velocity based features (Beta function parameters). In fact,kinematic properties involved perform to joint angle trajec-tory which obeys an elliptic form. The parameters charac-terizing an elliptic trajectory are performed according tothe Beta curvilinear velocity profile (Kherallah et al., 2004).

According to the harmonic oscillator description of themuscle action involved in handwriting production, velocityprofile of the cursive handwriting can be viewed as asequence of overlapped Beta-functions.

2.1. Beta velocity modeling

In our work, we consider that handwriting movement,like any other highly skilled motor process, is partially pro-grammed in advance, and we suppose that movements arerepresented and planned in the velocity domain, since themost widely accepted invariant in movement generationis the Beta shape of the velocity profiles. In this context,the modeling of a complex trajectory pattern is the resultof the activation of n neuromuscular subsystems character-ized by an impulse response that is real, normalized, andnon-negative. If n is sufficiently large, applying the centrallimit theorem, the global impulse response will converge toa Beta curve (Alimi and Plamondon, 1994; Alimi, 2002;Bezine et al., 2003a,b; Hafsa et al., 2004; Kherallah et al.,2002, 2004).

The curvilinear velocity V(t) (see Eq. (1)) is then com-puted using a second-order derivative filter with finiteimpulse response.

V rðtÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffidxðtÞ

dt

� �2

þ dyðtÞdt

� �2s

ð1Þ

Handwritten scripts are, then, segmented into simplemovements, as already mentioned, called strokes, and arethe result of a superimposition of time-overlapped velocityprofiles.

The curvilinear velocity of each individual strokes obeysthe Beta approach. So, the generation of a complex trajec-tory pattern is the result of an algebraic addition of strokesvelocity terms (see Eq. (2)).

V ðtÞ ¼Xn

i¼1

V iðt � tiÞ ð2Þ

Many researchers use ‘significant’ or ‘critical’ points tosplit the pen-path into smaller entities. Commonly used sig-nificant points are local extrema in horizontal or verticaldirection (Heutte et al., 1998), local extrema in velocity(Bezine et al., 2003a; Kherallah et al., 2004; Plamondonand Alimi, 1997; Uno et al., 1989), local extrema in curva-ture (Chen et al., 1997), and points of inflection (see Fig. 2).

In our case, the inflection points trajectory with themaximum and the minimum of the velocity signals arelocated. These points are considered of significance. Basedon the inflection points given by the acceleration of the penmovement, we attributed the overlapped form of Beta tothe velocity extremum profile. Therefore, after being calcu-lated, the velocity profile of handwriting will be modulatedby the Beta signals (see Fig. 3).

Consequently, the complete velocity profile of the neu-romuscular system will be described by a Beta model asfollows:

bðt; q; p; t0; t1Þ ¼t�t0tc�t0

� �pt1�tt1�tc

� �qif t 2 ½t0; t1�

0 elsewhere

( )ð3Þ

where p, q are intermediate parameters, which have aninfluence on the symmetry and the width of Beta shape(see Fig. 4b).

t0 is the starting time of Beta function; tc is the instantwhen the curvilinear velocity reaches the amplitude of theinflexion point; t1 is the ending time of Beta function;t0 < t1 2 IR and

Fig. 5. Final Beta model representation of the velocity signal.

Fig. 4b. Different shapes of the mono-dimensional Beta function.


tc ¼p � t1 þ q� t0

p þ qð4Þ

One Beta signal can be represented as shown in Fig. 4a.The parameter k is the amplitude of the Beta signal (k = 1in this case).

The result of Beta model reconstruction of velocity sig-nal is shown in Fig. 5.

2.2. Elliptical trajectory modeling

Dynamic data contains the information about how theshapes were written. Static data conveys the result of thewriting process, i.e. what has been written. In this para-graph, we focus on the description of static model. In fact,strokes executed from an arbitrary starting position are

characterized by three parameters. These parameters arecollected from the Beta function. Each elementary compo-nent called ‘‘stroke” is also characterized in the spacedomain by three statistical parameters. These parametersglobally reflect the geometric properties of the set of mus-cles and joints used in a particular handwriting movement.The parameters a and b are respectively the half dimensionsof the large and the small axes of the elliptic shape. X0 andY0 are the cartesian coordinates of the elliptic center rela-tive to the orthogonal reference (A, X and Y).

