Designing a new software tool for digital imagery based on P systems

Designing a new so wa e ool o Digi al Image y based on P sys ems Daniel Dı ´az-Pe nil •Miguel A. Gu ie ´ ez-Na anjo • Helena Molina-Ab il •Ped o Real Published online: 4 Sep embe 2011 Sp inge Science+Business Media B.V. 2011 Abs ac In his pape we p esen a new so wa e ool o dealing wi h he p oblem o segmen a ion in Digi al Image y. The implemen a ion is inspi ed in he design o a issue-like P sys em which sol es he p oblem in cons an ime due he in insic pa allelism o Memb ane Compu ing de ices. Keywo ds Memb ane compu ing Digi al Image y  Segmen a ion 1 In oduc ion Na u e is a big inspi a ion sou ce o designing solu ions o a b oad panoply o p oblems. Na u al Compu ing s udies compu a ional pa adigms inspi ed om a ious well known na u al phenomena in physics, chemis y and biol- ogy 1 . I abs ac s he way in which na u e ac s, concei ing new compu ing models. The ield is g owing apidly and he e a e many open esea ch lines based on na u e. Among hem, Cellula Au oma a ( on Newmann 1966) concei ed by Ulam and on Newman as a spa ial dis ibu ion o cells able o ep oduce he beha io o complex sys ems; Gene ic Algo i hms in oduced by Holland (1992) which is inspi ed by na u al e olu ion and selec ion in o de o ind a good solu ion in a la ge se o easible candida e solu ions; Neu al Ne wo ks in oduced by McCulloch and Pi s (1988) based on he in e connec ions o neu ons in he b ain; DNA-based molecula compu ing, ha was bo n when Adleman (1994) published a solu ion o an ins ance o he Hamil onian pa h p oblem by manipula ing DNA s ands in a lab; Swa m In elligence (Engelb ech 2005) based on he beha io and communica ion o mobile o ganisms as an s o bees ac ing in he en i onmen ; A i icial Immune Sys ems (de Cas o and Timmis 2002) based on he na u al immune sys em o biological o gan- isms; Amo phous Compu ing (Abelson e al. 2000) inspi ed om he de elopmen o mo phogenesis in biological o ganisms o Memb ane Compu ing (Pa ˘un 2000,2002) based on he unc ioning and mo phology o li ing cells and issues. All hese compu a ional pa adigms ha e in common he use o an al e na i e way o encoding he in o ma ion, adap ed o he bio-inspi ed subs a e and he use o in insic pa allelism o na u al p ocesses. In his pape we p esen a bio-inspi ed so wa e o sol ing he Segmen a ion P oblem in Digi al Image y. Segmen a ion in compu e ision (see Shapi o and S ock- man 2001), e e s o he p ocess o pa i ioning a digi al image in o mul iple segmen s (se s o pixels). The goal o segmen a ion is o simpli y and/o change he ep esen a ion o an image in o some hing ha is mo e meaning ul and easie o analyze. Image segmen a ion is ypically used o D. Dı ´az-Pe nil H. Molina-Ab il P. Real Resea ch G oup on Compu a ional Topology and Applied Ma hema ics, Uni e si y o Se ille, Se ille, Spain e-mail: [email p o ec ed] H. Molina-Ab il e-mail: [email p o ec ed] P. Real e-mail: [email p o ec ed] M. A. Gu ie ´ ez-Na anjo (&) Resea ch G oup on Na u al Compu ing, Depa men o Compu e Science and A i icial In elligence, Uni e si y o Se ille, Se ille, Spain e-mail: [email p o ec ed] 1 An in oduc ion on Na u al Compu ing can be ound in Ka i and Rozenbe g (2008). 123 Na Compu (2012) 11:381–386 DOI 10.1007/s11047-011-9287-4 loca e objec s and bounda ies (lines, cu es, e c.) in images. Mo e p ecisely, image segmen a ion is he p ocess o assigning a label o e e y pixel in an image such ha pixels wi h he same label sha e ce ain isual cha ac e is ics. Segmen a ion in Digi al Image y has se e al ea u es which make i sui able o echniques inspi ed by na u e. One o hem is ha i can be pa allelized and locally sol ed. Rega dless how la ge is he pic u e, he segmen- a ion p ocess can be pe o med in pa allel in di e en local a eas o i . Ano he in e es ing ea u e is ha he basic necessa y in o ma ion can be easily encoded by bio- inspi ed ep esen a ions. In he li e a u e, one can ind se e al a emp s o b idg- ing p oblems om Digi al Image y wi h Na u al Compu ing as he wo ks by Sub amanian and cowo ke s (2003a,b]o he wo k by Chao and Nakayama (1996) whe