FUZZY-SYNTACTIC APPROACH TO PATTERN RECOGNITION

AND SCENE ANALYSIS

Marzena Bielecka

Department of Geoinformatics and Applied Computer Science

Faculty of Geology, Geophysics and Environmental Protection

AGH University of Science and Technology, Kraków, Poland

Marek Skomorowski, Andrzej Bielecki

Institute of Computer Science, Jagiellonian University, Kraków, Poland

Keywords: Syntactic pattern recognition, graph grammars, fu

zzy graphs, parallel parsing, robot vision system.

Abstract: In syntactic pattern recognition an object is described by symbolic data. The problem of recognition is to

determine whether the describing mathematical structure, for instance a graph, belongs to the language

generated by a grammar describing the mentioned mathematical structures. So called ETPL(k) graph

grammars are a known class of grammars used in pattern recognition. The approach in which ETPL(k)

grammars are used was generalized by using probabilistic mechanisms in order to apply the method to

recognize distorted patterns. In this paper the next step of the method generalization is proposed. The

ETPL(k) grammars are improved by fuzzy sets theory. It turns out that the mentioned probabilistic approach

can be regarded as a special case of the proposed one. Applications to robotics are considered as well.

1 INTRODUCTION

The fundamental idea in syntactic pattern

recognition is using of symbolic data like strings,

trees and graphs for representation of a class of

recognized objects (Chen et al., 1991; Fu, 1982;

Jakubowski, 1997; Jakubowski and Stąpor, 1999).

The general scheme of syntactic pattern recognition

and a scene analysis is following (Fu, 1982). After

pre-processing the recognized object is segmented in

order to recognize the primitives the pattern consists

of and relations between them. Decision whether the

analysed pattern representation belongs to the class

of objects describing by a given grammar is made

basing on the parsing algorithm. This classical

approach can be applied in robotics, for instance in

vision systems and in manufacturing for description

and analysis of the production process (Chen et al.,

1991; Yeh et al. 1993). It seems also be effective for

applying in multi-agent systems, particularly in

embodied cognitive ones because such agents should

be equipped with symbolic and explicit

representation of the surrounding world in order to

analyse the scene they act on (Ferber, 1999; Scheier

and Pfeifer, 1999). For instance in (Kok et al., 2005)

so called coordination graphs are used for solving a

behaviour management problem in a multi-robot

system. In this graph a node represents an agent and

an edge indices that a corresponding agents have to

coordinate their actions.

The use of graph grammars for syntactic pattern

recognition is

relatively rare because of difficulties

in building a syntax analyser of such grammars.

Therefore every result in building efficient parser for

graph grammars is valuable. An example of such

result is a parser for, so called, ETPL(k) (embedding

transformation-preserving production-ordered k-left

nodes unambiguous) grammars introduced in

(Flasiński, 1993 and 1998). An efficient parsing

algorithm for ETPL(k) graph grammars, which the

computational complexity is O(n

), has been

constructed in (Flasiński, 1993). The so-called IE

(indexed edge-unambiguous) graphs have been

defined in (Flasiński, 1993) for a description of

pattern (scenes) in syntactic pattern recognition.

Nodes in an IE graph denote pattern primitives.

Edges between two nodes in an IE graph represent

Bielecka M., Skomorowski M. and Bielecki A. (2007).

FUZZY-SYNTACTIC APPROACH TO PATTERN RECOGNITION AND SCENE ANALYSIS.

In Proceedings of the Fourth International Conference on Informatics in Control, Automation and Robotics, pages 29-35

DOI: 10.5220/0001625300290035

 SciTePress

spatial relations between pattern primitives.

However, in practice, structural descriptions may

contain pattern distortions. An idea of a probabilistic

improvement of syntactic recognition of distorted

patterns represented by graphs is described in

(Flasiński and Skomorowski, 1998, Skomorowski

1998) and (Skomorowski, 1999). To take into

account all variations of a distorted pattern under

study, a probabilistic description of the pattern was

introduced. A random IE graph approach (Flasiński

and Skomorowski, 1998, Skomorowski, 1999,

Skomorowski, 2000) is proposed for such a

description and an efficient parsing algorithm for IE

graphs is presented. Its computational complexity is

O(n

) as well.