As shown in Fig. 5, the angle h defines the deviation ofthe elliptic portion according to the orthogonal reference(A, x and y).

From two points (A, B) of one stroke, we calculate the(h, a and b) parameters. These points A and B correspondrespectively to the minimum and the maximum values ofthe velocity profile. C is rightly before the point B, we joina tangent line crossing B and C. By an orthogonal projec-tion on B, we get the center O and the different axes a and b

of the ellipsis (see Fig. 6).Consequently, a single movement, also called stroke is

represented in the space and velocity domains by a curvilin-ear velocity starting at time t0 at an initial point, and mov-ing along an elliptic path. The latter obeys a variablecurvature C. This curvature is not a constant one as itwas proposed by few models in this direction by literature(Denier and Thuring, 1965; Flash and Hogan, 1985; Hol-lerbach, 1981; Plamondon et al., 1993; Plamondon andAlimi, 1997; Wada et al., 2001).

Elliptic model is a static model. In the spatial state, thetrajectory is represented by a sequence of elliptic arcs (Khe-rallah et al., 2004).

The elliptic equation is written as follows:

X 2

a2þ Y 2

b2¼ 1 ð5Þ

Each elliptic arc is drawn by the calculation of (h, a andb) parameters. Some examples are presented in Fig. 7.

2.3. Combination between Beta and elliptical models

As shown previously, the Beta–elliptic model considers asimple movement as the response to the neuromuscularsystem, which is described by an elliptic trajectory and aBeta velocity profile. In our approach of modeling, a sim-ple stroke is approximated by a Beta profile in the dynamicdomain which corresponds in turn to an elliptic arc in thestatic domain such that the distance AO is the half-largeaxe dimension a. As reported by Viviani et al. for humandrawing curves, the instantaneous tangential velocity ofthe hand decreases as the curvature increases, and then A

and B, which are characterized by minimum tangentialvelocity, correspond to the maximum of curvature in thestatic domain.

Consequently, a stroke is characterized by seven param-eters. The first four Beta parameters (t0, t1, p and k) reflectthe global timing properties of the neuromuscular networks

Fig. 6. Elliptical arc representation.

Fig. 7. Examples of digit elliptic representation.


involved in generating the movement, whereas the lastthree elliptic parameters (h, a and b) describe the global

geometric properties of the set of muscles and jointsrecruited to execute the movement.


3. On-line recognition of handwritten digits

The recognition process is divided into pre-processingsteps and subsequent classification. Facing up to the com-plex problems of the handwriting recognition, the use ofthe multiple, hybrid and an association of classifier systemsproves an increasing interest during the last years (Akselaand Laaksonen, 2005; Chiang and Gader, 1997; Hafsaet al., 2004; Hebert et al., 1998; Ianakiev and Govindaraju,2000; Kittler et al., 1998; Lam and Suen, 1999; Prevostet al., 2005; Suen and Tan, 2005; Xu et al., 1992). Basedon their complementarities, the association of classifiersincreases the performance of the recognition system whilelimiting the error bound to the use of a unique classifier.The use of the multiple classifier systems benefits fromthe strong points of every classifier. Among these systems,we mention the neuro-fuzzy approach. It is about a neuro-nal approach developed in a fuzzy concept (Alimi, 1997,2003; Chiang and Gader, 1997; Gader et al., 1995a,b,1997; Gomez Sanchez et al., 1998; Keller et al., 1985; Kit-tler et al., 1998).

Digit recognition was studied 10 years ago and, con-veyed that the fuzzy approach enhance the classificationperformance Vuori and Laaksonen (2002). In our work,

9 strokes MLPNN

Recognitionrate /

squarederror

5 strokes MLPNN

Training dataset (Semantic classes )

Trainingprocess

Input vectors

Fig. 8. Detail steps of th

one of the main classification problem is the variability ofthe feature vector size (35, 42, . . ., 63) depending of eachdigit number of strokes. Our new fuzzy architecture com-bined the neural fuzzy approach in a hierarchical waywhich offers a solution to the variability of feature vectorsize.

An interesting comparative study was done by Gaderand Keller in (1995, 1997) showing the interest of the fuzzyand neural networks approaches and their complementarit-ies (Gader et al., 1995a,b, 1997).

