Published in the Proceedings of the Third European Congress on Intelligent Techniques and Soft Computing (EUFIT‘95), Aachen, pp. 1430-1434, 1995.
Handwriting Recognition with Fuzzy Linguistic Rules Ashutosh Malaviya and Liliane Peters German National Research Center for Computer Science (GMD) Schloß Birlinghoven, 53757 St. Augustin, Germany
[email protected]
Abstract With fuzzy linguistic rules complex handwriting patterns can be represented in a broad linguistic domain, thus facilitating a flexible and widely valid recognition scheme. Based on the multi-layered human visual recognition system a multilevel fuzzy rule based classification system is proposed and explained. The constraints which influence the structure of this system applied to handwritten symbols are briefly discussed. 1. Introduction In recent years various handwriting recognition methods have been developed for both on-line and off-line applications[4][1][10][7]. These methods include statistical methods like the hidden Markov model [1], connective learning based methods like neural networks[4] and syntactic methods[2]. The advantages of neural networks are automatic learning and quick classification, once the networks are trained. Their drawbacks are the long time required for learning and moreover their lack of capability to learn new patterns on-line. The performance of the statistical methods such as the hidden Markov model is dependent on the amount of data used in the definition of the statistical model parameters, and is not flexible enough to adapt to new handwriting constraints. Another approach to handwritten character classification is based on the syntactic methods [2][16]. Until now its success has been limited due to the large number of rules needed to cover the different handwriting styles. These difficulties partially originate from the crispness of the definition of the patterns, which in turn hinders the description of complexity and style variations of handwritten characters. Considering the limitations and drawbacks of the existing systems we can define some major features which a handwriting recognition system should possess: fast response, on-line adaptability, and flexibility. To achieve the fast responding and flexible recognition requirements, the designed method has to encompass a small but robust knowledge-base with which the incoming patterns are compared. Changes in style or orientation should be covered by the flexible prototypes which contain a widely valid description of character information. Linguistic description (rules) has this property, e.g. the character ‘b’ has a “very straight” “vertical line” in the “beginning” followed by an “almost” “circular curve” in the “end”. On-line adaptability refers to the ability to incorporate new handwriting features of a writer during the recognition process itself. No matter how good the training phase is, there are always some unexpected features to which the given rules don’t fit. To overcome this problem, there must be an automatic training method which just changes a part of, or extends, the knowledge base. There are several solutions which fit this requirement, like fuzzy-neuro or genetic algorithm approaches[11]. The above mentioned constraints clearly demonstrate the need for a more robust and flexible handwriting recognition system. These constraints and experience with other handwriting recognition systems such as back propagation neural networks have motivated us to develop a multilevel fuzzy rule based pattern recognition system. This paper presents the experience we have gathered during the last two years in working with fuzzy rule based systems for handwriting recognition and consequently it proposes a general implementation scheme. First we demonstrate the significance of employing a fuzzy rule based approach for such problems. Following that we give some criteria for the multilevel fuzzy rule based pattern recognition method. The required fuzzy tools and an illustrative example are described in section 4. We conclude with some general remarks related to the proposed method.
2. Multilevel fuzzy rule based pattern recognition The modeling of the visual recognition system from neurobiological constraints has shown that the visual system employs a multilayered network[13][15]. The number of identified layers is dependent on the chosen model and is represented by a number of processing layers between two and seven[13]. The same is valid for the designed fuzzy rule based pattern matching. It is a multifold recognition procedure with different levels of semantics. Let us assume that the pattern space is partitioned into various fuzzy subspaces. These subspaces represent the domains of the local fuzzy features. The first layer of the knowledge-base is constructed by combining the existing local features in the form of linguistic relations. These relations are the input for the next processing stage and the conclusions are then subsequently given as premises for the next stage of relations. At each level through the combination of certain relations an implication is achieved. It can be a part of the forthcoming semantic stage. Rule
→ If Premise then Conclusion
Premise
→
Premise
→ IS [ ]
Conclusion
( Premise Premise*) | ( of Object IS ), →
AND Conclusion
where are of type AND, OR, NOT (fuzzy operators); can be of type: “low”, “medium”, “high”, “very high”; is a linguistic feature like “Vertical line”, “C-Like curve” or for higher semantic levels a linguistic clause like “a long vertical line at the beginning”; can be of type: “between”, “above”, “below”,” sort of”, “more or less”. The fuzzy attributes and meta attributes are linguistic variables which are modeled by possibility distributions over an appropriate domain of discourse. If we convert this relation into multi-level linguistic rules the generic form of one such rule can be written as: Let us consider the premises A, ..., Y, the conclusion B, ..., Z, and the number of levels to be N. Level 1:if [[Ai1 Aj1]... An1] then B1 and if [[Ai2 Aj2]... An2] then B2 and ...
