APPROACHES TO IMAGE PROCESSING USING THE TOOLS OF FUZZY SETS. Technologies at the Tashkent University of Information Technologies

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1 Internatonal Journal of Computer Scence Engneerng and Informaton Technology Research (IJCSEITR) ISSN (P): ; ISSN (E): Vol. 8, Issue, Feb 208, -2 TJPRC Pvt. Ltd. APPROACHES TO IMAGE PROCESSING USING THE TOOLS OF FUZZY SETS R. KH. KHAMDAMOV & E. A. SALIYEV 2 Doctor of Techncal Scences, prof. Drector of the Scentfc and Innovaton Center of Informaton and Communcaton Technologes at the Tashent Unversty of Informaton Technologes 2 Research., Assocate Professor. The compettor of the Scentfc and Innovaton Center of Informaton and Communcaton Technologes at the Tashent Unversty of Informaton Technologes. ABSTRACT In ths paper, an approach to processng mages by applyng the concept of fuzzy sets s consdered for the purpose of mprovng the qualty of mages of mage segmentaton and contour extracton n mages. Studed method of mage segmentaton that use the algorthms of fuzzy clusterng KEYWORDS: Fuzzy Sets, Image Segmentaton & Fuzzy Clusterng Receved: Jul 20, 207; Accepted: Aug 09, 207; Publshed: Dec 29, 207; Paper Id.: IJCSEITRFEB208. INTRODUCTION In recent years n developed countres of the world conduct studes on the use of fuzzy technques n mage processng, whch s assocated wth the followng: ) these methods are powerful tools for the representaton and processng of nowledge; 2) they can manage the uncertanty and ambguty effcently. In many applcatons of mage processng requred to use expert nowledge to overcome some of the dffcultes (e.g. Object recognton, scene analyss). In fuzzy set theory and fuzzy logc are powerful tools to represent and process human nowledge n the form of fuzzy IF-THEN rules. On the other hand, many dffcultes n mage processng arse because of the randomness, ambguty and uncertanty n the data used n ths tas. To wor wth accdents n the processng of the mages can be used n probablty theory for other nds of mperfectons, for example, geometrc blurrng can be present on the bass of fuzzy sets and fuzzy logc. On the bass of the goals and objectves of the research defned the archtecture of mage processng system based on the concept of fuzzy sets. A functonal scheme of ths system s shown n Fgure. Orgnal Artcle Fgure : Functonal Scheme of the Developed System In ths artcle the ssue of magng wth the applcaton of the concept of fuzzy sets s consdered n relaton edtor@tjprc.org

2 2 R. KH. Khamdamov & E. A. Salyev to the followng objectves: mprovng the qualty of mages, mage segmentaton and contour extracton on mages. Despte the progress made n the feld of dgtal mage processng usng fuzzy sets, there are a number of outstandng tass. Among them nclude the problem of adequate dsplay subject regon n a fuzzy system, selecton of models, fuzzy logc and ther ntegraton nto a sngle ntellgent system. Thus, ssues of dgtal mage processng usng the tools of fuzzy sets are nvestgated nsuffcently. Therefore, the development and mprovement of methods of dgtal mage processng based on fuzzy set theory, are very mportant. 2. IMPROVING THE QUALITY OF THE IMAGES In [] were among the frst consdered to mprove qualty by usng fuzzy logc. It extracton method of fuzzy propertes of grayscale mages that can be used to enhance the contrast of ths mage. Improvng the qualty of the source mage s usually one of the frst steps n computer vson tass. Methods of mprovng mage qualty, as a rule, allow you to remove nose, to smooth the regons where the gray levels dd not sgnfcantly change, and hghlght sharp changes n gray levels. Snce fuzzy logc allows ncludng heurstc nowledge about ts specfc applcaton n the form of rules, t s deal to buld the system of mage mprovement. Ths led to the development of varous methods of mage enhancement based on fuzzy logc. Next, a bref loo at some of them. In [2] proposes a dynamc flter to reduce the constrcton of the range of values of the brghtness and ncreasng contrast, usng an approach based on fuzzy rules. The method s based on the algorthm gven n [3]. In [4] proposed a nonlnear fuzzy flter for mage processng. It s nown that the averagng flter effectvely removes Gaussan nose, and flters based on order statstcs, such as medan flter, are used effectvely for the removal of mpulse nose. To combne these two flters n [5] used fuzzy logc. The followng s the algorthm of lnear ncreasng contrast wth fuzzy ntal nformaton. Image entered nto the computer, often low contrast,.e. they have a change of brghtness s small compared to ts mean value. The brghtness are not changng from blac to whte and from gray to a brghter gray. That s the real brghtness range s much less than acceptable (grayscale). The tas of mprovng contrast s to "stretch" the range of brghtness of the mage on the entre scale. The essence of feature-based mage processng s as follows. Let ( x, y) f and g( x, y) - the brghtness values of the source and obtaned after mage processng, respectvely, n frame wth Cartesan coordnates x lne number and y column number. Element wse processng means that there s a functonal dependence between the brghtness g ( x, y) = F( f ( x, y)), Allowng the value of the orgnal sgnal to determne the value of the output sgnal. The tas of onstrastom s assocated wth mproved matchng of the dynamc range of the mage and the screen on whch you are renderng. If the dgtal representaton of each reference mage s assgned byte (8 bts) memory Impact Factor (JCC): NAAS Ratng: 3.76