Since the work of Wang et al. (2000), it was proved thatthe performance of SVM and MLPNN is better than theKNN algorithm in case of big number of classes (Wanget al., 2000). Whereas, FKNN algorithm is specialized todiscriminate between classes especially in the boundaryzone which presents a confusion and inference.

In our approach, we use a sequential version of multipleclassifiers. The complementarities between the developedclassifiers are explained in the following paragraphs. Oursystem is based on the use of neural networks developedin a fuzzy concept. The desired outputs of MLPNN areformed using SOM and FKNNA (see Fig. 8). Therefore,our system is about neuro-fuzzy networks based on SOMand FKNNA association used in the learning process.

9 Strokes FKNNA

FKNNA6 strokes

5 Strokes FKNNA

9 Strokes SOM

FKNNA 6 strokes

5 Strokes SOM

Desired outputs

Testing dataset

e proposed system.

Table 1Classification of the database digit by their strokes number

Digits Fivestrokessub-system

Six strokessub-system

Sevenstrokessub-system

Eightstrokessub-system

Ninestrokessub-system

‘‘0” 4475 1277‘‘1” 1135 977 937‘‘2” 613 595 701‘‘3” 1412 832 610‘‘4” 2495 1395 633‘‘5” 760 919 883‘‘6” 1496 658‘‘7” 600 959‘‘8” 674 609‘‘9” 2221 1137 632


According to Fig. 8, the first step of the training pro-cess of the recognition system consists in the use of theSOM algorithm. This method is applied in order to orga-nize the input prototype vectors. The advantages of thismethod are: This algorithm is a powerful tool for givingthe real classes’ number and not the semantic one (Kivilu-oto, 1996; Mezghani et al., 2002; Morasso et al., 1993). Infact, it is an unsupervised algorithm. It makes a projec-tion of the disordered input vectors on an organizedmap of different clusters and it is able to reduce the highdimensionality of our system to two dimensions. Theresult given by this algorithm will be used in the nextstage.

In the second step, we adjusted the means of clusterselements, and we calculated the degree of membership ofdata vectors to each cluster by the Fuzzy K-NearestNeighbor Algorithm (FKNNA), which gives a more real-istic description. Finally, we attributed the membershipmatrix obtained by FKNNA to the target of the MLPNNin the training process as a desired output of MLPNN.Finally, we applied the MLPNN to test the handwrittendigits.

Note that the pre-processing system reduces the com-plexity existing in the principal recognition system by ahierarchical representation as explained in the next para-graph. Then, we detail the different sequences of the pro-posed system of on-line handwritten digit recognition.

3.1. Pre-processing system

For the handwriting, we used a Wacom 4 electronic dig-itizing tablet. The information collected from this tabletwas represented as the raw data x(t) and y(t) and was sam-pled at 200 Hz. A smoothing operation is applied to thedata provided by the tablet to eliminate the hardwareimperfections, the trembles in writing, etc. A filtering stepis necessary to eliminate duplicated date points by forcinga minimum distance between consecutive points. For thisreason, we applied a Chebyshev second-order low-pass fil-ter with a cut-off frequency of about 12 Hz. We used thisfilter because it has an acceptable stability in pass-bandand the band of transition is narrow.

Due to the variability of the handwriting, the vector sizeof digits is variable. In our case, the strokes number ofhandwritten digits is limited between 5 and 9 (see Table1). In fact, our method aims to represent our system intoa hierarchical architecture. The complexity of the recogni-tion system was reduced by the five subsystems develop-ment. Every subsystem was specialized in the samestrokes number of digits.

All handwritten digits are classified by their number ofstrokes, which was determined automatically from the cur-vilinear velocity signal as it is explained in the previous sec-tion, and the same handwritten digit can have a differentnumber of strokes. Therefore, we have a hierarchical repre-sentation of the digits pre-classification system. Table 1shows five subsystems.

3.2. Real class detection by self-organizing map

The self-organizing map (SOM), first introduced byKohonen (1990), is a powerful clustering and data presen-tation method. A SOM consists of a grid shaped set ofnodes. The self-organizing feature maps (SOFMs) usedwith pyrolysis mass spectrometry (PyMS) data consists ofa two-dimensional network of neurons arranged on asquare grid. Each neuron is connected to its eight nearestneighbors on the grid.