Context dependent FG L5
if [[Aik Ajk]... Ank] then Bk Level 2:
Context- free fuzzy grammar(FG) (linguistic rule generation) L4 Feature reduction with fuzzy aggregation L3 functions
if [[Bi1 Bj1]... Bn1] then C1 and if [[Bi2 Bj2]... Bn2] then C2 and ... if [[Bik Bjk]... Bnk] then Ck Level N: L2
if [[Yi1 Yj1]... Yn1] then Z1 and if [[Yi2 Yj2]... Yn2] then Z2 and ... if [[Yik Yjk]... Ynk] then Zk.
L1
“Words and Sentences”
“Characters”
Fuzzy feature extraction from partitioned subspaces Fuzzy partition in pattern subspaces Handwriting Data
Fig. 1 Multilevel fuzzy rule based system
where i,j,k are indices with i, j ∈ P , k = [1,M ] ; where P is the maximum number of features, and M is the maximum number of rules at each level. (A, ..., Z) are membership vectors in the universe of infinite discourse [0,1]. The processing of these levels L1 ,..., LN can be accomplished with several fuzzy techniques e.g. aggregation functions, formal methods of fuzzy grammars, or fuzzy automata[5][9]. The choice of the applied technique depends on the semantic level and the possible syntactic relations. At the lower level, aggregation methods are more appropriate and similarly at the higher level due to syntactic complexity, fuzzy grammars should be used.
Formal methods of syntax and semantics are often employed to describe symbols[14]. Methods which describe characters in a linguistic form have been presented by various researchers over the last 30 years. The linguistic techniques in pattern recognition are based on the structure of the underlying relationships between features in a two dimensional pattern. If such a structure is identified then a complex pattern can be described in terms of basic primitives and subpatterns. But the precision of formal languages in pattern recognition conflicts with the imprecision or ambiguity of real life patterns. To overcome this difficulty it is natural to introduce an uncertainty factor or fuzziness into the structure of formal languages. This leads to the development of stochastic and fuzzy languages [2][8][9]. A dedicated fuzzy language FOHDEL [10] supports the description of handwritten symbols. Through its compact form the number of prototypes needed for classification is small and the chosen attributes facilitate a hierarchical classification of the handwritten symbols. We have used FOHDEL syntax as input to the grammatical inference engine of the classification scheme. 3. Rule based handwriting recognition The multilevel strategy proposed in Section 2 is implemented in our algorithm for handwriting recognition. The process stages of handwriting recognition starting from the level of data acquisition (L1) to the peak of the semantic identification process(L5) are shown in Fig. 1. The algorithm integrates the imprecision and the vagueness of the acquired handwritten symbols in various processing stages. The input to the bottom level L1 is the raw handwriting data, which is divided into various subspaces. The division is accomplished in the time domain for on-line handwriting[10] and in topographical spaces[1] for off-line handwriting. To illustrate the proposed algorithm we give an example of on-line handwriting acquired from a pentop. The on-line handwritten information is in the form of a set of coordinates in a time sequence. These coordinates facilitate the evaluation of the pen motion dynamics like sudden changes of motion, jerks, high curvature etc, in a fuzzy linguistic manner. We have termed this as a fuzzy sharpness measure[12]. The partitioning into fuzzy subspaces in our example segments is done with the help