e Na u al Compu ing and Algeb aic Topology a e linked by using Neu al Ne wo ks (ex ended Kohonen mapping). In his pape , we will use an in o ma ion encoding and echniques bo owed om Memb ane Compu ing. Memb ane Compu ing is a heo e ical model o com- pu a ion inspi ed by he s uc u e and unc ioning o cells as li ing o ganisms able o p ocess and gene a e in o ma- ion. The compu a ional de ices a e called P sys ems (Pa ˘un 2000). Roughly speaking, a P sys em consis s o a mem- b ane s uc u e, in he compa men s o which one places mul ise s o objec s which e ol e acco ding o gi en ules. In he mos ex ended model, he ules a e applied in a synch onous non-de e minis ic maximally pa allel manne , bu some o he seman ics a e being explo ed 2 . Acco ding o hei a chi ec u e, hese models can be spli in o wo se s: P sys ems such ha hei memb ane s uc u e is a ee-like g aph, called cell-like P sys ems and P sys ems whose memb ane s uc u e is a gene al g aph. In his second g oup we can ind issue-like P sys ems and spiking neu al P sys ems. This pape is de o ed o he second app oach: is- sue-like P sys ems. In Ch is inal e al. (2009a,b,2010) s a ed a new bio-inspi ed esea ch line whe e he powe and e iciency o issue-like P sys ems (Dı ´az-Pe nil e al. 2008, 2009) we e applied o opological p ocesses o 2D and 3D digi al images. In his pape , we p esen a new so wa e ool o segmen 2D digi al images based in he wo ks o Ch is- inal e al. jus men ioned. This ool simula es he beha io o he issue-like P sys ems desc ibed in Ch is inal e al. (2009a) and allows us o wo k wi h images in JPG o ma . Simula ion o di e en a ian s o P sys ems ha e been widely s udied in he las yea s. Since he e do no exis implemen a ions o P sys ems in i o no in i o, he na u al way o explo e he beha io o designed P sys ems is o simula e i in con en ional compu e s. A sho desc ip ion o some o hese simula o s can be ound in Dı ´az-Pe nil e al. (2010), Gu ie ´ ez-Na anjo e al. (2006). In (Bo ego-Rope o e al. 2007), a i s simula o o issue-like P sys ems was p esen ed. Cu en ly, a big e o is being de eloped in he P- lingua p ojec (Dı ´az-Pe nil e al. 2008), by combining an e icien simula ion engine wi h an ad hoc desc ip ion language. The pape is o ganized as ollows: i s ly, we p esen ou bio-inspi ed o mal amewo k. Nex , we p esen he amily o issue-like P sys ems used o ob ain a segmen- a ion o a 2D digi al image. In Sec . 4we in oduce ou so wa e ool and illus a e i s use wi h some examples. Finally, some conclusions a e p esen ed. 2 Fo mal amewo k: issue-like P sys ems Tissue-like P sys ems we e p esen ed by Ma ı ´n-Vide e al. (2002). They ha e wo biological inspi a ions (see Ma ı ´n- Vide 2003): in e cellula communica ion and coope a ion be ween neu ons. The common ma hema ical model o hese wo mechanisms is a ne wo k o p ocesso s dealing wi h symbols and communica ing hese symbols along channels speci ied in ad ance. The main ea u es o his model, om he compu a ional poin o iew, a e ha he memb ane s uc u e is a gene al g aph and he objec s in he en i onmen a e a ailable in an a bi a ily la ge amoun o copies. Fo mally, a issue-like P sys em wi h inpu o deg ee qC1 is a uple P¼ðC;R;E;w1;...;wq;R;iP;oPÞ; whe e (1) Cis a ini e alphabe , whose symbols will be called objec s, (2) Rð CÞis he inpu alphabe , (3) EC( he objec s in he en i onmen ), (4) w1;...;wqa e s ings o e C ep esen ing he mul i- se s o objec s associa ed wi h he cells a he ini ial con igu a ion, (5) Ris a ini e se o communica ion ules o he ollowing o m: ði;u= ;jÞ o i;j2 0;1;2;...;qg;i6¼ j;u; 2C; (6) iP2 0;1;2;...;qgis he inpu cell, (7) oP2 0;1;2;...;qgis he ou pu cells. A issue-like P sys em o deg ee qC1 can be seen as a se o qcells (each one consis ing o an elemen a y memb ane) labelled by 1;2;...;q:We will use 0 o e e o he label o he en i onmen , iPdeno es he inpu cell and 2 We e e o Pa ˘un (2002) o basic in o ma ion in his a ea, o Pa ˘un (2010) o a comp ehensi e p esen a ion and he web si e P sys em web page o he up- o-da e in o ma ion. 382 D. Dı ´az-Pe nil e al. 123 oPdeno es he ou pu cell (which can be he egion inside