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Adaptive membership functions hand written character recognition by voronoi-based image zoning.bak

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Adaptive membership functions hand written character recognition by voronoi-based image zoning.bak

  1. 1. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 1 Adaptive Membership Functions for Hand-Written Character Recognition by Voronoi-based Image Zoning G. Pirlo, Member, IEEE, D. Impedovo, Member, IEEE Abstract— In the field of hand-written character recognition, image zoning is a widespread technique for feature extraction since it is rightly considered able to cope with hand-written pattern variability. As a matter of fact, the problem of zoning design has attracted many researchers that have proposed several image zoning topologies, according to static and dynamic strategies. Unfortunately, little attention has been paid so far to the role of feature-zone membership functions, that define the way in which a feature influences different zones of the zoning method. The results is that the membership functions defined to date follow non-adaptive, global approaches that are unable to model local information on feature distributions. In this paper, a new class of zone-based membership functions with adaptive capabilities is introduced and its effectiveness is shown. The basic idea is to select, for each zone of the zoning method, the membership function best suited to exploit the characteristics of the feature distribution of that zone. In addition, a genetic algorithm is proposed to determine – in a unique process - the most favorable membership functions along with the optimal zoning topology, described by Voronoi tessellation. The experimental tests show the superiority of the new technique with respect to traditional zoning methods. Index Terms—Adaptive Membership Functions, Handwriting Recognition, Optical Character Recognition, Genetic Algorithm, Voronoi Tessellation, Zoning Method.. —————————— —————————— 1 INTRODUCTION I MAGE zoning is a widespread feature extraction tech- shape. Blumenstein et al. [4] use a static topology obtained nique for hand-written character recognition. In fact, im- by a 3x2 regular grid for handwritten character recognition. age zoning is rightly considered effective for coping with The same topology is considered by Morita et al. [5], who http://ieeexploreprojects.blogspot.com the changeability of hand-written patterns, due to different derive contour–based features for digit recognition; by writing styles and personal variability of the writers. By let- Oliveira et al. [6], who adopt a 3×2 grid and extract contour- ting B be a pattern image, an image zoning method ZM can based features from each zone; and by Koerich [7] and Ko- be generally considered as a partition of B into M sub- erich and Kalva [8], who derives directional features. Suen images (M integer, M>1), named zones (i.e. ZM={z1, z2, ..., et al. [9, 10] also use a 3×2 regular grid to define a model to zM}), each one providing local information on pattern im- evaluate the distinctive parts of handwritten characters and ages [1, 2]. to compare human and machine capabilities in character In literature, the problem of zoning design has been mainly recognition by parts. A 3×3 regular grid for zoning design is considered as related to the design of the topology to be used by Baptista and Kulkarni [11] who extract geometrical used, that defines the way in which a pattern image must be feature distribution from each zone, and by Singh and Hew- segmented in order to extract as much discriminative infor- itt [12] that use a modified Hough transform method to ex- mation as possible. The approaches proposed so far for to- tract features for handwritten digit and character recognition. pology design can be divided into two categories: static and Phokharatkul et al. [13] present a system for handwritten dynamic [3]. character recognition based on Ant-minor algorithm. They Traditional approaches involve static topologies, that are use a 4×3 regular grid for zoning design in order to extract designed without using a-priori information on feature dis- closed-loop and end-point features from the pattern image. tributions in pattern classes. In this case, zoning design is A 4×4 regular grid is used by Cha et al. [14] to extract gra- performed according to experimental evidences or on the dient, structural and concavity information from the pattern basis of intuition and experience of the designer. In general, image, and by Negi et al. [15] to derive the density of pixels static topologies are designed considering u×v regular grids in the different zones. Kimura and Shridhar [15] use a zon- that are superimposed on the pattern image, determining ing topology based on a 4×4 regular grid to detect informa- uniform partitions of the pattern image into regions of equal tion from contour profiles of the patterns. In each zone the number of segments on the contour of the pattern with the ———————————————— same orientation is counted. Four basic orientations are con- • The authors are with the Dipartimento di Informatica of the Università sidered: 0°,90°,+45°,-45°. The same grid is used by Liu et degli Studi di Bari, via Orabona 4, 70126 Bari , Italy. E-mail: al. [16] to recognize Chinese characters by a directional de- pirlo@di.uniba.it. composition approach. Camastra and Vinciarelli [17] use a xxxx-xxxx/0x/$xx.00 © 200x IEEECopyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  2. 2. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 2 ID 4x4 regular grid for recognizing isolated cursive characters acter recognizer. extracted from word images. In this case, two sets of opera- Converse to previous approaches, in which dynamic zoning tors are applied to each zone. The operators of the first set methods were designed according to constrained topologies measure the percentage of foreground pixels in the zone based on pre-determined templates, Impedovo et al. [36] with respect to the total number of foreground pixels in the proposed Voronoi tessellation for zoning description, since character image. The operators of the second set estimate to Voronoi tessellation allows the design of dynamic zoning what extent the black pixels in the cell are aligned along methods based on unconstrained topologies. In fact, given a some directions. Xiang et al. [18] apply zoning to the recog- set of points (named Voronoi points) in continuous space, nition of car plates. They extract pixel density features di- Voronoi tessellation is a simple means of naturally partition- viding the character input image from car plates using a 4x4 ing the space into zones, according to proximity relation- regular grid. Impedovo et al. [19, 20] consider 3×2, 3×3 and ships among the set of points. More precisely, let B be a 4×4 regular grids and use a genetic algorithm to determine pattern image and P={p1, p2,…, pM} a set of M distinct the optimal weight vector to balance local decisions by using points in B. The Voronoi tessellation determined by P is the M zones. Sharma and Gupta [21] use 4×4, 6×6 and 8×8 partition of B into M zones {z1, z2, ..., zM} , with the property regular grids to extract pixel density from the pattern image. that each region zi defined by pi , contains all the points p Rajashekararadhya and Ranjan [22] use a 5x5 regular grid for which it results that distance(p, pi) < distance (p, pj) , for for zoning design. For each zone, the average distances from any pj ≠ pi. In addition, concerning the boundaries of the the character centroid to the pixels in each row/column are zones, it is also assumed that the points of B that are equidis- considered as features. A 5x5 regular grid is also used by tant from two (or more) points of P belong to the zone with Vamvakas et al. [23] to compute local density in the charac- minimum index. For instance, let p be a point for which ter image. Kato and Suzuki [24] used a 7x7 regular grid for distance(p, pi)=distance (p, pj) , for i≠ j, in this work it is Chinese and Japanese handwritten characters. A similar ap- assumed that p∈zi , if i<j; p∈zj , if i>j. Of course, chang- proach, which uses overlapped zones to reduce border ef- ing the position of the Voronoi points corresponds to the fects, has been also proposed by Kimura et al. [25]. modification of the zoning method. Therefore, zoning de- Dynamic topologies are designed according to the result of scription with Voronoi tessellation offers the possibility to optimization procedures. Aires et al. [26] and Freitas et al. easily adapt the zoning to the specific characteristics of the [27, 28] presented a perception-oriented approach that uses classification problem. In fact, a genetic algorithm for zon- non-regular grids for zoning design, resulting in a non- ing design has been also proposed [36], in which each indi- uniform splitting of the pattern image. They define manually vidual of the genetic population is a set of Voronoi points the zoning grid by using the confusion matrices looking for (corresponding to a zoning method) and the cost function the relation between the zones, in order to make the zoning associated to the classification is considered as a fitness design process less empirical. Other http://ieeexploreprojects.blogspot.com some examples of static and dy- approaches, based on function. Figure 1 shows automatic optimization schemes, generally concerns con- namic zoning topologies. Cases (a) and (b) show two uni- strained zoning methods based on pre-determined templates. form topologies obtained by 3x2 and 3x3 regular grids, re- Valveny and Lopez [29] use a zoning method for digit rec- spectively. Cases (c) and (d) show two examples (with 6 ognition located on surgical sachets which pass through a and 9 zones respectively) of optimized non-uniform topolo- computer vision system performing quality control. In this gies. In all cases, the Voronoi points of the zones are re- case, the authors divide the pattern image into five rows and ported. As Figure 1 demonstrates, Voronoi tessellations can three columns. The size of each row and column is deter- be used for describing both static and dynamic zoning to- mined in such a way to maximize the discriminating capa- pologies. Of course, when uniform topologies are consid- bilities of the diverse zones of the pattern image. Dimauro et ered, as the case in Figure 1a,b, the Voronoi point of each al. [30] performed zoning design according to the analysis of zone corresponds to the center of that zone. the discriminating capability of each zone, estimated by Unfortunately, although zoning methods are largely adopted means of the statistical variance of feature distributions. Di and advanced techniques for optimal topology design have Lecce et al. [31] designed the zoning problem as an optimi- been proposed, aspects related to the choice of feature-zone zation problem in which the discrimination capability of membership functions have not yet been sufficiently ad- each zone is estimated by the Shannon Entropy. Lazzerini dressed. Notwithstanding, membership function plays a cru- and Marcelloni [32] applied a method for fuzzy classifica- cial role in exploiting the potential of a zoning method since tion and recognition of two-dimensional shapes to handwrit- it should be able to model spatial distributions of features in ten characters. The character image is partitioned horizon- the different zones. Thus, when zoning is used, the choice of tally and vertically into stripes. For each dimension, a set of a membership function needs specific attention. weights is determined that define the importance of each In literature, the membership values are assigned on the ba- stripe in the classification process and a genetic algorithm is sis of the values of specific proximity-based functions. Ac- used to optimize stripe dimension with respect to the recog- cording to the type of values used to define membership nition rate. Radtke et al. [33, 34] presented an automatic weights, three classes of order-based membership functions approach to define zoning based on fixed position divisions can be defined [37]: abstract-level, ranked-level and meas- of pattern images. Gagné and Parizeau [35] used a tree- urement-level. When abstract-level membership functions based hierarchical zoning for handwritten character classifi- are considered, the membership values are given in the form cation and presented a genetic programming approach for of Boolean values. When ranked-level membership func- optimizing the feature extraction step of a handwritten char- tions are used, the membership values are integers. WhenCopyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  3. 3. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. AUTHOR ET AL.: TITLE 3 measurement-level membership functions are used the 2 FEATURE EXTRACTION BY ZONING METHODS membership values are real numbers. Fuzzy membership Let ZM={z1, z2, ..., zM} be a zoning method, a crucial as- functions have also been proposed, in which the membership pect for zoning-based classification concerns the way in weights are assumed to be fuzzy values derived by an opti- mization procedure [38]. It is worth noting that order-based which each feature detected in a pattern x has influence on functions are not able to cope with the specific characteris- each zone of ZM. In fact, let us consider the classification of tics of pattern distributions. Furthermore, both order-based a pattern x into one class of Ω={C1 ,..., CK} using the feature membership functions and fuzzy membership functions fol- set F={f1,...,fT}; In this case x can be described by the fea- low a global strategy, i.e. the membership functions are the ture matrix Ax of T rows (features) and M columns (zones): same for all zones of a zoning method. The result being that  Ax (1,1) Ax (1,2) ... Ax (1, j ) ... Ax (1, M )  they are unable to exploit the evidence that feature distribu-  A ( 2,1) A ( 2,2) ... A ( 2, j ) ... A ( 2, M )  tions in diverse zones of pattern images can be very differ-  x x x x   ... ... ... ... ... ...  ent. Ax =    Ax (i,1) Ax (i,2) ... Ax (i, j ) ... Ax (i, M )   ... ... ... ... ... ...     Ax (T ,1) Ax (T ,2) ... Ax (T , j ) ... Ax (T , M )    (1) with Ax (i, j ) = ∑w ins tan ces of fi ij in x (2) being wij the weight that defines the degree of influence of Fig. 1. Examples of Zoning Methods: Static vs Dynamic (Voronoi-based) an instance of feature fi (detected in x) on zone zj. Now, the influence weight wij of an instance of fi on zone Starting from this consideration, this paper introduces a new zj is determined on the basis of the proximity condition be- class of zone-based membership functions with adaptive tween the position of the instance of fi and zj (it is worth capabilities and presents a real-coded genetic algorithm for noting that the position of a feature fi is assumed to be lo- determining – in a single process - both the optimal zoning method, based on Voronoi tessellation of the pattern image, cated at the centre of gravity of fi when structural features and the adaptive membership function most profitable for a are considered, such as lines, loops, cavities, arcs, etc…). given classification problem. Contrary to other approaches More precisely, let ZM={z1, z2, ..., zM} http://ieeexploreprojects.blogspot.com be a zoning proposed in literature so far, the new class of membership method corresponding to the Voronoi points P={p1, p2, ..., functions allows the membership function to adapt to the pM}, where zj is the Voronoi region corresponding to the specific feature distribution of each zone of the zoning Voronoi point pj , j=1,2,…,M; let qi be the point in which method. feature the instance of fi is found; let dij=dist(qi, pj) be the The experimental tests were carried out in the field of hand- Euclidean distance between qi and pj; the Ranked Index Se- written digit and character recognition using datasets from quence (RISi) associated to the instance of feature fi , that CEDAR and ETL databases, respectively. As expected, the denotes the sequence of the zones ranked according to their results show that the effectiveness of a zoning method proximity to qi , is defined as: strongly depends on the membership function considered. In RISi = < i1, i2, …, ik, ik+1,…, iK > (3) addition, they demonstrate that adaptive membership func- with tions are superior to traditional functions, whatever zoning • ik∈{1,2,…,M} , ∀k=1,2,…K ; topology is used. Of course, when adaptive zone-based • ik1≠ik2 , membership functions were selected together with the opti- mal Voronoi-based zoning - according to the approach pro- ∀k1,k2=1,2,…K , k1≠k2 ; posed in this paper - the recognition and reliability rates and for which it results achieved the best results for both the numeral and character dik1 < dik2 , k1 < k2 , ∀k1,k2=1,2,…K (4) recognition. we also assume that in the case dik1 = dik2 then ik1 precedes The paper is organized as follows. The role of membership ik2 , if k1<k2). functions for feature extraction by zoning methods is fo- Furthermore, let Counti(j) be the function providing the cused on in Section II, which also illustrates the new class of position of the index j (i.e. concerning zone zj) in the se- adaptive membership functions proposed in this paper. Sec- quence RISi (i.e. counti(j)=k for j=ik, according to eq(3)), the tion III shows the new approach, based on a real-coded ge- following feature-zone membership functions can be con- netic algorithm, for the selection of adaptive membership sidered [37]: functions together with optimal zoning design by Voronoi Abstract-level membership functions: Member- Tessellation. Section IV reports the experimental results, ship functions at abstract-level assign Boolean in- carried out on handwritten numeral digits ad characters ex- fluence weights on the basis of the first k zones in tracted with the CEDAR and ETL databases, respectively. RISi: The conclusion of this work is reported in Section V. • The Winner-takes-all (WTA) membership function.Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  4. 4. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 4 ID This is the standard membership function used in traditional zoning-based classification. In this case results: o wij=1 if counti(j)=1 (5a) o wij=0 otherwise ; (5b) • The k-Nearest Zone (k-NZ) membership function. This is a generalization of the WTA function. In this case results: o wij=1 if counti(j)∈{1,2,…,k} (6a) o wij=0 otherwise; (6b) Ranked-level membership functions: Member- Fig. 2. Zoning Methods: RISi = < 3, 2, 6, 5, 1, 4, 9, 8, 7 > ship functions at ranked-level assign integer influ- ence weights on all zones, the basis of their position in the RISi : • The Ranked-based (R) membership function. In this case it results: o wij=M-k if counti(j)=k; (7) Measurement-level membership functions: Membership functions at measurement-level assign real influence weights according to the distance be- tween the zones and the instance of the feature fi. In TABLE I this paper three measurement-level membership MEMBERSHIP FUNCTIONS: A NUMERICAL EXAMPLE functions are considered : Linear Weighting Model (LWM) For this purpose, the new zone-based membership func- o wij=1/dij (8a) tions, for each zone zj , are here defined according to an Quadratic Weighting Model (QWM) Adaptive Weighted Model (AWM): o wij=1/dij2 (8b) −λ d Exponential Weighting Model (EWM) wij = e j ij . o wij=1/edij (8c) where λj is a positive parameter, named falling rate, un- For example, for the instance of fi (an end-point) shown in dergoing exponential decay of the adaptive membership http://ieeexploreprojects.blogspot.com Fig. 2, the numerical values of the membership functions are function. Larger falling rates make the value of the member- reported in Table I (for the sake of clarity the values of the ship function vanish much more rapidly, as the distance be- measurement-based membership functions have been nor- tween the position of the feature and the zone increases. The malized). In this case, we consider the zoning method membership functions for different values of λ are shown j. Z9={z1,z2,...,z9} (M=9) corresponding to the set of Voronoi in the example of Figure 3. It should be noted that these points P={p1,p2,...,pM}={(9,60),(27,60),(45,60),(9,36), work as a traditional WTA strategy, for λ =10. In fact, in this j (27,36),(45,36),(9,12),(27,12),(45,12)}, whereas the position case, feature f has influence (with w =1) only on the zone z i ij j of fi is qi=(qxi ,qyi)=(44, 57.8). Starting from the set of in which f is positioned. Conversely, when λ =0, f has an 2 i j i Euclidean distances dij = dist(qi,pj)= [(pxi - qxi) +(pyi - equal influence (with w =1) on all zones, no matter where f ij i qyi)2] ½, for j=1,2,…9, the values of the membership func- is positioned. tions are computed. It is worth noting that here the Ranked Index Sequence is equal to RISi = < 3, 2, 6, 5, 1, 4, 9, 8, 7 >. In this paper, starting from the basic idea that pattern fea- 1,2 λ=0 tures are spatially distributed according to local characteris- 1 λ=0,10 tics, a new adaptive technique to membership function de- 0,8 λ=0,30 weight sign is considered [39]. In fact, there are regions of the pat- 0,6 λ=0,70 tern image in which features are arranged into a small area 0,4 λ= 1,00 λ= 2,00 (stable regions) whereas there are regions in which features 0,2 λ=10,00 are spread over a very large area (variable regions). There- 0 1 2 3 4 5 6 7 8 9 fore, a membership function could be able to adapt itself to zone sequence the local distributions of patterns. In addition, this paper also takes advantage from the evidence that the membership function based on the exponential weighted model generally Fig. 3. Example of Adaptive Membership Functions (weight vs zone) leads to superior performance than other membership func- tions, as already discussed in the literature [40]. 3 CLASSIFICATION IN VORONOI TESSELLATION BYCopyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  5. 5. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. AUTHOR ET AL.: TITLE 5 ADAPTIVE MEMBERSHIP FUCNTIONS that corresponds to the Voronoi point of the zone As discussed before, the zoning design process concerns zj of ZM={z1, z2, ..., zM}; both the definition of the optimal topology along with the λj: a falling value that defines the adaptive model for the definition of the optimal membership functions. According membership function of the zone zj. to previous studies in the literature the cost function, which Consequently, the fitness value of the individual is taken depends on both zoning method (ZM) and membership func- as the classification cost CF(ZM, FM), obtained by eq. (10), tion (FM), is here defined as follows [40]: where: ZM={z1, z2, ..., zM} is the Voronoi Tessellation, CF(ZM , FM) = η ⋅Err(ZM , FM) + Rej(ZM , FM) (10) being zj the Voronoi region corresponding to pj , where: Err(ZM, FM) is the misrecognition rate (estimated using ∀j=1,2,…,M. FM ={ λ1, λ2,…, λM}, is the set of adaptive mem- the patterns of the learning set: Err(ZM, FM)=card{xr∈ bership functions, being λj the falling value of XL| xr∈Ck and D(S(xr))=Ck*, k≠k*}/ card(XL)); the adaptive weighing model associated to the Rej(ZM, FM) is the rejection rate (estimated using zone zj , ∀j=1,2,…,M. the patterns of the learning set: Rej(ZM, FM) = From the initial - population, the following genetic opera- card{xr∈ XL | D(S(xr))=C } / card(XL) ); tors are used to generate new populations of individuals: coefficient η is the cost value associated to the treat- individual selection, crossover, mutation and elitism. These ment of an error with respect to a rejection. four operations are repeated until Niter successive popula- Moreover, since Voronoi Tessellation is used for zoning tions of individuals are generated. When the process stops, description and the adaptive membership functions are con- the optimal zoning is obtained by the best individual of the sidered, the following formulation of the problem of optimal last-generated population. In the following a brief explana- zoning design is given: tion of the adopted operators is reported (the complete de- scription of these genetic operators can be found in refs. [41, Find the sets {p*1, p*2, ..., p*M} (Voronoi points) and 42]): {λ*1, λ *2, ..., λ*M} (falling values) so that: a) Individual Selection: Npop/2 random pairs of individuals are selected for crossover, according to a roulette-wheel CF(Z*M, F*M) = min{ ZM,F M} CF(ZM, FM) (11) strategy. with: b) Crossover: arithmetic crossover is used to combine in- Z*M ={z*1, z*2,…, z*M} , z*j being the Voronoi formation from diverse individuals. Let region corresponding to p*j , ∀j=1,2,…,M ; http://ieeexploreprojects.blogspot.com M  and  p 1 ,  p 2 ,..., p j ,..., p M   pa1  pa2   pa j   pa b b b b ZM ={z1, z2,…, zM} , zj being the Voronoi region  a ,  a ,..., a ,..., a   b b   b   b  corresponding to pj , ∀j=1,2,…,M . λ 1  λ 2  λ j  λ M   λ 1  λ 2  λ j   λ M  and (13a) F*M ={ λ*1, λ*2,…, λ*M} , λ*j being the falling be two individuals selected for crossover, the two off- value of