3 Approaches to Image Processng usng the Tools of Fuzzy Sets 3 devces, nput or output sgnals can be one of 256 values. Typcally, the worer uses the range , wth 0 representng when renderng the blac level and the value 255 whte level. Suppose that the mnmum and maxmum brghtness of the orgnal mage are equal to f mn and fmax accordngly. If these optons are or one of them s sgnfcantly dfferent from the boundary values of the lumnance range, the rendered mage loos le an uncomfortable, trng durng observaton. It s often useful to consder the mage as a realzaton of a fuzzy random process. We ntroduce a generatve mage contnuous random functon ( x, y) ( x, y) f fully descrbed by the jont probablty densty [ A] f two varables o,.al coordnates x, y. Random process P. Ths Problem can be Solved wth a Pecemeal Converson of a Lnear Contrast: g( x, y) = af ( x, y) + b, e, are these аandb, that lead the fuzzy values of the feld brghtness to some standard values. Here are prelmnarly estmated M[ f ( x, y)], σ[ f ( x, y)], get M[g( x, y)], σ [g( x, y)] : f ( x, y) M[ f ( x, y)] g( x, y) = σ[ g( x, y)] + M[g( x, y)] = σ[ f ( x, y)] σ[ g( x, y)] σ[ g( x, y)] = f ( x, y) + M[ g( x, y)] M[ f ( x, y)], σ[ f ( x, y)] σ[ f ( x, y)].e. σ[ g( x, y)] σ[ g( x, y)] a = ; b = M[ g( x, y)] M[ f ( x, y)]. σ[ f ( x, y)] σ[ f ( x, y)] Here and the oddsа, bare selected so that for the output feld f f ( x, y) µ ( x, y) = [ (, )] =, f µ ( x, y) = M f x y g g ( x, y) µ ( x, y) = [ (, )] = ; g µ ( x, y) = M g x y 0, g( x, y) < 0, g( x, y) = F( f ( x, y)) = g( x, y), 0 g( x, y) 255, 255, g( x, y) > 255. Thus, at mage processng s requred for some sgns to dentfy some homogeneous areas of the mage. The stages of mage pre-processng can reduce the nfluence of dstorton on the recognton process. In Fgure 2 shows the edtor@tjprc.org