A node’s activation level is defined as:ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼0

ðweighti � inputiÞ2

sð6Þ

This is a simply Euclidean distance between the pointsrepresented by the weight vector and the input vector inn-dimensional space. Thus, a node whose weight vectorclosely matches the input vector will have a small activa-tion level, and a node whose weight vector is very differentfrom the input vector will have a large activation level. Thenode in the network with the smallest activation level isdeemed to be the ‘‘winner” for the current input vector(Kherallah et al., 2004; Keller et al., 1985; Kohonen,1990; Mezghani et al., 2002; Morasso et al., 1993; Samer-vuo and Kohonen, 1999).

In our system, 10 digits have not got the same number ofstrokes (see Table 1), therefore we proposed a hierarchicalrepresentation of 5 SOM subsystems.

Under such an environment, we proceeded to determinethe number of clusters existing in every map. The output ofthe hierarchical system is represented by 5 maps. Each mapcontains the different clusters of characters having the samenumber of strokes. The map size was fixed to 60 � 60 neu-rons. Therefore, we obtained 3600 neurons. The optimizednumber of the training algorithm iterations is 500.

If we take an example of a five strokes subsystem, wehave four semantic classes which are (0 1 4 6), whereasFig. 9 shows five classes which are the real classes (0 1 14 6) existing in the map, one class of ‘‘0”, two classes of‘‘1”, one class of ‘‘4” and one class of ‘‘6”.

Fig. 9. Example of five strokes Map representation.


As a result, the SOM algorithm which is an unsuper-vised algorithm, gives us the real classes number and notthe semantic one. The output information given by theSOM algorithm will be used in the next stage. Note thatthe output of these algorithms will be injected to the targetof MLPPNN. The SOM and the FKNNA are also usedonly in the learning process of our recognition system.

3.3. Membership assignment of the training data set to real

classes by the Fuzzy K-Nearest Neighbor Algorithm

The fuzzy logic has been conceived to adapt a specialtechnique that consists in human thought, therefore, it isapplicable in several domains. It is proved as a straightfor-ward success in the sectors of automatic device, roboticsand artificial intelligence where the information to treat isvague and imprecise, even in the engineering domain, man-agement and making decision (Bezdek, 1981; Chiang andGader, 1997; Gader et al., 1995a,b, 1997; Gomez Sanchezet al., 1998; Govindaraju and Ianakiev, 2000; Kelleret al., 1985).

Sometimes, the alphanumerical digits are ambiguouswhen read out of context. To minimize these difficulties,crisp classification is often replaced by fuzzy classification(Alimi, 1997, 2002; Bezdek, 1981; Chiang and Gader,1997; Keller et al., 1985).

The FKNNA was designed by Keller et al. (1985). Near-est neighbor classifier is chosen because it requires rela-tively low memory requirements and it is a nonparametric classifier. The idea is to assign membership

based on percentage of characters in each class amongthe neighbors of a training sample. The result of this algo-rithm will be used in the training process of the MLPNNoutputs. The class memberships are assigned to the sample,as a function of the sample’s distance from its KNN train-ing samples.

uiðxÞ ¼Pk

j¼1uij 1=kx� xjk2

ðm�1Þ� �

Pkj¼1 1=kx� xjk

2ðm�1Þ

� � ð7Þ

The parameter m is a scaling value, it takes a value lim-ited between 1 and 2. The memberships of the training sam-ples Uij can be defined in several ways. The crispest way isto give them complete membership in their own class andnon-membership in all other classes. A more ‘‘fuzzy” alter-native is to assign the training sample memberships basedon the distance from their main class. After calculatingthe memberships of the training samples, we attribute thisresult to the target of a MLPNN as a training phase. Thealgorithm used in this task is presented as follows:

1. Compute distance from data point to labeled samples2. If KNN has not been found yet, then3. Include data point.4. Else, if a labeled sample is closer to the data point than5. Any other KNN, then6. Replace the farthest with the new one.7. Compute membership8. Repeat for the next labeled sample.

Stroke 1

Input layer Output layer

Stroke 2

Hidden layer

Recognizeddigit

.

.

.

.