the adaptive membership functions as- spring individuals sociated to the zone z*j , ∀j=1,2,…,M ; FM ={λ1, λ2,…, λM}, λj being the falling value of pa1   pa2   pa j   pa M   pb1  pb2   pb j   pbM  the adaptive membership functions associated to λa1 , λa2 ,...,λa j ,...,λa M  and λb1 , λb2 ,...,λb j ,...,λbM                the zone zj , ∀j=1,2,…,M . (13b) In order to solve the optimization problem (11), a real- of the next generation are obtained as linear combination of coded genetic approach is used since it has potential for the parent individuals, according to the random values α, β solving non-linear optimization problems in which the ana- ∈[0,1] : lytical expression of the object function is not known [41]. In the following, the genetic algorithm is described for the pas =α⋅pas+(1- α)⋅pbs ; (14a) design of the adaptive membership functions together with p s =α⋅p s+(1-α)⋅p s . b b a (14b) the optimal zoning. and The initial – population λbs =β⋅λbs+(1- β)⋅λas (14c) Pop={Φ1, Φ2, ...,Φι, ... ,ΦΝποπ} for the genetic algorithm is created by generating Npop random individuals (Npop even). c) Mutation: a non-uniform mutation operator has been Each individual is a vector used. Let (12)  p1   p2   p j   pM  Φi =  ,  ,..., ,...,   p1   p2   p j   pM  λ1  λ2  λ j  λM  Φi =  ,  ,..., ,...,  λ1  λ2  λ j  λM   pj  where each element λ  consists of: pj: a point defined as  j pj=(xj,yj) ,Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  6. 6. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 6 ID  pj  4 EXPERIMENTAL RESULTS   be an individual and  λ j  (being p j = ( x j , y j ) ) an Two groups of experiments have been carried out, using element of Φi selected for mutation, according to a mutation the following datasets of pattern classes: probability Mut_prob. The non-uniform mutation operator ~  p ~ ~ ~ Ω1={0,1,2,…,9}: the dataset of 10 handwritten numeral changes  j  in the new element  ~j  (being p j = ( x j , y j ) ) p λ  λ j   j  as follows: digits extracted from the CEDAR database [43]: 18468 that is defined training digits (BR Directory), 2213 test digits (BS Di- c.1) Concerning ~ = (~ , ~ ) pj xj yj , we have (see rectory); Figure 4): Ω2={A,B,C,…,Z}: the dataset of 26 English handwrit- ~j = x j + δ ⋅ cos(ϕ ) x ten characters from the ETL database [44]: 29,770 train- ~ (15)  y j = y j + δ ⋅ sin(ϕ ) ing characters, 7,800 test characters. After normalization of each the pattern image to a size of where 72x54 pixels, the skeleton of the pattern is derived through - φ is a random value generated according to a uniform dis- the Safe Point Thinning Algorithm [45]. Successively, the tribution, φ∈[0,2π[; feature set F={f1,...,f9} is considered for pattern description, - δ is a displacement determined according to the following where: f : holes; f : vertical-up cavities; f : vertical-down 1 2 3 equation: cavities; f4: horizontal-right cavities; f5: horizontal-left cavi- ties; f6: vertical-up end-points; f7: vertical-down end-   iter   1− iter  b points;f8: horizontal-right end-points; and f9: horizontal-left δ = δ _ displ⋅ 1−ν  N ,   (16)   end-points. Please note that the description of this feature set   is behind the aims of this paper and the interested reader can found a detailed description in the literature [46]. For pattern being ν a random value generated in the range [0, 1], accord- classification, a k-NN classifier (k=1) was considered. Pat- ing to a uniform distribution; δ_displ the maximum dis- tern rejection occurred when the two training vectors closest placement allowed; b a parameter determining the degree of to the test vector were related to two diverse classes and the non-uniformity; iter the counter of the generations per- iter difference of the distances between each one of the two formed; N the maximum number of generations. training vectors and the test vector was smaller that a suit- It is worth noting that eq. (16) causes the operator to able threshold ξ (ξ=0.7 in the tests), In addition, the follow- search the space almost uniformly initially, when iter is ing parameter values for the Genetic Algorithm were se- small, and locally in later stages. ~ λ c.2) Similarly, concerning j , we have: lected by k-fold cross validation (k=10) on the training sets: NPop=10; Niter=300; Mut_prob=0.35; δ_displ=5 ; b=1.0; http://ieeexploreprojects.blogspot.com  1− iter   c   λ_displ=0.5, c=3.0. An example of convergence of the Ge- ~ λj = λj + (−1)s ⋅ λ _ displ⋅ 1−η Niter   netic Algorithm is shown in Fig. 5, for M=9.   (17)   where s is a random Boolean value generated according to a equally-distributed probability function; η is a random value generated in the range [0, 1], according to a uniform distri- bution; λ_displ is the maximum displacement allowed; c is a parameter determining the degree of non-uniformity; and iter denotes the counter of the generations performed while Niter denotes the maximum number of generations. Fig. 5. Genetic Algorithm: Cost Function vs iterations (M=9) Figure 6 shows the results obtained for the specific case of M=9, when handwritten digits are considered. Figure 6a shows the optimal zoning Z*9 and Figure 6b reports the set of optimal adaptive membership functions F*9. Concerning time complexity of the new technique, it can be measured by the number of fitness function evaluations done during the Fig. 4. The Mutation Operator course of a run [41, 42]. Hence, for fixed population sizes, the number of fitness function evaluations is given (in the d) Elitist Strategy: from the Npop individuals generated by worst case) by the product of population size (NPop) per the above operations, one individual is randomly removed number of generations (Niter). Of course, faster convergence and the individual with the minimum cost in the previous of the genetic algorithm can be expected if the initial popu- population is added to the current population. lation is not random, but it is defined starting from the analysis of local properties of statistical feature distributions.Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  7. 7. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. AUTHOR ET AL.: TITLE 7 Anyway, it is worth noting that time complexity is not a ship-functions are used the average recognition rate is 0.50, limitation of the new technique since it concerns the optimi- 0.55 and 0.84 for LWM, QWM and EWM, respectively. The zation of the zoning topology and membership functions that average recognition rate is 0.89 when AWM is used. More- occurs during the tuning phase of the system, before the over, Table IIa shows that the best result occurs for Z*9. In running phase. Therefore the time complexity of the tech- this case REC(Z*9, AWM)=0.97 results and the improve- nique has no effect on the classification speed of the zoning- ment is equal to 8% with respect to WTA, 15% with respect based classifier, which remains the same as that of tradi- to 2-NZ, 25% with respect to 3-NZ, 83% with respect to R, tional zoning methods. 98% with respect to LWM, 67% with respect to QWM and 4% with respect to EWM. Concerning the reliability rate (REL), Table IIb shows that AWM always outperforms other membership functions. In particular, when abstract membership-functions are used, the average reliability rate is 0.87, 0.84 and 0.79 for WTA, 2-NZ and 3-NZ, respec- tively. When ranked membership-function is considered (R) the reliability rate is 0.58 on average. When measurement membership-functions are used the average reliability rate is 0.56, 0.62 and 0.87 for LWM, QWM and EWM, respec- Fig. 6. Adaptive Membership Functions for the optimal Z*9 zoning method: tively. Finally, when the new adaptive weighting model an example (AWM) is used, the average reliability rate is 0.91. TABLE IIa The main results of the experimental tests are summarized PERFORMANCE ANALYSIS ON Ω1: Recognition Rate (REC) in Tables II and III, which report the performance obtained on Ω1 and Ω2, respectively. The effectiveness of different membership functions is compared on both static zonings and dynamic, Voronoi-based zoning methods. The perform- ance is reported in terms of recognition rate (REC) and reli- ability rate (REL), for η=10 (see eq. (10)). The result shows that dynamic zoning methods based on optimal Voronoi tessellation always outperforms static methods, whatever number of zones (M) and Membership Function (F) are con- TABLE IIB http://ieeexploreprojects.blogspot.comNALYSIS ON Ω1: Reliability Rate (REL) sidered. In particular, when handwritten numerals are con- PERFORMANCE A sidered, Table IIa shows that the improvement in recogni- tion rate ranges from 7% when M=16 and F=WTA (REC(Z*16,WTA)=0.88 vs REC(Z4×4,WTA)=0.82) up to 34% when M=16 and F=QWM (REC(Z*16, QWM)=0.63 vs REC(Z4×4, QWM)=0.47), whereas improvement in reliabil- ity rate (Table IIb) ranges from 4% when M=16 and F=2- NZ (REL(Z*16, 2-NZ)=0.88 vs REL(Z4×4, 2-NZ)=0.84) up to 35% when M=6 and F=R (REL(Z*6,R)=0.73 vs Furthermore, Table IIb shows that the best reliability REL(Z3×2,R)=0.54). Conversely, when handwritten charac- occurs for Z*9. In this case REL(Z*9, AWM)=0.99 results ters are used, improvement in recognition rate (Table IIIa) and the improvement is equal to 7% with respect to WTA, ranges from 3% when M=16 and F=WTA 8% with respect to 2-NZ, 19% with respect to 3-NZ, 57% (REC(Z*16,WTA)=0.87 vs REC(Z4×4, WTA)=0.84) up to with respect to R, 70% with respect to LWM, 50.0% with 14% when M=9 and F=QWM (REC(Z*9, QWM)=0.71 vs respect to QWM and 4% with respect to EWM. REC(Z3×3, QWM)=0.62), whereas improvement in reliabil- In order to evaluate the statistical significance of the clas- ity rate (Table IIIb) ranges from 3% when M=6 and sification results on handwritten digits, the two way analysis F=AWM (REL(Z*16, AWM)=0.95 vs REL(Z4×4, of variance (ANOVA) has been performed on data of Tables AWM)=0.92) up to 16% when M=9 and F=2-NZ IIa,b. The ANOVA test (with the significance level equal to (REL(Z*9,2-NZ)=0.79 vs REL(Z3×3,2-NZ)=0.68). =0.05) demonstrated that differences between traditional Furthermore, Tables II and III show that AWM is superior zoning methods and optimized methods based on Voronoi to other membership functions, whatever zoning methods tessellation and adaptive membership functions are signifi- are used. In particular, concerning handwritten digit recogni- cant in terms of both recognition rates and reliability rate. tion, Table IIa shows that, when abstract membership- Concerning handwritten character recognition, Table IIIa functions are used, the average recognition rate is 0.83, 0.80 shows AWM provides the best results. Precisely, when ab- and 0.75 for WTA, 2-NZ and 3-NZ, respectively. When stract membership-functions are used, the average recogni- ranked membership-function is considered (R) the recogni- tion rate is 0.82, 0.71 and 0.67 for WTA, 2-NZ and 3-NZ, tion rate is 0.51 on average. When measurement member- respectively. When ranked membership-function is consid-Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  8. 8. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 8 ID ered (R) the recognition rate is 0.55 on average. When pose, zoning techniques are first introduced and static and measurement membership-functions are used the average dynamic zoning methods already presented in literature are recognition rate is 0.56, 0.65 and 0.83 for LWM, QWM and discussed, with specific consideration to the use of Voronoi EWM, respectively. Finally, when the AWM is used, the tessellation for the design of optimal zoning topologies. Af- average recognition rate is 0.87. More precisely, Table IIIa ter that, traditional membership functions, based on non- shows that the best result occurs for Z*25. In this case adaptive global strategies, are presented and a new class of REC(Z*25, AWM)=0.95 results and the improvement is adaptive zone-based membership functions is introduced. equal to 4% with respect to WTA, 18% with respect to 2- The main idea is to have, for each zone of the zoning NZ, 26% with respect to 3-NZ, 58% with respect to R, 50% method, a membership function well-suited for exploiting with respect to LWM, 35% with respect to QWM and 3% the specific characteristics of feature distribution in that with respect to EWM. Table IIIb shows that, the AWM is zone. Successively, in order to take advantage of the poten- always superior to other Membership Functions, when the tial of both adaptive zone-based membership functions and reliability rate (REL) is considered. More precisely, when dynamic Voronoi-based zoning topologies, a new formula- abstract membership-functions are used, the average