4 4 R. KH. Khamdamov & E. A. Salyev result of a lnear ncrease n contrast wth fuzzy ntal nformaton. Fgure 2: The Result of Lnear Increasng n Contrast wth Fuzzy Intal Informaton 3. IMAGE SEGMENTATION Conceptual relatonshp between the segmentaton and the theory of fuzzy sets s based on the fact that the structurng of complex mages t s necessary to consder the fact that there are many real objects that do not have clear boundares n nature. Requrement of the need to ensure unqueness n segmentaton and fuzzy data n ths case s nadequate, especally when tang account of mnor dfferences or for segments of complex shape, the overlappng between them. On the bass of classcal (crsp) methods of mage segmentaton s the determnaton of the values (the centrod) that characterze each segment n a gven feature space and the classfcaton of an object to a class based on some measure, usually a dstance n the feature space. Fuzzy or soft segmentaton, ntroduces the noton of fuzzy segments and the membershp functon of pxels to them, varyng n the nterval [0 ], whch allows to assess the degree of belongng of a pxel to a partcular class. Methods of mage segmentaton based on fuzzy set theory are dvded nto the followng groups. Threshold Segmentaton Methods of ths group are one of the smplest methods of mage segmentaton and dvde the mage nto the object area and the bacground. Thus, these methods are based on comparson wth a threshold to form a bnary mage n whch the pxel value belongng to the objects s, and the value of the pxels belongng to the bacground 0. There are several tradtonal methods for the determnaton of thresholds, adequate orgnal mage [6,7]. To determne the optmal threshold, t s possble to calculate measures such as lnear/quadratc ndex of fuzzness [8], fuzzy compactness [9] or the ndex of coverage [0]. Fuzzy devaton and probablty measures can also be used to segment mages nto object and bacground []. Segmentaton Based on Clusterng Technques The frst method of fuzzy clusterng was the method of fuzzy C-means (Fuzzy C-means FCM) [40, 45], whch has currently a lot of modfcatons [2]. FCM method s based on the use of deas and mathematcal tools of fuzzy logc. In the FCM algorthm, each pxel n the mage corresponds to a vector of membershp functons to each class on the bass of whch to draw conclusons about the nature of the object. Impact Factor (JCC): NAAS Ratng: 3.76

5 Approaches to Image Processng usng the Tools of Fuzzy Sets 5 Result of segmentaton usng the FCM algorthm depends strongly on the chosen measure. The Eucldean dstance s effectve only when the clusters are well-separated and approxmately equal n sze. Otherwse, t can be used by other algorthms such as the algorthm proposed n [3], or the algorthm of decomposton of the Gaussan mxture. Let ths real set s,... < s2 < < s X = x, x,.., xm} R { 2 and real numbers 2 s, s,.., s n ascendng order, namely: Fuzzy parttonng A,..,, A2 A for a set X can be organzed usng trangular functons. When developng algorthm of fuzzy clusterng for mage segmentaton, frst, we consder the membershp functons of: µ ( x) = µ ( x, s ; s ), 2 For =2,3,..., µ ( x) = µ ( x, s ; s ) µ ( x, s ; s + ), µ ( x) = µ ( x, s ; s ). Functons µ, µ 2,.., µ dentfy the partton splt n the followng equalty: µ + µ µ =. Secondly, determned the defuzzfcaton operator τ(µ, γ), whch apples to a fuzzy partton: (, ) = (,,.., ) τ µ γ τ τ2 τ where τ ( x, µ, γ ) = γ µ ( x) j= γ µ ( x),. Letν andf are defned as follows: v ( x) = µ ( x) τ ( x, µ ; γ ) m v ( x ) x j= F ( )., s = m v ( x ) j= j j Let us now consder the followng restrcton for the parameters s, s2,.., s : s = F ( s ). () j Fuzzy seta s determned by the equaton (). Center s belongs to the convex hull of a set X, and t s a fxed pont for the functon F. edtor@tjprc.org

6 6 R. KH. Khamdamov & E. A. Salyev Results are obtaned usng the followng fuzzy clusterng algorthm. Step : Intalzed the number of clusters, defuzzfcaton parameterγ, parameter stop procedure δ, ndex of the teraton l= 0 and cluster centers. Next, calculated fuzzy membershp functons and functons d.zzfcaton components τ τ τ. (0) (0) (0), 2,.., cluster Step 2: Index of the teraton ncreased,.e. l l +. We calculate the centers of ( ) ( ) ( ) s = F ( s ), s = F ( s ),..., s = F ( s ), fuzzy membershp functons µ l, µ l,.., µ l, ( l) ( l ) ( l ) ( l ) ( l) ( l ) defuzzfcaton components τ τ ( l) ( l), 2,.., τ ( l) ( l) ( l) ( l) and functon v, v v. 2,.., 2 Step 3: Calculate ( l) ( l ). Ifd>δ, then return to step 2, otherwse go to step 4. = d = µ µ Step 4: Savng data and end. In Fgure 3 shown results of the consdered algorthms on dfferent mages. а) b) Fgure 3: The Results of the Algorthms Dscussed n a) Frst, b)second Images Impact Factor (JCC): NAAS Ratng: 3.76