The maximum number of iteration cycles can be used asa termination criterion. We optimized m and k values intwo times. First, we fixed the parameter m, and for eachvalue of k, we calculated the recognition rate obtained bythe neuro-fuzzy system. At the second time, we took thebest value of k as constant and for each value of m, we cal-culated the recognition rate obtained by the neuro-fuzzysystem (see Figs. 10a and 10b).

According to these figures, we fixed respectively the mand k available values to the FKNNAs associated to differ-ent subsystems as the best values.

Stroke n

.

.

.

.

Fig. 11. OCON architecture.

Table 2From semantic classes to real classes

Classes Fivestrokessubsystem

Six strokessubsystem

Sevenstrokessubsystem

Eightstrokessubsystem

Ninestrokessubsystem

Semanticclasses

Digit 0 Digit 0 Digit 1 Digit 2 Digit 2Digit 1 Digit 1 Digit 2 Digit 3 Digit 3Digit 4 Digit 4 Digit 3 Digit 5 Digit 5Digit 6 Digit 6 Digit 4 Digit 7 Digit 7

Digit 5 Digit 8 Digit 9Digit 8 Digit 9Digit 9

3.4. Classification by the MLPNN system

Our system is composed of 33 neural networks of typeOCON (one class one network). Each class of handwrittendigit corresponds to one of OCON. The architecture ofOCON is presented in Fig. 11.

Because of the multi-variability of the handwriting,every digit has not got the same strokes number. One orseveral writers can also write the same digit in differentshapes.

All handwritten digits of our database are composed ofn strokes. This number is variable and takes a value from 5to 9. Each stroke is represented by seven features (t0, t1, p,k, h, a and b).

According to Table 2, we obtained five sets. Each set iscalled subsystem and is composed of N clusters of digits,which have the same number of strokes. For each subsys-tem, we constructed N neural networks i.e ‘‘OCON”, withN = real class number of all maps. Our system contains 33neural networks. Consequently, we developed 33 OCONs.

10 15 20

(m=2)87

89

91

93

95

97

99100

2 3 4 5 6(k)

(Rec

%)

5 Strokes (k=5)6 Strokes (k=4)

8 Strokes (k=6)9 Strokes (k=5)

7 Strokes (k=2, k=5)

Fig. 10a. Parameter m optimization of FKNN.

(m)1.5 1.3 1.1 0.9287

89

91

93

95

97

99100 5 Strokes

7 Strokes (k=2)

7 Strokes (k=5)

6 Strokes

8 Strokes

9 Strokes

(Rec

%)

Fig. 10b. Parameter k optimization of FKNN.

Realclasses

Digit 0 Digit 0 Digit 1 Digit 2 Digit 2Digit 1 Digit 1 Digit 2 Digit 2 Digit 3Digit 1 Digit 1 Digit 3 Digit 3 Digit 5Digit 4 Digit 1 Digit 3 Digit 5 Digit 7Digit 6 Digit 4 Digit 4 Digit 5 Digit 9

Digit 6 Digit 5 Digit 7Digit 5 Digit 8Digit 8 Digit 9Digit 9

The targets of these OCONs are fixed by the degree ofmembership between the data vector Xi and the cluster N

obtained from the FKNNA.To evaluate the handwriting modeling design and the

recognition system paradigm, we calculated the recognitionrate which is a standard measure of performance for char-acter recognizers. We also calculated the squared average(SA) error which is a standard measure used in trainingneural networks. Standard wisdom is that high recognitionrates and low SA error values are good. In this task, weprepared the data set test, we calculated the recognitionrate by introducing the test prototypes to the neural net-work system, and we forced the networks to decide at thecharacter level.

The calculation of the SA error will be explained later.


3.5. Digit database formulation

Database for character recognition algorithms is of fun-damental interest for the training of recognition methodbased on neural networks.

As it was explained in Section 3.1, the segmentation ofdigits was based on stroke detection that divides our systemon some subsystems. Every subsystem was specialized ondigit having the same number of strokes as it was shown inTable 1. However, we cannot find the required repartitionnumber of digits as it was shown in Table 2, neither in UNI-PEN nor in IRONOFF datasets. So, using the (SOM–FKNN–MLP) and UNIPEN database is not possible.