The purpose of this paper is to present an idea of

approach to syntactic recognition of fuzzy patterns

represented by fuzzy IE graphs, followed the

example of random IE graphs used for distorted

pattern description. It turns out that, in a way, the

fuzzy approach is a generalization of the

probabilistic one. Fuzziness allows us not only

described distortions in analysed patterns but also

give us possibility to describe in proper way patterns

that can not be presented univocally. Furthermore

there are a wide class of problems in which objects

and/or spatial relations are described by fuzzy sets.

2 MOTIVATIONS

In this section a few example, in which the fuzzy-

syntactic approach seems to be natural, are

presented.

2.1 First Example

Assume that during a manufacturing process a

robotic inspection system checks type of a hole in a

making elements, for instance plates, and spatial

relations between holes. Assume also that there are a

few standard types of holes and circular and

quadratic ones are among them – Fig.1a. Let,

furthermore, the inspection system be based on a

syntactic pattern recognition approach in which the

holes are represented by nodes of graphs and spatial

relations between holes by graph edges – see Fig.1b.

A quadratic hole with rounded vertices can be

regarded as a fuzzy object with partial membership

to classes of both circular and quadratic holes – see

Fig.1. In this example nodes description as fuzzy

sets is a natural approach. In this case membership

functions describing fuzzy sets can be define basing

on axiomatic method (Bielecka, 2006).

a) b)

Figure 1: Holes in plate and their graph representation.

2.2 Second Example

Considering the previous example assume that

robotic inspection of technological process is based

on statistical distribution of inaccuracy frequencies

(Flasiński and Skomorowski, 1998, Noori and

Radford, 1995). If a hole is made in a sufficient

accuracy it is accept by the system. Not only the

hole shape but also its location should be taken into

consider. Since inaccuracies of holes location

influence each other, the simple statistical analysis

can be insufficient to make a decision. In such a case

a fuzzy inference can be applied. Then, holes and

their locations can be represented by fuzzy sets and

membership functions can be calculated using the

statistical distribution according to the methodology

described in (Bielecka, 2006). Let, like in the first

example, the inspection system is based on a

syntactic pattern recognition in which the holes are

represented by nodes of graphs and spatial relations

between holes by graph edges. In this example both

the graph nodes and its edges would be described as

fuzzy sets. Automatic focusing vision system for

inspection of size and shape and positions of small

holes in the context of precision engineering,

described in (Han and Han, 1999), is an example of

a system performing such type of task.

2.3 Third Example

Consider an autonomous mobile agent. Assume that

it has to navigated in an unchanging environment. A

helicopter flying autonomously in a textured urban

environment is an example of such agent (Muratet et

al., 2005). As it has been already mentioned it

should be equipped with symbolic representation of

the surrounding world in order to analyse the scene

they act on (Ferber, 1999; Scheier and Pfeifer,

1999). Let its vision system be a syntactic one based

on graph representation of the spatial relationships

between obstacles the agent should navigate among.

Let according to, for instance, the optimization

requirements, the system prefers one direction but

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

admits also another ones allowing to navigate

without collision. In such a case the scene would be

represented by a classical (i.e. not fuzzy) IE graph

but directions the agent can choice would be

represented by fuzzy sets – see Fig.2. The decision

making system would be based on fuzzy inference.

Figure 2: Detection of possible directions of motion.

2.4 Fourth Example

Let us consider computer-aided analysis and

recognition of pathological wrist bone lesions

(Tadeusiewicz and Ogiela, 2005; Ogiela et al.,

2006). This method consists on analysis of the

structure of the said bones based on palm

radiological images. During pre-processing

operations in the examined X-ray images the bones

contours were separated and a graph representing

bones and spatial relation between them was

spanned. In the beginning, spatial relationships

given by the graph edges were represented by single

directions (Tadeusiewicz and Ogiela, 2005) but later

each basic spatial relationship was represented as

angular interval (Ogiela et al., 2006). The second

approach can be interpreted in such a way that every

basic spatial relationship is described as a fuzzy set

for which its membership function has positive

values on the specified angular interval and is equal

to zero outside this interval. It should be mentioned

that in (Ogiela et al., 2006) such interpretation was

not considered.

Recapitulating, four examples in which various

aspects of possibility of improve syntactic

approach by fuzzy sets has been discussed. The

classical IE graphs can be generalized by including

fuzzy sets to description their nodes (example 1),

edges (example 4), both the nodes and edges

(example 2) and fuzzy inference approach can be

applied to classical graphs (i.e. non-fuzzy ones) –

example 3.