7 Approaches to Image Processng usng the Tools of Fuzzy Sets 7 4. ALLOCATION OF THE CIRCUITS Polygon selecton s an mportant part of many computer vson system. Ideally, the contours correspond to the boundares of objects, and therefore, the allocaton of contours allows segmentng the mage nto meanngful regons. However, the term "crcut" s rather vague, heurstc, and even subjectve concept. In [4] gven the followng defnton of the contour: the contour pont s a pxel n the neghborhood of whch there s a sgnfcant local change of ntensty; the contours are mage fragments representng a set of ponts of the contour. As can be seen from ths defnton, there are several possbltes of fuzzfcaton of the concept of "contour", because t nvolves two varables: spatal poston and ntensty. At present, there are several fuzzy models, whch try to hghlght the contours n the mage, and ths secton dscusses some of them. In [5] descrbed the method of allocaton of contours, based on the FIRE (fuzzy nference ruled by else-acton fuzzy concluson on the bass of OTHERWISE-acton) paradgm, whch s relatvely mmune to nose. It uses the dfferences of the gray levels n a neghborhood of 3x3 as nputs n the fuzzy rules. In [6] t s shown that usng statstcs such as range and varance of wndow ntenstes can be as effectve as the use of tradtonal, such as the evaluaton of gradents. In [7] proposes a method for contour extracton based on fuzzy logc, where local features such as gradent, symmetry, and straghtness are combned n order to ntroduce the concept of "contour" and "angle". It argues that the tradtonal defnton of contour ponts as ponts wth hgh gradent between two unform plasma regons s not vald n the corners (where the unform regon has an acute angle). Object Detecton Based on Color There are a large number of tass, one part of whch s the queston of automatc recognton of persons n mages. Approaches to ths queston are many, but ths materal we wll consder a method of automatc face detecton n mages based on color analyss. Read a source mage (Fgure 4-7). Fgure 4: -Th Orgnal Image Fgure 5: 2nd Source Image edtor@tjprc.org

8 8 R. KH. Khamdamov & E. A. Salyev Fgure 6: 3rd orgnal mage Fgure 7: 4 th orgnal mage Next, we need on the facal mage, select the pxels wth the characterstc color, to calculate the average ntensty and standard devaton. On the bass of nowledge about the values of the ntenstes of pxels and ther possble varatons s the mage segmentaton (Fgure 8 ). Fgure 8: st Source Image After Segmentaton Fgure 9: 2nd Source Image After Segmentaton Fgure 0: 3rd Source Image After Segmentaton Fgure : 4th Source Image After Segmentaton The am of such segmentaton s the selecton of the face n the mage. However, t s only natural that the mage was present and other objects, the values of the ntenstes of pxels whch concded wth the ntensty of the pxels of the face. As a result, the segmented mage except the face stand out and other objects. Now on the segmented mage to fnd the Impact Factor (JCC): NAAS Ratng: 3.76

9 Approaches to Image Processng usng the Tools of Fuzzy Sets 9 mage of the desred object,.e. person. Search crtera may be dfferent. Ths may be area, shape, etc. In ths example, the crteron for the search face choose a square. On the bass of the prevously selected segmentaton method, we can assume that the person occupes the largest area. Therefore, the selecton crtera for fndng persons on the bass of the square wll allow you to delete other objects that are smaller n area (Fgure 2 5). Fgure 2: Orgnal Image after Nose Removal Fgure 3: Orgnal Image after Nose Removal Fgure 4: Orgnal Image after Nose Removal Fgure 5: Orgnal Image after Nose Removal Remove other objects on the segmented face mage (Fgure 6 9). Fgure 6: Orgnal Image After Removal of Small Nose Objects Fgure 7: Orgnal Image After Removal of Small Nose Objects edtor@tjprc.org

10 0 R. KH. Khamdamov & E. A. Salyev Fgure 8: Orgnal Image after Removal of Small Nose Objects Fgure 9: Orgnal Image after Removal of Small Nose Objects It should be noted that the chosen crtera may be nsuffcent for relable determnaton of a search object,.e., face mage. Ths can occur f the mage contans other objects wth smlar color, a person may be n the shade, slope, etc. t s Therefore necessary to use other crtera to search the mage of the face. Such crtera can be based on a pror nformaton about the shape of the face. Thus, to mprove the relablty recognton crteron search of the person n the mage must be ntegrated. Second, we perform the selecton of the selected person, for example, a rectangle (Fgure 20 23). Fgure 20: The Selected - Face, By Rectangle Fgure 2: The Selected 2 - Face, By Rectangle Fgure 22: Selected 3 - Face, by Rectangle Fgure 23: Selected 4-Person by Rectangle Impact Factor (JCC): NAAS Ratng: 3.76