of if-then rules from the evaluated dynamics information. In the processing level L2, fuzzy geometrical and topological features for each segment are computed. Following this the features from various domains are combined to generate global features in level L3. The combination of these fuzzy features is accomplished with the help of fuzzy aggregation algorithms[6]. In the subsequent level L4, relations between the extracted global features are represented in terms of fuzzy if-then rules with corresponding attributes and fuzzy operators. In order to describe a class of patterns the corresponding grammar for each symbol is extracted from the training set through a grammatical inference process[10] [3]. To build the pattern grammar, two methodological steps have to be performed: 1) the transformation of the existing information into a semantic description; 2) the generation of production rules which provide a syntactic meaning to the isolated semantic expressions[10]. The rule based handwriting recognition algorithm can be summarized as follows: Algorithm: (Rule based handwriting recognition) Step 1: Divide the data space into smaller pattern domains like segments in on-line handwriting (Level L1). Step 2: Compute the geometrical features as fuzzy linguistic variables for each domain (Level L2). Step 3: Aggregate the features for all domains (from step 2) to form global features (Level L3). Step 4: (a)Learning Phase: Form linguistic rules with global linguistic features from Step 3 and integrate them in a fuzzy rule base. (b)Classification Phase: Classify the unknown information by parsing the rule base created in Step 4(a). “Characters Level”. (Level L4) Step 5: Cross-check the “recognized” character in the given context. In case of error go to Step 4(b) for the next option. In case of failure go to Step 4(a) for on-line adapting. Else list recognized character. (Level L5) Example: Rule generation for character “b” from on-line handwriting data Input Pattern is P= {0, 1},{0, 0},{1, 0},{1, 2},{1, 4},{1, 6},{1, 10},{1, 13},{1, 16},{0, 19},{1, 20},{2, 16},
{3, 15},{4, 13},{10, 11},{13, 13},{13, 15},{12, 18},{8, 21},{6, 22},{3, 23},{2, 23},{0 ,22} in the form of coordinate pairs {x,y}. Step 1: The pattern space P is divided into segments(seg1 and seg2) according to the fuzzy sharpness measure[12]: Seg 1= {0, 1},{0, 0},{1, 0},{1, 2},{1, 4},{1, 6},{1, 10},{1, 13},{1, 16},{0, 19},{1, 20} Seg 2= {2, 16},{3, 15},{4, 13},{10, 11},{13, 13},{13, 15},{12, 18},{8, 21},{6, 22}, {3, 23},{2, 23},{0 ,22} Step 2: For each of these segments the membership to the following geometrical features is computed: “Straight line”:SL, “Curved line”:Arc, ”Horizontal line”:H, ”Vertical line”:V, ”Positive slant”:PS, ”Negative slant”:NS, ”Vertical curve”:VC, ”Horizontal curve”:HC, ”C-Like curve”: C, ”D-Like curve”:D, ”A-Like curve”:A, ”U-Like curve”:U, ”O-Like curve”:O, “Relative X position”:RX, ”Relative Y position”:RY, ”Relative length:L. µSL
µArc
µHL
µVL
µPS
µNS
µVC
µHC
µC
µD
µA
µU
µO
µRX
µRY
µL
Seg 1
.86
.36
0
.94
0
.05
.97
.02
.27
1.0
.27
.38
.81
.06
.46
.37
Seg 2
.07
.96
0
.59
.40
0
.79
.20
.05
.47
.55
.27
.50
.16
.88
.60
Step 3: With the help of a two phase aggregation scheme[12] the membership values of various segments are combined to create global features. For example “vertical line”- VL and “relative X position”- RX and “relative length”L are combined into the global feature ”Vertical line at left of enough length”-VL_L. For the character “b” the aggregated global features are VLL:”Vertical line at left of enough length”;LOR:”An O-like loop at right side”;LAR:”An A-like curve at right side”;LDR:”A D-like curve at right side;PEN:”Number of penups”;SEG:”Number of segments”;E_X:”Ending horizontal position relative to the whole symbol”. Their corresponding membership function values are: µPEN