The dimension of the representative feature vector ishigh, for each digit we need ‘‘seven features per stroke x

number of strokes” parameters (from 35 parameters to63 parameters) per digit. Consequently, for every neuralnetwork we need 400 prototypes (300 for the learning sys-tem and 100 prototypes for the testing system). For thisreason, we developed our own database which contains30,000 digits. Twenty four participants were invited to con-tribute to the development of the handwritten digits data.The data for each participant are stored in one data file.When producing the data file, each participant was askedto write a set of all digits (1000–1500 samples of digits).We imposed to the writer just to write 10 times the samedigit, from 0 to 9 in the same page. One page contains100 digits. He asked to prepare only one page per day.We have collected 30,000 digits in total. More than halfof them are regularly written. The remaining ones are thoseeither with noise in the data, poorly written or deliberatelywritten in strange and unusual ways.

About two thirds of the writers were male, about 90%were right handed, the youngest writer was 8 years old,and the oldest was 66. In the online domain, the forms havebeen sampled with a spatial resolution of 200 dpi and a sam-pling rate of 100 points/s (Wacom UltraPad A4) and werestored using the UNIPEN format (Guyon et al., 1994).

4. Experimental results and discussions

To test the performance of our recognition system, wedivided our data base into two parts, 2/3 was used forthe training system and 1/3 for the testing system. We haveperformed experiments to evaluate the modeling systemand also the on-line recognition system of the digits. Ourrecognition system is summarized in three levels: SOM,FKNN and MLPNN.

In the first step of the training system, we developed allmaps using the SOM algorithm in order to obtain the realclasses of every subsystem. The configuration of the SOMalgorithm used is as follows:

1. Weights initialization: we used a random initializationof the map.

2. Map lattice: in our application, we considered the rect-angular lattice.

3. Neighborhood function: we chose the Gaussian functionas being a function of neighborhood.

4. Map shape: we considered the cylindrical shape thatgenerates a junction between the left and right extremi-ties of the map.

According to the variability of the handwriting existingbetween writers, the same digit can be written in differentshapes. Thanks to SOM algorithm development, the realclasses detection of the same digit was established. In ourwork we proceeded to separate these real classes by a rightline and calculate the antecedent input vectors. Note thatthere are sometimes an inference (confusion and ambigu-ity) in the boundary zone of classes. The use of FKKNAgives the membership degree values of every digit class tothe other classes existing in the same map (subsystem).This information will be used as a desired output ofMLPNN.

Regarding the five stroke map, we did not have a dis-crimination level problem of the real classes. Therefore,there were no overlaps between the different real classes(see Fig. 9). However, the distribution of digits in the othermaps (six strokes, seven strokes, eight strokes and ninestrokes), showed difficulties resulting from classes overlap.In fact, samples far from the center, which tend to fall onthe boundaries of classes, are error-prone.

To resolve this problem, we proceeded to separate thesemantic classes by a distribution of every class alone inone map.

After the organization of different maps, we obtainedtwo essential pieces of information. The first one conveysthe real number of classes. The second one deals with theidentification of prototype groups corresponding to differ-ent classes figured in the map.

As a result, the SOM, which is an unsupervised algo-rithm, gives us the real number of classes and not thesemantic one (see Table 2).

In the second step, we developed FKNNAs in order tomake a fuzzy membership matrix of the different real clas-ses obtained by SOM algorithm. According to Figs. 10aand 10b, we optimized the best values of k and m parame-ters in order to maximize the performance of the FKNNA.The membership matrix calculated was used as a desiredoutput of the MLPNN.

Each neural network was trained by the standard backpropagation algorithm. The performance of this algorithmis very sensitive to the proper setting of the training rate.The back propagation training parameters (The trainingrate: l = 0.01; the momentum factor: a = 25; and the iter-ative number for training: epochs = 4000) are adjusted totrade off speed and accuracy. The maximum number ofiteration cycles can be used as a termination criterion.

To test our system, we calculated the global recognitionrate and the global squared error. We proceeded to calcu-late the recognition rates by an affectation to a prototype totest the class that had the best membership degree. Theresults of the recognition rate are presented in Table 3.

Table 3Recognition rates of the hierarchical system

Subsystems Fivestrokes

Sixstrokes

Sevenstrokes

Eightstrokes

Ninestrokes

Recognition rate(%)

98.6 95.58 96.47 94.81 90.24

Global recognitionrate (%)

95.08


The global recognition rate obtained is about 95.08%. Inthis context, we forced our recognition system to give us acrisp result.