reliabil- tion of the problem of zoning design is given and a real- ity rate is 0.84, 0.76 and 0.73 for WTA, 2-NZ and 3-NZ, coded genetic approach is proposed for determining – in a respectively. When ranked membership-function is consid- unique optimization process - the adaptive membership ered (R) the reliability rate is 0.65 on average. When meas- functions and the optimal Voronoi-based topology most urement membership-functions are used the average reliabil- profitable for a given classification problem. ity rate is 0.63, 0.70 and 0.88 for LWM, QWM and EWM, The experimental results, carried out on standard bench- respectively. Finally, when the AWM is used, the average mark databases of handwritten numerals and characters, reliability rate is 0.91. demonstrate that the new class of adaptive membership TABLE IIIa functions along with the optimal Voronoi-based zonings PERFORMANCE ANALYSIS ON Ω2: Recognition Rate (REC) leads to better classification results than traditional ap- proaches. More precisely, when handwritten numerals are considered, the best classification results are achieved for M=9 zones. In this case, the recognition rate and the reliabil- ity rate are equal to 97% and 99%, respectively. When handwritten characters are considered, the best classification results are achieved for M=25 zones. In this case, the recog- nition rate and the reliability rate are equal to 95% and 97%, TABLE IIIb http://ieeexploreprojects.blogspot.com respectively. These results are very satisfying compared to PERFORMANCE ANALYSIS ON Ω2: Reliability Rate (REL) results concerning other approaches in the literature that employ the same datasets [47, 48, 49, 50, 51]. For instance, when handwritten digits are considered, a recognition rate higher than 98% was achieved only when using high- performance features and classification methods [47, 48, 49], whereas a recognition rate higher than 99% was ob- tained with Multi-Classifier Systems [50, 51], without as- suming any rejection. Furthermore, it worth be noting that Furthermore, Table IIIb shows that the best reliability oc- the new technique is not optimized in term of recognition curs for Z*25. In this case REL(Z*25, AWM)=0.97 results rate, but in term of minimal cost function (that is here de- and the improvement is equal to 4% with respect to WTA, fined by eq. (10)). Of course this characteristic, which dif- 14% with respect to 2-NZ, 15% with respect to 3-NZ, 25% ferentiate the new technique with respect to other ap- with respect to R, 31% with respect to LWM, 24% with re- proaches in the literature, leads to different performance spect to QWM and 3% with respect to EWM. levels even though it makes the new technique easily adapt- Also in the case of the classification results of Tables able to different application requirements. For example, in IIIa,b, the ANOVA test (with the significance level equal to some applications (like for instance those based on mobile =0.05) demonstrated that traditional zoning methods and hand-held devices) it may be desirable to carry out the clas- optimized methods based on Voronoi tessellations and adap- sification not considering the risk of a high error rate since tive membership functions provide statistically different the classification results are manually checked afterwards; in classification performances on handwritten characters, in other cases (like for instance those concerning administra- terms of both recognition rates and reliability rate. tive form recognition and bank-check processing systems) the treatment of a substituted pattern has a high cost hence 5 DISCUSSION AND CONCLUSION the error rate must be kept as low as possible. This paper addresses the problem of membership function A further important consideration is that the proposed selection for zoning-based classification in the context of technique for zoning design can be applied to any zoning- handwritten numeral and character recognition. For this pur- based classifier, without limitations in terms of feature typeCopyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.
  9. 9. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. AUTHOR ET AL.: TITLE 9 and classification technique. In fact, depending on the re- and C.Kimpan “Off-Line Hand Written Thai Character Recogni- quirements of the specific application - that are formalized tion Using Ant-Miner Algorithm,” Transactions on ENFOR- through the cost function associated to the classification MATIKA on Systems Sciences and Engineering, vol. 8, pp. 276-281, October 2005. performance – the new technique is able to determine the [14] S.-H.Cha, C.C. Tappert, S.N. Srihari, “Optimizing Binary Feature optimal zoning topology and to select the best adaptive Vector Similarity using Genetic Algorithm and Handwritten membership functions depending on the feature set and clas- Character Recognition”, Proc. ICDAR 2003, pp. 662-665, Edin- sification technique considered. Of course, a main weakness burgh, UK, Aug. 2003. of the proposed approach is that the number of zones must [15] F. Kimura , M. Shridhar, “Handwritten Numerical Recognition be defined a priori. Therefore, an important advancement in Based on Multiple Algorithms”, Pattern Recognition, Vol. 24, n. the technique can be certainly achieved by optimizing also 10, pp. 969-983, 1991. the number of zones of the zoning method. In addition, it [16] C.L. Liu, I.J. Eim, and J.H. Kim, “High Accuracy Handwritten Chinese Character Recognition by Improved Feature Matching should be pointed out that the proposed technique is general Method”. Proc. 4th ICDAR, pp. 1033-1037, 1997. and can be applied to other image processing tasks, since it [17] F. Camastra and A. 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  10. 10. This article has been accepted for publication in a future issue of this journal, but has not been fully edited. Content may change prior to final publication. 10 ID [31] V. Di Lecce, G. Dimauro , A. Guerriero , S. Impedovo , G. Pirlo, Theory and Practice, S.-W. Lee and Y. Nakano (Eds.), Springer, A.Salzo, “Zoning Design for Handwritten Numeral Recognition”, Berlin, 1999, pp. 173–187. Proc. of 7th International Workshop on Frontiers in Handwirting Rec- [51] A.Filatov, V.Nikitin, A.Volgunin, P.Zelinsky, “The Address ognition (IWFHR-7), pp. 583-588, 2000. Script TM recognition system for handwritten envelops”, [32] B. Lazzerini, E.Marcelloni, “A fuzzy approach to 2D-shape recog- Document Analysis Systems: Theory and Practice, S.