µE_X
µSEG
µVLL
µLOR
µLAR
µLDR
0
.12
.40
.83
.75
.30
.89
Step 4: (a) The above extracted global features are integrated in a linguistic rule. The corresponding FOHDEL sentence is; Rule b: Z#PEN & (VH#VLL) & ( (H || VH)#LOR | (>H#LDR)) & (L#E_X) & M#SEG & (>VH#VLL) & (M#LOR & (>H#LAR)) & ( is greater than; || is between these values. Step 4: (b) The classification of five characters based on the rules extracted in step 4(a) with a fuzzy inference process
[10] are: • Symbols µ Input ( b )
.86
.75
.55
.18
.03
µ Input ( h )
.07
.35
.75
.83
.92
Step 5: The possibility of the unknown character to be symbol “b” decreases from left to right while the possibility of being “h” increases correspondingly. 4.Conclusion We have shown the applicability of the fuzzy methods to processing handwriting information. With a fuzzy language, linguistic rules, and aggregation operators, a robust handwriting multilevel recognition system is built. Through a simple example we have shown the wide domain of handwriting styles which is covered by just two rules. Moreover such a multilayered recognition model is suitable with additional semantic levels to recognize even more complex patterns like words, sentences, and equations. 5. References [1]C.B. Bose,”Connected and degraded text recognition using hidden Markov model,” Pattern Recognition, Vol.27,No.10,pp.1345-1363, 1994. [2]K.S. Fu, Syntactic Pattern Recognition and applications, NJ, Prentice-Hall, 1982. [3]M.T. Gary et al,”A Fuzzy-Attributed Graph Approach to Handwritten Character Recognition,” FUZZ-IEEE-93, pp. 570-575, 1993. [4]I. Guyon,”Applications of Neural Networks to Character Recognition,” in Character and Handwriting Recognition: Expanding frontiers,Ed: P.S.P. Wang, World Scientific,pp.353-382,1991. [5]J.A. Jorge,”Fuzzy Relational Grammars for Interactive Gesture Recognition,”2nd International Conf. on Fuzzy Set Theory and Technology, Durham, NC, Oct.13-16, 1993. [6]J. M. Keller et al.,”Evidence Aggregation networks for fuzzy logic inference,” IEEE T. on Neural Networks, vol.3, No.5,pp.761-769,Sept. 1992. [7]M.-S. Lan et al,”Character Recognition using Fuzzy Rules Extracted from Data,” FUZZ-IEEE-94, pp.415-420, Orlando, June,1994. [8]E.T. Lee and L.A. Zadeh, "Note on Fuzzy Languages," Information Sciences-1, pp. 421-434, 1969. [9]E.T. Lee,”Fuzzy Tree Automata and Syntactic Pattern Recognition,” IEEE-PAMI-4,No. 4, July 1982. [10]A. Malaviya et al,”FOHDEL - a fuzzy handwriting description language,” FUZZ-IEEE, June 1994. [11]A. Malaviya et al,”Automatic generation of fuzzy rule base for online handwriting recognition,” EUFIT-94, Aachen, 1994. [12]A. Malaviya and L. Peters,”Extracting meaningful handwriting features with fuzzy aggregation method,”3rd Intnl’ Conf. on Document Analysis and Recognition,Montrael Canada,1995.(submitted) [13]M.W. Oram and D.I. Perrett,”Modeling visual recognition from neurobiological constraints,” Neural Networks, vol.7, No.6,7, pp.945-972, 1994. [14]A.C. Shaw, “A Formal Picture Description Scheme as a Basis for Picture Processing Systems,” Information and Control-14, pp. 9-52, 1969. [15]A. Sloman,”On designing a visual system(Towards a Gibbsonian computational model of vision),”J.Exp.Theor.A.I., No.1 pp.289-337,1989. [16]K.C. Yau and K.S. Fu,”A Syntactic Approach to Shape Recognition Using Attributed Grammars,” IEEE-SMC-9, No. 6, pp. 334-345, 1979.