3 FUZZY IE GRAPHS

Recall a definition of IE graph (Flasiński, 1993).

Definition 3.1

An IE graph is a quintuple H=(V, E, Σ, Γ, ϕ) where:

V is a finite, non-empty set of nodes of a graph with

assigned indexes in univocally way,

Σ is a finite, non-empty set of node labels,

Γ is a finite, non-empty set of edge labels,

E is a set of graph edges represented by triplet

(v, λ, w) where v, w∈V, λ∈Γ and an index of v

is smaller than an index of w,

ϕ:V→Σ is a nodes labeling function.

Let us assume that, due to pattern fuzziness, possible

IE graphs associated with a given example pattern

(scene) may look like IE graphs shown in Fig.3.

(a) (b)

Figure 3: Possible IE graphs describing a given scene.

In the case of the IE graph shown in Fig.3a fuzziness

concerns pattern primitives represented by the node

2 labeled by tree and the node 3 labeled by bus. In

the case of the IE graph shown in Fig.3b fuzziness

concerns a pattern primitive represented by the node

4 labeled by bus and a spatial relation between

pattern primitives represented by the edge

connecting the node 3 with the node 4. Assume that

both labeled objects in nodes of a graph and spatial

relations are represented by fuzzy sets of a first order

(Zadeh L.A., 1965) with membership functions μ

and ν

respectively. Let, furthermore, the set of all

objects Σ be m-elemental and the set of all spatial

relations be k-elemental. Let us define, informally, a

fuzzy IE graph as an IE graph in which nodes labels

are replaced by a vector μ = [µ

,...,µ

] of values of

membership functions μ

, i∈{1,...,m} and edges

labels are replaced by vector ν = [ν

,...,ν

] of values

of membership functions ν

, j∈{1,...,k}.

Let propose a formal definition of a fuzzy IE

graph

FUZZY-SYNTACTIC APPROACH TO PATTERN RECOGNITION AND SCENE ANALYSIS

Definition 3.2

A fuzzy IE graph is a quintuple H=(V, E, Σ, Γ, Φ)

where:

V is a finite, non-empty set of nodes of a graph with

assigned indices in univocal way,

Σ is a finite, non-empty set of node labels,

containing, say, n elements,

Γ is a finite, non-empty set of edge labels,

containing, say, k elements,

E = V× ×V is a set of fuzzy graph edges

represented by triplet (v

, Θ

, w) where v, w∈V

and i(v) < i(w) i.e. an index of v is smaller than an

index of w, is represented by

where

],...,[

ΘΘ=Θ

}],(),...,,[(

νλνλ

is a value of a

membership function of succeeding edge labels

for a s-th edge,

Φ: V → Π

×…×Π

where for every nodes

where ,

),...,()(

ΠΠ=Φ

),(

μσ

=Π

Σ∈

, is a value of a membership function

of succeeding nodes labels for an i-th node.

The fuzzy measure of an outcome IE graph,

obtained form a given fuzzy IE graph, is equal to the

value of T-norm of the values components of the

node and edge vectors. Recall axiomatic definition

of T-norms which is given in, for instance,

(Rutkowski, 2005) - definition 4.22, page 80.

Definition 3.3

T-norm is a function T:[0,1]×[0,1]→[0,1] satisfying

the following axioms:

(i) T(a,b) = T(b,a),

(ii) T( T(a,b),c ) = T( a,T(b,c) ),

(iii) if a ≤ b and c ≤ d then T(a,b) ≤ T(c,d),

(iv) T(a,0) = 0 and T(a,1) = a.

Theorem

The functions T

and T

given by the formulae

(a,b) = min{a,b} and T

(a,b) = a⋅b

(1)

are T-norms. The function T

given by the formulae

(a,1) = a, T

(a,b) = 0 for a≠1 and b≠1

(2)

is a T-norm as well. Furthermore, for every

a,b∈[0,1] if a function T is a T-norm then

(a,b) ≤ T(a,b) ≤ T

(a,b)

(3)

Thanks to the property (ii) in Definition 3.3 T-norm

being a function of n variables can be introduced:

)),(()(),...,(

1 ni

aaTTaTaaT

−

(4)

Having a fuzzy IE graph R the fuzzy measure of an

outcome graph r is calculated as

))(),(()(

)(

νμλ

TTTr

= (5)

where α is a number of a regarded node, β is a

number of an edge, f(α) - is a chosen component

number of a vector μ

whereas g(β) is a number of

component of a vector ν

. If a product is used as a T-

norm then the presented parsing (see section 4) is

identical as the random parsing described in

(Skomorowski, 1998). In calculations presented in

the next section the minimum T

-norm is used.