Thanks to the membership degrees of character to everyclass assignment, the introduction of the fuzzy logic givesus a wealth of information at the level of the ambiguousrepresentation. Whereas, when using the maximum mem-bership degree and ignoring the others which means decideabout only one class of character, then, the network com-mits errors of classification. For this reason, we consideredthe average squared error as criterion to give more preciseresults of the neuro-fuzzy system (Gader et al., 1995a). Inthis task, we applied the SOM algorithm to test the set ofdigits in order to visualize the real classes.

Then, we applied the FKNNAs to test these prototypesin order to find the membership degree of every prototypetest according to the real classes existing in the trainingmap. These degrees are supposed to be the desired outputof every OCON.

We calculated the average squared error Ei (see formula(9)) of every subsystem and the average squared error Eg

(see formula (10)) of the global system. This error permitsto evaluate the performance of our system. The trainingerror Er is committed by the MLPNN after the trainingprocess. The equations used for this task are:

Er ¼ kyd � yrk2 ð8Þ

Ei ¼POCON nber

j¼1 Erj

prototypes test nberð9Þ

Eg ¼PSub sys nber

i¼1

POCON nberj¼1 ErjPSub sys nber

i¼1 prototypes test nberð10Þ

In formula (8), yd is the desired output (membership vec-tor) and yr is the real vector found by the MLPNN. The re-sults of the average squared errors are presented in Table 4.

To summarize, the learning process which was based onSOM and FKNNA association was done only one timeand it was made in a fuzzy concept. Note that the output

Table 4Average squared error results

Subsystems Fivestrokes

Sixstrokes

Sevenstrokes

Eightstrokes

Ninestrokes

Squared error (%) 0.012 0.03 0.1027 0.054 0.0963Squared average

error (%)0.065

of the learning process was integrated as a desired outputof MLPNN. After the learning process, if we want to rec-ognize one digit, we use only the MLPNN and the outputgives the membership degree of this digit to the other digitsexisting in the same subsystem.

When testing our system, the global average squarederror obtained is about 0.065.

In Table 5, some recognition systems of the handwrittencharacters were shown. Several modeling approaches arebased on geometric features only, while others are basedon kinematic features. Furthermore, several recognitionsystems were based either on one classifier (unsupervisedalgorithm as SOM algorithm Mezghani et al., 2002), or ahybridization between HMM and MLPNN approach(Hafsa et al., 2004). Compared to these systems, our pro-posed system is based on a combination of trajectory (geo-metrical features) and velocity (kinematic features)modeling.

In this instance, our recognition system revolves arounda mixture of unsupervised and supervised algorithms in asequential architecture of (SOM, FKNN and MLPNNalgorithms).

The studies of Hebert et al. (1998) consist of a fuzzy rep-resentation of feature extraction of digits (the feature wasbased on stroke direction: horizontal, vertical, positive ornegative oblique) and recognition system based on Koho-nen and MLP classifiers, it was demonstrated that the rec-ognition result (95%) proves an interesting methodology ofthe modeling system. In our system, we used the fuzzy con-cept in the recognition system.

Compared with Hafsa’s recognition system (Hafsa et al.,2004) which use the same database and based on hybridiza-tion of MLP and MMC, the recognition rate is about 93%,our recognition system which based on SOM, FKNNAand MLP association performs better and gives 95.08%as a recognition rate.

We have already made a new experimentation in orderto compare (Beta–circular/Beta–elliptic) modeling systemkeeping the same classification process (MLP) and weproved that the Beta–elliptic representation gives a betterperformance than the Beta-circular representation. Therecognition rate that obtained by using the Beta-circularapproach is about 93.20%; however, using the Beta–ellipticapproach, this rate was increased to 94.14%.

We have also made a new experimentation in order tocompare the classification system (SOM–FKNN–MLP/MLP) keeping the same features and database. The associ-ation of SOM–FKNN–MLP proves a better performancethan the use of only MLP. In fact, the use of the one clas-sifier MLP gives only 94.14% as a recognition rate.