Published in the Proceedings of the Third European Congress on Intelligent Techniques and Soft Computing (EUFIT‘95), Aachen, pp. 1430-1434, 1995.
Handwriting Recognition with Fuzzy Linguistic Rules Ashutosh Malaviya and Liliane Peters German National Research Center for Computer Science (GMD) Schloß Birlinghoven, 53757 St. Augustin, Germany
[email protected]
Abstract With fuzzy linguistic rules complex handwriting patterns can be represented in a broad linguistic domain, thus facilitating a flexible and widely valid recognition scheme. Based on the multi-layered human visual recognition system a multilevel fuzzy rule based classification system is proposed and explained. The constraints which influence the structure of this system applied to handwritten symbols are briefly discussed. 1. Introduction In recent years various handwriting recognition methods have been developed for both on-line and off-line applications[4][1][10][7]. These methods include statistical methods like the hidden Markov model [1], connective learning based methods like neural networks[4] and syntactic methods[2]. The advantages of neural networks are automatic learning and quick classification, once the networks are trained. Their drawbacks are the long time required for learning and moreover their lack of capability to learn new patterns on-line. The performance of the statistical methods such as the hidden Markov model is dependent on the amount of data used in the definition of the statistical model parameters, and is not flexible enough to adapt to new handwriting constraints. Another approach to handwritten character classification is based on the syntactic methods [2][16]. Until now its success has been limited due to the large number of rules needed to cover the different handwriting styles. These difficulties partially originate from the crispness of the definition of the patterns, which in turn hinders the description of complexity and style variations of handwritten characters. Considering the limitations and drawbacks of the existing systems we can define some major features which a handwriting recognition system should possess: fast response, on-line adaptability, and flexibility. To achieve the fast responding and flexible recognition requirements, the designed method has to encompass a small but robust knowledge-base with which the incoming patterns are compared. Changes in style or orientation should be covered by the flexible prototypes which contain a widely valid description of character information. Linguistic description (rules) has this property, e.g. the character ‘b’ has a “very straight” “vertical line” in the “beginning” followed by an “almost” “circular curve” in the “end”. On-line adaptability refers to the ability to incorporate new handwriting features of a writer during the recognition process itself. No matter how good the training phase is, there are always some unexpected features to which the given rules don’t fit. To overcome this problem, there must be an automatic training method which just changes a part of, or extends, the knowledge base. There are several solutions which fit this requirement, like fuzzy-neuro or genetic algorithm approaches[11]. The above mentioned constraints clearly demonstrate the need for a more robust and flexible handwriting recognition system. These constraints and experience with other handwriting recognition systems such as back propagation neural networks have motivated us to develop a multilevel fuzzy rule based pattern recognition system. This paper presents the experience we have gathered during the last two years in working with fuzzy rule based systems for handwriting recognition and consequently it proposes a general implementation scheme. First we demonstrate the significance of employing a fuzzy rule based approach for such problems. Following that we give some criteria for the multilevel fuzzy rule based pattern recognition method. The required fuzzy tools and an illustrative example are described in section 4. We conclude with some general remarks related to the proposed method.
2. Multilevel fuzzy rule based pattern recognition The modeling of the visual recognition system from neurobiological constraints has shown that the visual system employs a multilayered network[13][15]. The number of identified layers is dependent on the chosen model and is represented by a number of processing layers between two and seven[13]. The same is valid for the designed fuzzy rule based pattern matching. It is a multifold recognition procedure with different levels of semantics. Let us assume that the pattern space is partitioned into various fuzzy subspaces. These subspaces represent the domains of the local fuzzy features. The first layer of the knowledge-base is constructed by combining the existing local features in the form of linguistic relations. These relations are the input for the next processing stage and the conclusions are then subsequently given as premises for the next stage of relations. At each level through the combination of certain relations an implication is achieved. It can be a part of the forthcoming semantic stage. Rule
→ If Premise then Conclusion
Premise
→
Premise
→ IS [ ]
Conclusion
( Premise Premise*) | ( of Object IS ), →
AND Conclusion
where are of type AND, OR, NOT (fuzzy operators); can be of type: “low”, “medium”, “high”, “very high”; is a linguistic feature like “Vertical line”, “C-Like curve” or for higher semantic levels a linguistic clause like “a long vertical line at the beginning”; can be of type: “between”, “above”, “below”,” sort of”, “more or less”. The fuzzy attributes and meta attributes are linguistic variables which are modeled by possibility distributions over an appropriate domain of discourse. If we convert this relation into multi-level linguistic rules the generic form of one such rule can be written as: Let us consider the premises A, ..., Y, the conclusion B, ..., Z, and the number of levels to be N. Level 1:if [[Ai1 Aj1]... An1] then B1 and if [[Ai2 Aj2]... An2] then B2 and ...