4 PARALLEL PARSING

Given an unknown pattern represented by a fuzzy IE

graph R, the problem of recognition of a pattern

under study is to determine if an outcome IE graph r,

obtained from the fuzzy IE graph R, belongs to a

graph language L(G) generated by an ETPL(k) graph

grammar G. In the proposed parallel and cut-off

strategy of fuzzy IE graph parsing for an efficient,

that is with the computational complexity O(n

analysis of fuzzy patterns (scenes) a number of

simultaneously derived graphs is equal to a certain

number limit. In this case, derived graphs spread

through the search tree, but only the best, that is with

maximum measure value, limit graphs are expanded.

Let us consider a graph shown in Fig.4a and a

production shown in Fig.4b. Suppose that the

embedding transformation for the production shown

in Fig.4b is C(r, input) = {(d, b, r, input)} and C(u,

output) = {(e, B, r, input)}. During a derivation, a

non-terminal A in the node 2 of a graph shown in

Fig.4a is removed and the graph of the production

shown in Fig.4b is put in the place of the removed

non-terminal A. The first item of the embedding

transformation for the production: C(r,input) = {(d,

b, r, input)} means that the edge r of the graph

shown in Fig.4a should connect the node d of the

production graph with the node b of the graph shown

in Fig.4a. The second item of the embedding

transformation for the production: C(u, output) =

{(e, B, r, input)} means that the edge u of the graph

shown in Fig. 4a should be replaced by the edge r

connecting the node e of the production graph with

the node B of the graph shown in Fig.4a. Thus, after

the application of the production shown in Fig.4b to

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

the node indexed by 2 of the graph shown in Fig.4a

we obtain a graph shown in Fig.4c.

Figure 4: An example derivation step in an ETPL(k) graph

grammar.

Suppose that we analyze an unknown fuzzy pattern

represented by a fuzzy IE graph shown in Fig.5. (for

clarity, only non-zero membership functions vectors

components are specified).

Figure 5: An example fuzzy IE graph representing an

unknown distorted pattern.

Let us assume that a number of simultaneously

derived graphs is equal to 2 (that is limit = 2).

Furthermore let us assume that we are given an

ETPL(k) graph grammar G with a starting graph Z

shown in Fig.6 and a set of productions shown in

Fig.7.

Figure 6: A starting graph Z of an example ETPL(k) graph

grammar G.

(1)

C(r, input) = {(b, a, r, input)}

C(t, output) = {(b, A, t, output), (c, A, r, input)}

(2)

C(r, input) = {(b, a, r, input)}

C(t, output) = {(b, A, t, output), (a, A, r, input)}

(3)

C(r, input) = {(d, a, r, input)}

C(t, output) = {(d, A, t, output), (E, A, r, input)}

(4)

C(s, input) = {(d, a, s, input)}

(5)

C(s, input) = {(d, a, s, input)}, C(t, input) = {(d, b, t, input)}

C(r, output) = {(d, c ,r, output)}, C(v, output) = {(d, D ,v, output)}

(6)

C(s, input) = {(d, a, s, input)}, C(t, input) = {(d, b, t, input)}

C(r, output) = {(d, c ,r, output), (d, a, r, output)}

C(v, output) ={(d, D ,v, output)}

(7)

C(s, input) = {(b, a, s, input)}, C(t, input) = {(b, b, t, input)}

C(r, output) = {(b, c, r, output),(b, a, r, output)}

C(v, output) = {(b, D , v, output)}

(8)

C(s, input) = {(g, b, s, input)}

C(v, output) = {(g, f, v, output)}

(9)

C(s, input) = {(a, b, s, input)}, C(v, output) = {(a, f, v, output)}

(10)

C(t, input) = {(g, a, t, input)}

C(v, input) = {(h, d ,u, input), (h, b, u, input)}

(11)

C(t, input) = {(a, a, t, input)}

C(v, input) = {(b, d, u, input), (b, b, u, input)}

Figure 7: A set of productions of an ETPL(k) graph.

grammar G.