-W. Lee and Y. nition”, IEEE T-FS, Vol. 9, No. 1, 2001, pp. 5-16. Nakano (Eds.), Springer, Berlin, 1999, pp. 157–171. [33] P.V.W. Radtke, T. Wong and R. Sabourin, “A Multi-objective Memetic Algorithm for Intelligent Feature Extraction”, Lecture Notes in Computer Science, 2005, Volume 3410, pp. 767-781. Giuseppe Pirlo received the Computer [34] P. V. W. Radtke, L.S. Oliveira, R. Sabourin, T. Wong, “Intelligent Science degree cum laude in 1986 at the Zoning Design Using Multi-Objective Evolutionary Algorithms”, Department of Computer Science of the Proc. 7th International Conference on Document Analysis and Recogni- University of Bari, Italy. Since then he has tion (ICDAR2003), p.824-828, 2003. been carrying out research in the field of [35] C. Gagné and M. Parizeau, “Genetic engineering of hierarchical pattern recognition and image analysis. fuzzy regional representations for handwritten character recogni- He received a fellowship from IBM in 1988. tion”, International Journal of Document Analysis, 2006, Vol. 8, n. 4, Since 1991 he has been Assistant Professor pp. 223-231. at the Department of Computer Science of [36] S. Impedovo, M.G. Lucchese, G. Pirlo, “Optimal Zoning Design the University of Bari, where he is currently by Genetic Algorithms”, IEEE Transactions on Systems, Man and Associate Professor. His interests cover the areas of pattern recogni- Cybernetics - Part A: Systems and Humans, Vol. 36, n. 5, pp. 833- tion and biometry, image analysis, intelligent systems, computer 846, Sept. 2006. arithmetic, communication and multimedia technologies. He has [37] S. Impedovo, D. Impedovo, R. Modugno, G. Pirlo, “Analysis of developed several scientific projects and published over one- membership Functions for Voronoi-based Classification”, Proc. hundred fifty papers in the field of handwriting recognition, auto- International Conference on Frontiers in Handwriting Recognition – matic signature verification, document analysis and processing, ICFHR 2010, Kolkata, India, 2010, pp. 220-225. parallel architectures for computing, multimedia technologies for [38] G. Pirlo, D. Impedovo, “Fuzzy Zoning-based Classification for collaborative work and distance learning. Handwritten Characters”, IEEE Transactions on Fuzzy Systems, Prof. Pirlo is reviewer for many international journals including Vol. 19, No. 4, 2011, pp. 780-784. IEEE T-PAMI, IEEE T-SMC, Pattern Recognition, IJDAR, Information [39] S. Impedovo, G. Pirlo, “Tuning between Exponential Functions Processing Letters, etc. . He has been in the scientific committee of and Zones for Membership Functions Selection in Voronoi-based many International Conferences and has served as reviewer of Zoning for Handwritten Character Recognition”, Proc. ICDAR ICPR, ICDAR, ICFHR, IWFHR, ICIAP, VECIMS, CISMA, etc. . He is 2011, Bejing, China, 2011 general co-chair of the International Conference on Frontiers in [40] L.Xu, A. Krzyzak and C.Y.Suen, “Methods of Combining Handwriting Recognition (ICFHR 2012). Multiple Classifiers and Their Applications to Handwriting He is IEEE member and member of the IAPR - Technical Committee http://ieeexploreprojects.blogspot.com Recognition”,IEEE T-SMC,Vol.22,No.3,pp.418-435,May/June 1992. on “Reading Systems” (TC-11). He serves as member of the SIe-L [41] Z. Michalewicz, Genetic Algorithms + Data Structure=Evolution Head Committee and is member of the e-learning Committee of the Programs, Springer Verlag, Berlin, Germany, 1996. University of Bari. [42] D.E.Goldberg, Genetic Algorithms in Search, Optimization and Machine Learning, Addison – Wesley, New York, 1989. [43] J.Hull, “A database for handwritten text recognition research”, Donato Impedovo received the MEng IEEE T-PAMI, Vol. 16, n. 5, pp. 550–554, 1994. degree cum laude in Computer Engi- [44] T.Saito, H.Yamada, K.Yamamoto, “On the data base ETL 9 of neering in 2005 and the PhD degree in hand-printed characters in JIS chinese characters and its analy- Computer Engineering in 2009 both sis”, IEICE Trans. Fund. Electr. Comm. and Comp. Sciences, Vol. from the Polytechnic of Bari (Italy). In J68-D(4), pp.757–764, 1985. 2011 he received the M.Sc. (II Level [45] N.J. Naccache, R. Shinghal, “SPTA: A proposed algorithm for italian Master degree) on Remote Sci- thinning binary patterns”, IEEE T-SMC, Vol. 14, n.3, pp. 409- ence Technologies from the University 418, 1994. of Bari. He is, currently, with the De- [46] L. Heutte , T. Paquet , J.V. Moreau, Y. Lecourtier, C. Olivier, “A partment of Computer Science (Univer- Structural / Statistical Features Based Vector for Handwritten sity of Bari). His research interests are in Character Recognition”, Pattern Recognition Letters, Vol.9, the field of pattern recognition and biometrics. He is co-author of pp.629-641, 1998. more than 20 articles on these fields in both international journals [47] R. G. Webster, M. Nakagawa, “A recognition based on a dy- and conference proceedings. He received ‘The Distinction’ for the namic model“, Pattern Recognition, Vol. 31, No. 2, Feb. 1998, pp. best young student presentation in May 2009 at the International 193-203. Conference on Computer Recognition Systems (CORES – endorsed [48] J.-H. Cai, Z.-Q. Liu, “Integration of structural and statistical by IAPR). He serves as reviewer for the Elsevier Pattern Recognition information for unconstrained handwritten numeral recogni- journal, IET Journal on Signal Processing and IET Journal on Image tion”, IEEE T-PAMI, Vol. 21, No. 3, 1999, pp. 263–270. Processing and for many International Conferences including ICPR [49] I.-S. Oh, J.-S. Lee, C.Y. Suen, “Analysis of class separation and and ICASSP. He is IAPR and IEEE member. combination of class-dependent features for handwriting rec- ognition”, IEEE T-PAMI, Vol. 21, No. 10, 1999, pp.1089–1094. [50] C.Y. Suen, K. Liu, N.W. Strathy, “Sorting and recognizing cheques and financial documents”, Document Analysis Systems:Copyright (c) 2011 IEEE. Personal use is permitted. For any other purposes, permission must be obtained from the IEEE by emailing pubs-permissions@ieee.org.

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