are two specific neighboring points, F( x, y)

Transcription

1 $33/,&$7,212)7+(6(/)$92,',1* 5$1'20:$/.12,6(5('8&7,21$/*25,7+0,17+(&2/285,0$*(6(*0(17$7,21 %RJGDQ602/.$+HQU\N3$/86'DPLDQ%(5(6.$ 6LOHVLDQ7HFKQLFDO8QLYHUVLW\'HSDUWPHQWRI&RPSXWHU6FLHQFH $NDGHPLFND*OLZLFH32/$1' EVPROND#LDSROVOJOLZLFHSO $EVWUDFW The paper presets a ew techique of colour image ehacemet. The algorithm is based o a cocept of a virtual particle, which performs a special kid of radom walk - the so called self-avoidig radom walk. Segmetatio effect obtaied usig this method, together with its ability to elimiate impulsive ad Gaussia oise, makes the ew method a iterestig preprocessig tool for colour image segmetatio.,1752'8&7,21 Colour image processig has bee the subject of extesive research durig the last years. With the expadig use of colour i various applicatios, the iterest i the preprocessig of colour images has bee growig rapidly. As a result, a large umber of techiques of colour image ehacemet has bee proposed. These techiques seek to reduce the image oise, while preservig importat image details, such as edges ad image texture. Especially the edge iformatio is of high importace to huma perceptio ad therefore its preservatio ad possibly ehacemet is a very desired feature of the performace of the filterig techiques. I this paper a ew approach to the colour image ehacemet is preseted. The ew filterig techique is based o a self-avoidig radom walk ad it eables the suppressio of oise ad cotrast ehacemet of documet images. 6(/)$92,',1*5$1'20:$/.$/*25,7+0 The algorithm described here, eables the suppressio of oise ad cotrast ehacemet of colour images. This combiatio is quite ovel sice the commoly used algorithms are mostly ot able to perform both of the tasks simultaeously, as the ew procedure does [1,2,6,8]. The stadard techiques of oise elimiatio, like low-pass filter, media filterig, Fourier trasform based operatios, cause the blurrig of edges, which is a very udesirable effect. Ufortuately, the cotrast ehacemet of oisy images makes the oise compoet eve stroger, so that a compromise has to be foud. The preseted algorithm solves this dilemma, by performig at the same time cotrast ehacemet ad oise smoothig. I this paper the cocept of a walkig particle performig a self-avoidig radom walk is itroduced for the ehacemet of colour images. Self-avoidig radom walk (SAW) is a special walk alog a m-dimesioal lattice such that adjacet pairs of edges i the sequece share a commo vertex of the lattice, but o vertex is visited more tha oce ad i this way the trajectory ever itersects itself. I other words SAW is a path o a lattice that does ot pass through the same poit twice. O the