In the first step of the derivation, after the

application of the production (1), shown in Fig.7, to

the node indexed by 2 of the starting graph Z, shown

in Fig.6, we obtain a graph q

shown in Fig.8a.

Similarly, after the application of the production (2)

FUZZY-SYNTACTIC APPROACH TO PATTERN RECOGNITION AND SCENE ANALYSIS

to the node indexed by 2 of the starting graph Z we

obtain a graph q

shown in Fig.8b. The graphs q

(a) (b)

Figure 8: Derived graphs q

and q

(Fig.8) are admissible for further derivation,

that is they can be outcome graphs obtained from the

fuzzy IE graph shown in Fig.5. The application of the

production (3) to the node indexed by 2 of the

starting graph Z does not lead to a graph which can

be an outcome graph obtained from the fuzzy IE

graph shown in Fig.5. Thus, a graph obtained after

the application of the production (3) to the node

indexed by 2 of the starting graph Z is not

admissible for further derivation. As in the analyzed

example a number of simultaneously derived graphs

is equal to 2 we expand the graphs q

and q

in the

second step of derivation.

In the second step of derivation, after the application

of the productions (6) and (7) (Fig.7) to the node

indexed by 3 of the graph q

(Fig.8a) we obtain

graphs q

1,6

and q

1,7

shown in Fig.9. Similarly, after

the application of the productions (6) and (7) to the

node indexed by 3 of the graph q

(Fig.8b) we obtain

graphs q

2,6

and q

2,7

shown in Fig.10. The

application of the production (5) to the node indexed

by 3 of the graphs q

and q

(Fig.8) leads to graphs

which can not be outcome graphs obtained from the

fuzzy IE graph shown in Fig.5, as they miss the node

indexed by 7 and labeled by f of the fuzzy IE graph

shown in Fig.5. Thus, graphs obtained after the

application of the production (5) to the nodes

indexed by 3 of the graphs q

and q

(Fig.8) are not

admissible for further derivation. The graphs q

1,6

1,7

(Fig.9) and q

2,6

, q

2,7

(Fig.10) are admissible for

further derivation, that is they can be outcome

graphs obtained from the fuzzy IE graph shown in

Fig.5.

Because in the analyzed example a number of

simultaneously derived graphs is equal to 2 we

should choose only two graphs from among the

graphs q

1,6

, q

1,7

(Fig.9) and q

2,6

, q

2,7

(Fig.8) for

further derivation. In order to do it, compute the

following values:

1,6

) = 0.7 and

1,7

) = 0.3.

The contributions of nodes indexed by 6 of the

graphs q

1,6

and q

1,7

are not taken into account in this

case as the node indexed by 6 and labeled by F in

the graph q

1,7

is not a terminal one. Consequently,

the contribution of the edge connecting nodes

indexed by 3 and 6 as well as the contribution of the

edge connecting nodes indexed by 6 and 7 in the

graphs q

1,6

and q

1,7

are not taken into account.

Similarly, we compute the following values:

2,6

)

= 0.2 and

2,7

) = 0.2. As λ(q

1,6

) > λ(q

1,7

) >

2,6

)

2,7

) we choose the graphs q

1,6

and q

1,7

for

further derivation, that is we choose two graphs with

maximum value (limit = 2). Similarly, in two next

steps of derivation the final outcome IE graph is

obtained – see Fig.11. The derived graph q

1,7,10,8

also an outcome IE graph obtained from the parsed

fuzzy IE graph shown in Fig.5.

Figure 9: Derived graphs q

1,6

and q

1,7

Figure 10: Derived graphs q

2,6

and q

2,7

Figure 11: A derived graph q

1,7,10,8

ICINCO 2007 - International Conference on Informatics in Control, Automation and Robotics

5 CONCLUSIONS

In this paper we have proposed an idea of a new

approach to recognition of fuzzy patterns

represented by graphs. The problem has been

considered in the context of pattern recognition and

scene analysis with references to robotics (Han and

Han, 1999; Kok et al., 2005; Muratet et al., 2004;

Petterson, 2005) and applications in medicine

(Tadeusiewicz and Ogiela, 2005, Ogiela et al.,

2006). To take into account variations of a fuzzy

pattern under study, a description of the analysed

pattern based on fuzzy sets of the first order was

introduced. The fuzzy IE graph has been proposed

here for such a description. The idea of an efficient,

that is with the computational complexity O(n

parsing algorithm presented in (Flasiński, 1993) is

extended, so that fuzzy patterns, represented by fuzzy

IE graphs, can be recognized. In the algorithm a T-

norm is used for calculation of value of membership

measure of output graphs. Such solution makes that

the algorithm is very flexible. In particular if

arithmetic product is used as a T-norm, the

algorithm is the same as the random one described in

(Skomorowski, 1998).