Context dependent FG L5
if [[Aik Ajk]... Ank] then Bk Level 2:
Context- free fuzzy grammar(FG) (linguistic rule generation) L4 Feature reduction with fuzzy aggregation L3 functions
if [[Bi1 Bj1]... Bn1] then C1 and if [[Bi2 Bj2]... Bn2] then C2 and ... if [[Bik Bjk]... Bnk] then Ck Level N: L2
if [[Yi1 Yj1]... Yn1] then Z1 and if [[Yi2 Yj2]... Yn2] then Z2 and ... if [[Yik Yjk]... Ynk] then Zk.
L1
“Words and Sentences”
“Characters”
Fuzzy feature extraction from partitioned subspaces Fuzzy partition in pattern subspaces Handwriting Data
Fig. 1 Multilevel fuzzy rule based system
where i,j,k are indices with i, j ∈ P , k = [1,M ] ; where P is the maximum number of features, and M is the maximum number of rules at each level. (A, ..., Z) are membership vectors in the universe of infinite discourse [0,1]. The processing of these levels L1 ,..., LN can be accomplished with several fuzzy techniques e.g. aggregation functions, formal methods of fuzzy grammars, or fuzzy automata[5][9]. The choice of the applied technique depends on the semantic level and the possible syntactic relations. At the lower level, aggregation methods are more appropriate and similarly at the higher level due to syntactic complexity, fuzzy grammars should be used.
Formal methods of syntax and semantics are often employed to describe symbols[14]. Methods which describe characters in a linguistic form have been presented by various researchers over the last 30 years. The linguistic techniques in pattern recognition are based on the structure of the underlying relationships between features in a two dimensional pattern. If such a structure is identified then a complex pattern can be described in terms of basic primitives and subpatterns. But the precision of formal languages in pattern recognition conflicts with the imprecision or ambiguity of real life patterns. To overcome this difficulty it is natural to introduce an uncertainty factor or fuzziness into the structure of formal languages. This leads to the development of stochastic and fuzzy languages [2][8][9]. A dedicated fuzzy language FOHDEL [10] supports the description of handwritten symbols. Through its compact form the number of prototypes needed for classification is small and the chosen attributes facilitate a hierarchical classification of the handwritten symbols. We have used FOHDEL syntax as input to the grammatical inference engine of the classification scheme. 3. Rule based handwriting recognition The multilevel strategy proposed in Section 2 is implemented in our algorithm for handwriting recognition. The process stages of handwriting recognition starting from the level of data acquisition (L1) to the peak of the semantic identification process(L5) are shown in Fig. 1. The algorithm integrates the imprecision and the vagueness of the acquired handwritten symbols in various processing stages. The input to the bottom level L1 is the raw handwriting data, which is divided into various subspaces. The division is accomplished in the time domain for on-line handwriting[10] and in topographical spaces[1] for off-line handwriting. To illustrate the proposed algorithm we give an example of on-line handwriting acquired from a pentop. The on-line handwritten information is in the form of a set of coordinates in a time sequence. These coordinates facilitate the evaluation of the pen motion dynamics like sudden changes of motion, jerks, high curvature etc, in a fuzzy linguistic manner. We have termed this as a fuzzy sharpness measure[12]. The partitioning into fuzzy subspaces in our example segments is done with the help