2 two-dimesioal lattice (m=2) SAW is a fiite sequece of distict lattice poits (x 0,y 0 ), (x 1,y 1 ), (x 2,y 2 ),..., (x,y ), which are i a eighbourhood relatio ad (x i, y i ) ¹ (x j,y j ) for all i ¹ j [3,5,7,9,12]. Let us itroduce a virtual walkig particle, which performs a SAW o a two-dimesioal gray scale image lattice with eight-eighbourhood system ad let the trasitio probabilities betwee poits ( x0, y ad ( x1, y 1) i oe step be described by F( x0 y F( x1 y1) } β F( x y ) F( x y ) exp,, P«( x0, y,( x1, y1) áã= Ç exp,, {( x0, y0 ) ( x1, y1 )} { } (1) where ( x0, y, ( x1, y 1) are two specific eighborig poits, F( x, y) is the gray scale value of ( xy, ) ad {( x0, y ( x1, y1) } is a set of all eighbours of the pixel at positio ( x0, y. Let us ow defie a smoothig operator based o the self-avoidig walk model ( 0, = «,( 0, 0 ) (, ) á (, ) J x y Ç P x y x y F x y (2) ã {( x0, y0 ) ( x, y) } where the sum is take over all pixels ( x, y ), which are coected by a trajectory of the walkig particle startig at the poit ( x0, y ad edig at ( x, y ) ; { ( x0, y0 ) ( x, y) } deotes all trajectories leadig from ( x0, y to ( x, y ). Let the probability of a trasitio betwee poits ( x0, y to ( x, y ) be defied as [ F x0 y0 F x1 y1 + + F x 1 y 1 F x y ]} exp (, ) (, ) L (, ) (, ) ( 3) P«( x0, y0 ) ( x, y) áã = Ç exp β Ç F( xκ 1, yκ 1) F( xκ, yκ) {( x0, y0 ) ( x, y) } κ = 1 the for = 1 we obtai (1). I this way the operator J is defied as [ ]} exp F( x, y ) F( x, y ) L F( x, y ) F( x, y) F( x, y ) (4) J( x0, y = Ç exp β Ç F( xκ 1, yκ 1) F( xκ, yκ) {( x0, y0 ) ( x, y) } κ = 1 If β = 0 the (4) defies the movig average ad for β Ž this operator assigs at ( x0, y the value of F( x, y ) for which ( x, y) = arg mi F( x, y ) F( x, y ) Ç κ 1 κ 1 κ κ κ = 1 (5)

3 The ew operator has the ability of image sharpeig while preservig image edges. It also elimiates strog impulse oise ad performed i a iterative maer ca be viewed as a segmetatio algorithm. To some extet the preseted algorithm resembles the aisotropic diffusio, but it seems, that the ew method solves may problems, which caot be overcome by the classical models of diffusio. I case of colour images, istead of the absolute value of the differece of the gray scale values of the eihbourig poits, we take the orm of the differece of vectors represetig the colour image pixels i a specific colour space. Thus we have « á} exp )( x, y ) )( x, y ) L )( x, y ) )( x, y) ã )( x, y ) (6) -( x0, y = Ç exp βç )( xκ 1, yκ 1) ) ( xκ, yκ) {( x0, y0 ) ( x, y) } κ = 1 I this paper the 5*% colour space ad the L1 metric was used while calculatig (6). 6(*0(17$7,212)&2/285,0$*(686,1*7+(1(:),/7(5,1*7(&+1,48( I [13] a ew method for colour image segmetatio has bee preseted. The algorithm is based o a regio growig procedure ad is usig a homogeeity criteria for the distace betwee colour pixels i differet colour spaces (RGB, YUV ad IHS). Amog tested homogeeity criteria, best results were obtaied usig the followig HS-criterio with the Euclidea distace metric i the cylidrical coordiate system: ( ) 2 2 S S 2SScos H H d Ê (7) where HadS are curret values of colour compoets of the tested pixel, H ad S are mea values related to a regio ad dis tuig parameter, which determies the umber of segmets. The choice of a specific value of d is image depedet. The lower the value of d, the more segmets are created ad the risk of oversegmetatio is growig. Very ofte the segmetatio algorithm geerates too may segmets. It is possible to limit the umber of segmets by differet additioal pre-processig (filtratio) ad post-processig (elimiatio) procedures. Each filtratio procedure (e.g. Media Filter, Vector Media etc.) decreases the umber of regios i segmeted image. Also, the elimiatio procedure ca be used to avoid oversegmetatio. The algorithm aalyses the area of all segmeted regios. The elimiatio procedure locates all regios smaller tha a give value ad elimiates these regios from the cotour image. Below, the segmetatio result of the LENA image is show for d = 0.1 (Fig.1.). If we decide to elimiate all regios, with area lower tha 50 pixels, the regio umber decreases from the iitial value of 5874 to 172. The results obtaied usig the PEPPERS image were similar, whe the parameter d = 0.35 was take (Fig.2.). The umber of regios decreased from 231 to 31. It must metioed however that small regios ot always are caused by oise compoet ad sometimes caot be eglected. A good example of this effect are the pupils of Lea ad that is why we prefer to do a good filterig of oise before the segmetatio.