11 Approaches to Image Processng usng the Tools of Fuzzy Sets If an mage s several persons at the same tme, the consdered above method must be modfed. To dscuss ths n more detal. The frst few steps (read the orgnal mage, the selecton of characterstc pxels, the segmentaton and flterng) the same as n the prevous method, so we show only the results of these operatons. 5. CONCLUSIONS The paper presents fuzzy clusterng algorthms for the space R, the method of mage segmentaton that use clusterng algorthms. Advantages of ths approach are: A Wde Range of Applcatons: Due to the choce of mappngs and measures to adapt the algorthm for dfferent tass; Flexblty: Changng the threshold and the measure, t s possble to change the senstvty of the algorthm; Speed: The algorthm wors substantally faster algorthm for fndng the boundares of the method; Stablty: The algorthm s more robust than methods based on fndng borders, snce the error, we lose not the entre regon, and only a small porton of t. REFERENCES. Pal S. K., Kng, R.A. (98). Image enhancement usng smoothng wth fuzzy sets, IEEE Trans. Syst., Man and Cyberns., (7), Mancuso M., Poluzz R., Rzzotto G. A. (994) Fuzzy flter for dynamc range reducton and contrast enhancement, Proc. IEEE Int. Conf. On Fuzzy Syst., IEEE Press, Pscataway, NJ, Pel T., Lm J. (982). Adaptve flterng for mage enhancement, Optcal Engneerng, 2, Peng S., Luce L. (994). Fuzzy flterng for mxed nose removal durng mage processng, Proc. IEEE Int. Conf. On Fuzzy Syst., IEEE Press, Pscataway, NJ, Сh Z. Fuzzy algorthms: Wth Applcatons to Image Processng and Pattern Recognton. London: Word Scentfc, p. 6. Pal N.R., Pal S.K. (993). A revew of mage segmentaton technques, Pattern Recognton, 26 (9), Sahoo P.K., Soltan S,Wong A.K., Chen Y.C. (988). A survey of thresholdng technques, CVGIP, 4 (2), Pal S.K., Kng, R.A., Hshm A.A. (983a). Automatc grey level thresholdng through ndex of fuzzness and entropy, Patt. Recog. Lett., Pal S.K., RosenfeldA. (988). Image enhancement and thresholdng by optmzaton of fuzzy compactness, Patt Recog. Lett, 7, Pal S.K., Ghosh A. (990). Index of area coverage of fuzzy subsets and object extracton, Patt. Recog. Lett.,, Bhandar D., Pal N.R., Dutta Majumder D. (992). Fuzzy dvergence, probablty measures of fuzzy events and mage thresholdng, Patt. Recog. Lett., 3, Boujemaa N., Stamon G., Lemone J., Pett E. (992a). Fuzzy ventrcular endocardogram detecton wth gradual focusng decson, Proc. IEEE Int. Conf. Of the Engneerng n Medcne and Bology Socety, 4, Gustafson E. E., Kessel W. (979). Fuzzy clusterng wth a fuzzy covarance matrx, Proc. IEEE Conf. On Decson and edtor@tjprc.org

12 2 R. KH. Khamdamov & E. A. Salyev Control, San Dego, IEEE Press, Pscataway, NJ, Jan, R., Kastur R., Schunc B. G. (995). Machne Vson, McGraw-Hll, NY. 5. Russo F., Rampon G. (994). Edge extracton by FIRE operators, Proc. IEEE Int. Conf. On Fuzzy Syst., IEEE Press, Pscataway, NJ, BezdeJ.C., ChandrasearR., Attouzel Y.A. (998a). A geometrc approach to edge detecton, IEEE Trans. Fuzzy Syst., 6 (), Law T., Itoh H., Se H. (996). Image flterng, edge detecton and edge tracng usng fuzzy reasonng, IEEE Trans. Pattern Analyss and Machne Intellgence, 8, Impact Factor (JCC): NAAS Ratng: 3.76