REFERENCES

Bielecka M, 2006. A method of membership function

construction in fuzzy systems. In: Cader A.,

Rutkowski L., Tadeusiewicz R., Żurada J. (eds):

Challenging Problems of Science – Computer Science,

Academic Publishing House EXIT, Warszawa, 111-

117.

Chen S.L., Chen Z., Li R.K., 1991. A DGR method for

extracting the topology of an upper-half profile of a

turned part from CAD data, Computer Integrated

Manufacturing, 4, 45-56.

Ferber J., 1999. Multi-Agent Systems. An Introducing to

Distributed Artificial Intelligence. Addison-Wesley,

Harlow.

Flasiński M., 1993. On the parsing of deterministic graph

languages for syntactic pattern recognition. Pattern

Recognition 26, 1-16.

Flasiński M., 1998. Properties of NLC graph grammars

with a polynomial membership problem. Theoretical

Computer Science 201, 189-231.

Flasiński M., Skomorowski M, 1998. Parsing of random

graph languages for automated inspection in

statistical-based quality assurance system. Machine

Graphics and Vision 7, 565-623.

Fu, K.S., 1982. Syntactic pattern recognition and

applications, Prentice-Hall, New York.

Han M., Han H., 1999. Automatic focusing vision system

for inspection of size and shape of small hole, Journal

of the Korean Society of Precision Engineering, 16,

no.10, 80-86.

Jakubowski R., 1997. Structural approach to modeling and

analysis of 2D-shapes, Bulletin of the Polish Academy

of Sciences – Technical Sciences, 45, 373-387.

Jakubowski J., Stąpor K., 1999. Structural method in

perceptual organization of 2D-curve detection,

representation and analysis, Bulletin of the Polish

Academy of Sciences – Technical Sciences, 47, 309-

324.

Kok J.R., Spaan M.T.J., Vlassis N., 2005. Non-

communicative multi-robot coordination in dynamic

environments, Robotic and Autonomous Systems, 50,

99-114.

Muratet L., Doncieux S., Briere Y., Meyer J.A., 2005. A

contribution to vision-based autonomous helicopter

flight in urban environments, Robotics and

Autonomous Systems, 50, 195-229.

Noori, H., Radford R., 1995. Production and Operation

Management. Tostal Quality and Responsiveness,

McGraw-Hill.

Ogiela M.R., Tadeusiewicz R., Ogiela L., 2006. Image

languages in intelligent radiological palm diagnostics,

Pattern Recognition, 39, 2157-2165.

Petterson Ola, 2005. Execution monitoring in robotics: A

survey, Robotics and Autonomous Systems, 53, 73-88.

Rutkowski L., 2005. Artificial Intelligence Techniques and

Methods, PWN, Warszawa (in Polish).

Scheier C., Pfeifer R., 1999. The embodied cognitive

science approach. In: Tschacher W., Dauwalde J.P.

(eds): Dynamics, Synergetics, Autonomous Agents,

Studies of Nonlinear Phenomena and Life Science

Vol.8., World Scientific, Singapore, New Jersey,

London, Hong Kong, 159-179.

Skomorowski M., 1998. Parsing of random graphs for

scene analysis, Machine Graphics and Vision 7, 313-

323.

Skomorowski M., 1999. Use of random graph parsing for

scene labeling by probabilistic relaxation, Pattern

Recognition Letters 20, 949-956.

Skomorowski M., 2006. Syntactic recognition of syntactic

patterns by means of random graph parsing, Pattern

Recognition Letters 28, 572-581.

Tadeusiewicz R., Ogiela M.R., 2005. Picture languages in

automatic radiological palm interpretation,

International Journal of Applied Mathematics and

Computer Science, 15, 305-312.

Yeh S., Kamran M., Nnaji B., 1993. CAD-based

automatic object recognition, Journal of Design and

Manufacturing, 3, 57-73.

Zadeh L.A., 1965. Fuzzy sets, Information and Control, 8,

338-353.

FUZZY-SYNTACTIC APPROACH TO PATTERN RECOGNITION AND SCENE ANALYSIS