4 If the colour images are very oisy, the the umber of the geerated segmets icreases dramatically. If the PEPPERS image is cotamiated by a Gaussia oise with σ= 30 ad additioal 4% impulsive oise, the umber of regios reaches The elimiatio of small regios d = 0.35 lowers their umber to 42 (Fig. 3). As ca be see the oise compoet is resposible for geeratig of tiy segmets which is the cause of the oversegmetatio. We compared the ew filterig techique with the media applied to the RGB compoets ad with the Vector Media as defied by Astola [14]. Filterig the oisy image with the scalar media, we obtaied 224 regios ad after the post-processig, takig d = 0.35 their umber dropped to 73. Usig the Vector Media we obtaied 209 ad the 55 regios. Filterig the image with the ew oise reductio techique, the appropriate regio umbers were 85 ad 43 for oe pass of the filter ad 33, 23 for two filter iteratios. &21&/86,216 The ew filterig techique has iterestig properties. It has the ability of image smoothig while preservig the image edges. As ca be observed, the umber of regios obtaied whe applyig the algorithm described i [13] to the oisy image filtered usig the ew techique is sigificatly lower whe compared with the scalar ad vector media. It is eve lower tha the umber of regios created whe usig the origial PEPPERS image (for two iteratios of the ew filter). Figure 4 shows three examples of the performace of the ew colour image filterig techique. 5()(5(1&(6 [1] Pitas I., Veetsaopoulos A.N., Noliear Digital Filters : Priciples ad Applicatios, Kluwer Academic Publishers, Bosta, MA. [2] Plataiotis K.N., Veetsaopoulos A.N.: Color Image Processig ad Applicatios, Spriger Verlag, ISBN , May [3] Hayes B., How to avoid yourself, Amer. Sci. 86, Jul. /Aug, [5] Lawler G.F., Itersectios of radom walks (Probability ad its Applicatios), Birkhauser Bosto, [6] Lee J. S., Digital Image Ehacemet ad Noise Filterig by Use of Local Statistics, PAMI 2, , [7] Madras N., Slade G., The Self-Avoidig Walk (Probability ad its Applicatios), Birkhauser Bosto, [8] Pratt W. K., Digital Image Processig, New York, Joh Wiley ad Sos, [9] Roberts F. Applied Combiatorics, Pretice-Hall, Eglewood Cliffs, New Yersey, [10] Smolka B., Wojciechowski K., Edge Preservig Probabilistic Smoothig Algorithm, Lecture Notes i Computer Sciece, 1689, 41 48, [11] Smolka B., Wojciechowski K., Cotrast Ehacemet of Grey Scale Images Based o the Radom Walk, Lecture Notes i Computer Sciece, 1689, , [12] Spitzer F., Priciples of Radom Walk, D. Va Nostrad Compay, Priceto, [13] Palus H., Bereska D., Regio-based Colour Image Segmetatio, Proc. of 5th Workshop Farbbildverarbeitug, 67-74, Ilmeau [14] Astola J., Haavisto P., Neuovo Y., Vector media filters, Proceedigs of the IEEE, 78, , 1990.

5 )LJ Segmetatio results: the umber of regios usig the algorithm described i [13] applied to LENA image (left) was 5874 (middle), takig the parameter 0.1 d = it decreased to 172 (right). )LJ The results obtaied usig the PEPPERS image (left). Whe the parameter d = 0.35 was take, the regio umber decreased from 231 (middle) to 31 (right). )LJ Segmetatio of the oisy image (PEPPERS cotamiated with Gaussia oise σ = 30 ad 4% impulsive oise, left) produced 1605 regios, this umber decreased to 42 for d = If the image was filtered two times with the ew oise reductio algorithm, the regio umber was 33 without ay postprocessig (right).

6 Fig. 4. Examples of the efficiecy of the ew filterig techique.