of if-then rules from the evaluated dynamics information. In the processing level L2, fuzzy geometrical and topological features for each segment are computed. Following this the features from various domains are combined to generate global features in level L3. The combination of these fuzzy features is accomplished with the help of fuzzy aggregation algorithms[6]. In the subsequent level L4, relations between the extracted global features are represented in terms of fuzzy if-then rules with corresponding attributes and fuzzy operators. In order to describe a class of patterns the corresponding grammar for each symbol is extracted from the training set through a grammatical inference process[10] [3]. To build the pattern grammar, two methodological steps have to be performed: 1) the transformation of the existing information into a semantic description; 2) the generation of production rules which provide a syntactic meaning to the isolated semantic expressions[10]. The rule based handwriting recognition algorithm can be summarized as follows: Algorithm: (Rule based handwriting recognition) Step 1: Divide the data space into smaller pattern domains like segments in on-line handwriting (Level L1). Step 2: Compute the geometrical features as fuzzy linguistic variables for each domain (Level L2). Step 3: Aggregate the features for all domains (from step 2) to form global features (Level L3). Step 4: (a)Learning Phase: Form linguistic rules with global linguistic features from Step 3 and integrate them in a fuzzy rule base. (b)Classification Phase: Classify the unknown information by parsing the rule base created in Step 4(a). “Characters Level”. (Level L4) Step 5: Cross-check the “recognized” character in the given context. In case of error go to Step 4(b) for the next option. In case of failure go to Step 4(a) for on-line adapting. Else list recognized character. (Level L5) Example: Rule generation for character “b” from on-line handwriting data Input Pattern is P= {0, 1},{0, 0},{1, 0},{1, 2},{1, 4},{1, 6},{1, 10},{1, 13},{1, 16},{0, 19},{1, 20},{2, 16},
{3, 15},{4, 13},{10, 11},{13, 13},{13, 15},{12, 18},{8, 21},{6, 22},{3, 23},{2, 23},{0 ,22} in the form of coordinate pairs {x,y}. Step 1: The pattern space P is divided into segments(seg1 and seg2) according to the fuzzy sharpness measure[12]: Seg 1= {0, 1},{0, 0},{1, 0},{1, 2},{1, 4},{1, 6},{1, 10},{1, 13},{1, 16},{0, 19},{1, 20} Seg 2= {2, 16},{3, 15},{4, 13},{10, 11},{13, 13},{13, 15},{12, 18},{8, 21},{6, 22}, {3, 23},{2, 23},{0 ,22} Step 2: For each of these segments the membership to the following geometrical features is computed: “Straight line”:SL, “Curved line”:Arc, ”Horizontal line”:H, ”Vertical line”:V, ”Positive slant”:PS, ”Negative slant”:NS, ”Vertical curve”:VC, ”Horizontal curve”:HC, ”C-Like curve”: C, ”D-Like curve”:D, ”A-Like curve”:A, ”U-Like curve”:U, ”O-Like curve”:O, “Relative X position”:RX, ”Relative Y position”:RY, ”Relative length:L. µSL
µArc
µHL
µVL
µPS
µNS
µVC
µHC
µC
µD
µA
µU
µO
µRX
µRY
µL
Seg 1
.86
.36
0
.94
0
.05
.97
.02
.27
1.0
.27
.38
.81
.06
.46
.37
Seg 2
.07
.96
0
.59
.40
0
.79
.20
.05
.47
.55
.27
.50
.16
.88
.60
Step 3: With the help of a two phase aggregation scheme[12] the membership values of various segments are combined to create global features. For example “vertical line”- VL and “relative X position”- RX and “relative length”L are combined into the global feature ”Vertical line at left of enough length”-VL_L. For the character “b” the aggregated global features are VLL:”Vertical line at left of enough length”;LOR:”An O-like loop at right side”;LAR:”An A-like curve at right side”;LDR:”A D-like curve at right side;PEN:”Number of penups”;SEG:”Number of segments”;E_X:”Ending horizontal position relative to the whole symbol”. Their corresponding membership function values are: µPEN