In order to validate our modeling approach, we alsoconducted another new experimentation consisting of theuse of SVM classifier and UNIPEN dataset of digits keep-ing the modeling system which was based on Beta–ellipticapproach. The recognition rate obtained is about 94.78%.Compared to the Ratzlaff studies which consist of methods,report and survey for the comparison of diverse isolated

Table 5Some results from the literature on handwritten character recognition

Authors Method Accuracy Notes

Gader et al. (1995a) Comparison of Crisp and Fuzzycharacter neural networks inhandwritten word recognition

86.24% on uppercase and 83% onlowercase

Features vector reaches 100 parameters basedon pixel normalization and descenderascender detection

Hebert et al. (1998) Combination of SOM and MLP 95% on 13,000 digits collected fromUNIPEN database

The modeling system based on fuzzyrepresentation

Mezghani et al. (2002) Sel Organization Map, SOM, it is anunsupervised Algorithm

88.38% on 24,000 samples of Arabicletters for testing and 5000 Arabicletters samples for training

Features vector based on elliptic Fourierdescriptors

Ratzlaff (2003) Methods, report and survey for thecomparison of diverse isolatedcharacter recognition results on theUnipen database

95% confidence limits are given whereavailable

Six UNIPEN isolated character subsets. 1adigits, 1b uppercase, 1c lowercase, 1dpunctuation and other symbols, 2 mixed and 3mixed, with 10, 26, 26, 32, 94, and 94 classes,respectively

Hafsa et al. (2004) Hybridizing of NN and HMM 93% on 24,000 prototypes of digits Database was collected by REGIM members

Prevost et al. (2005) Hybrid generative/discriminativeclassifier for unconstrained characterrecognition

99.1% on 14,000 digits divided intothree sets: 8000 digits for training,4000 digits for testing and 2000 digitsfor cross valid

Digits are collected from UNIPEN database.The sequence of (x, y) coordinates isresampled with 20 points per stroke

Aksela and Laaksonen(2005)

Elastic matching is used as dynamictime warping (DTW)

79.98% on characters (uppercaseand low case letters anddigits)

The member classifier was based on stroke-by-stroke distances between the given charactersand prototypes

Database is divided into three groups(9961 prototype characters, 8047 forevaluation and 80,077 for testing)


character recognition results on the UNIPEN database(Ratzlaff, 2003), our modeling approach gives a similarresults and that proves an acceptable performance of theBeta–elliptic modeling.

The execution time needed to recognize one digit is var-iable. It was estimated between 1 and 3 s. Whereas, thelearning process presents a considerable execution time, ittakes about (10 min to 1 h:13 min). It depends on subsys-tem strokes number. These experiments were done on IntelCoreTM Solo processor T1350 (1.86 GHz, 533 MHz FSB,2 MB L2 cache). Note that all algorithms were developedby MATLAB language which is an interpreted language.Eventually, we compiled all our algorithms to C++ lan-guage and the execution time was reduced to (13–35 ms).It depends on input vector size of the tested digit.

5. Conclusion

In this paper, the originality of our work resides in thedevelopment of a new method for handwritten trajectorymodeling based on inflection point detection, the over-lapped form of Beta signals and the elliptic arcs. Ourcontribution also deals with a novel approach of on-linerecognition of the Arabic handwritten digit. Novel archi-tecture of recognition system was developed, withwhich acceptable recognition accuracy was reached. Ourmodeling system gave good results and proved that theBeta–elliptic representation is a powerful tool for the hand-writing modeling.

Our system achieves a recognition rate of 95.08% and anSA error of 0.065%, which makes it an acceptable perfor-mance system.

The interaction between the different classifiers (SOM,FKNN and MLPNN algorithms) contributes to increasethe performance of our recognition design. The comple-mentarities between these classifiers were demonstrated.These developed modeling and recognition methods canbe extended to any size of feature vectors and can beapplied not only in digits but also in the Arabic, Latin, Chi-nese, etc. characters.

Note that the real classes taken into considerationenhance the performance of our recognition system result.

As a future work, we can improve the Beta–ellipticapproach by the Fuzzy Beta–elliptic approach. The fuzzyapproach will be integrated in the angle determination ofthe elliptic shape. The developed recognition system canbe extended to the global recognition of the cursive words.

Acknowledgements

The authors acknowledge the financial support of thiswork by grants from the General Direction of ScientificResearch and Technological Renovation (DGRSRT),Tunisia, under the ARUB program 01/UR/11/02.

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