µE_X
µSEG
µVLL
µLOR
µLAR
µLDR
0
.12
.40
.83
.75
.30
.89
Step 4: (a) The above extracted global features are integrated in a linguistic rule. The corresponding FOHDEL sentence is; Rule b: Z#PEN & (VH#VLL) & ( (H || VH)#LOR | (>H#LDR)) & (L#E_X) & M#SEG & (>VH#VLL) & (M#LOR & (>H#LAR)) & ( is greater than; || is between these values. Step 4: (b) The classification of five characters based on the rules extracted in step 4(a) with a fuzzy inference process
[10] are: • Symbols µ Input ( b )
.86
.75
.55
.18
.03
µ Input ( h )
.07
.35
.75
.83
.92
Step 5: The possibility of the unknown character to be symbol “b” decreases from left to right while the possibility of being “h” increases correspondingly. 4.Conclusion We have shown the applicability of the fuzzy methods to processing handwriting information. With a fuzzy language, linguistic rules, and aggregation operators, a robust handwriting multilevel recognition system is built. Through a simple example we have shown the wide domain of handwriting styles which is covered by just two rules. Moreover such a multilayered recognition model is suitable with additional semantic levels to recognize even more complex patterns like words, sentences, and equations. 5. References [1]C.B. Bose,”Connected and degraded text recognition using hidden Markov model,” Pattern Recognition, Vol.27,No.10,pp.1345-1363, 1994. [2]K.S. Fu, Syntactic Pattern Recognition and applications, NJ, Prentice-Hall, 1982. [3]M.T. Gary et al,”A Fuzzy-Attributed Graph Approach to Handwritten Character Recognition,” FUZZ-IEEE-93, pp. 570-575, 1993. [4]I. Guyon,”Applications of Neural Networks to Character Recognition,” in Character and Handwriting Recognition: Expanding frontiers,Ed: P.S.P. Wang, World Scientific,pp.353-382,1991. [5]J.A. Jorge,”Fuzzy Relational Grammars for Interactive Gesture Recognition,”2nd International Conf. on Fuzzy Set Theory and Technology, Durham, NC, Oct.13-16, 1993. [6]J. M. Keller et al.,”Evidence Aggregation networks for fuzzy logic inference,” IEEE T. on Neural Networks, vol.3, No.5,pp.761-769,Sept. 1992. [7]M.-S. Lan et al,”Character Recognition using Fuzzy Rules Extracted from Data,” FUZZ-IEEE-94, pp.415-420, Orlando, June,1994. [8]E.T. Lee and L.A. Zadeh, "Note on Fuzzy Languages," Information Sciences-1, pp. 421-434, 1969. [9]E.T. Lee,”Fuzzy Tree Automata and Syntactic Pattern Recognition,” IEEE-PAMI-4,No. 4, July 1982. [10]A. Malaviya et al,”FOHDEL - a fuzzy handwriting description language,” FUZZ-IEEE, June 1994. [11]A. Malaviya et al,”Automatic generation of fuzzy rule base for online handwriting recognition,” EUFIT-94, Aachen, 1994. [12]A. Malaviya and L. Peters,”Extracting meaningful handwriting features with fuzzy aggregation method,”3rd Intnl’ Conf. on Document Analysis and Recognition,Montrael Canada,1995.(submitted) [13]M.W. Oram and D.I. Perrett,”Modeling visual recognition from neurobiological constraints,” Neural Networks, vol.7, No.6,7, pp.945-972, 1994. [14]A.C. Shaw, “A Formal Picture Description Scheme as a Basis for Picture Processing Systems,” Information and Control-14, pp. 9-52, 1969. [15]A. Sloman,”On designing a visual system(Towards a Gibbsonian computational model of vision),”J.Exp.Theor.A.I., No.1 pp.289-337,1989. [16]K.C. Yau and K.S. Fu,”A Syntactic Approach to Shape Recognition Using Attributed Grammars,” IEEE-SMC-9, No. 6, pp. 334-345, 1979.