a cell o he en i onmen ). The s ings w1;...;wqdesc ibe he mul ise s o objec s placed in he qcells o he sys em. We in e p e ha EC is he se o objec s placed in he en i onmen , each one o hem a ailable in an a bi a ily la ge amoun o copies. The communica ion ule (i,u/ ,j) can be applied o e wo cells labelled by iand jsuch ha uis con ained in cell i and is con ained in cell j. The applica ion o his ule means ha he objec s o he mul ise s ep esen ed by uand a e in e changed be ween he wo cells. No e ha i ei he i=0o j=0 hen he objec s a e in e changed be ween a cell and he en i onmen . Rules a e used as usual in he amewo k o memb ane compu ing, ha is, in a maximally pa allel way (a uni e sal clock is conside ed). In one s ep, each objec in a mem- b ane can only be used o one ule (non-de e minis ically chosen when he e a e se e al possibili ies), bu any objec which can pa icipa e in a ule o any o m mus do i , i.e., in each s ep we apply a maximal se o ules. Acon igu a ion is an ins an aneous desc ip ion o he sys em P:Gi en a con igu a ion, we can pe o m a com- pu a ion s ep and ob ain a new con igu a ion by applying he ules in a pa allel manne as i is shown abo e. A compu a ion is a sequence o compu a ion s eps such ha ei he i is in ini e o i is ini e and he las s ep yields a hal ing con igu a ion (i.e., no ules can be applied o i ). Then, a compu a ion hal s when he sys em eaches a hal ing con igu a ion. 3 Segmen ing digi al images in cons an ime In his sec ion, we segmen images based on edge-based segmen a ion. I consis s on inding bounda ies o egions which a e su icien ly di e en om each o he . The e exis di e en echniques o segmen an image. Some o hem a e clus e ing (Wang e al. 2005), his og am-based me h- ods (Tobias and Sea a 2002), wa e shed ans o ma ion me hods (Yazid and A o 2008), g aph pa i ioning (Yuan e al. 2009) and image py amids me hods (K opa sch e al. 2007). Some o he p ac ical applica ions o image seg- men a ion a e medical imaging (Wang e al. 2005), objec s classi ica ion and ace ecogni ion (Kim e al. 1998). We de ine a amily o issue-like P sys ems o segmen 2D images. 3.1 A amily o issue-like P sys ems o a 2D segmen a ion We can di ide he image in mul iple pixels o ming a ne wo k o poin s o N2:Le CNbe he o de ed se o all colo s in he gi en 2D image. Mo eo e , we will suppose each pixel is associa ed wi h a colo o he image. Then we can codi y he pixel (i,j) wi h associa ed colo a2Cby he objec a ij . The ollowing ques ion is o decide which pixel is adjacen o a gi en one. We ha e decided o use in his pape he 4-adjacency (Rosen eld 1970,1979). In his case, each pixel has ou (ho izon al and e ical) neighbo s. The ex ension o di e en adjacencies is s aigh o wa d. A his poin , we wan o ind he bo de cells o he di e en colo egions ha a e wi hin he image. Then, o each image wi h n9mpixels ðn;m2NÞwe will con- s uc a issue-like P sys em whose inpu is gi en by he objec s a ij codi ying a pixel, wi h a2C:The ou pu o he sys em is gi en by he objec s ha appea in he ou pu cell when he sys em s ops. Based on ha , we de ine a amily o issue-like P sys- ems o pe o m an edge-based segmen a ion o a 2D image. Fo each n;m2Nwe conside he issue-like P sys em P¼ðC;R;E;w1;w2;R;iP;oPÞ de ined as ollows: (a) C¼R[  aij :1in;1jm;a2Cg [ Aij :1in;1jm;A2Cg; (b) R¼ aij :a2C;1in;1jmg; (c) E¼CR; (d) w 1 =w 2 =;, (e) Ris he ollowing se o communica ion ules: (1) ð1;aijbkl= aijAijbkl;0Þ; o a;b2C;a b;1i; knand 1 Bj,lBm. These ules a e used when he image has wo adjacen pixels wi h di e en associa ed colo s (bo de pixels). Then, he pixel wi h lowe associa ed colo is ma ked and he sys em b ings om he en i onmen an objec ep esen ing his ma ked pixel (edge pixel). (2) ð1; aijaijþ1 aiþ1jþ1biþ1j= aij  aijþ1Aijþ1 aiþ1jþ1biþ1j;0Þ o a;b2C;a b;1in1;1jm1: ð1; aijai1j ai1jþ1bijþ1= aij  ai1jAi1j ai1jþ1bijþ1;0Þ o a;b2C;a b;2in;1jm1: ð1; aijaijþ1 ai1jþ1bi1j= aij  aijþ1Aijþ1 ai1jþ1bi1j;0Þ o a;b2C;a b;2in;1jm1: ð1; aijaiþ1j aiþ1jþ1bijþ1= aij  aiþ1jAiþ1j aiþ1jþ1bijþ1;0Þ o a;b2C;a b;1in1;1jm1: These ules ma k wi h a ba he pixels which a e adjacen o wo pixels o he same colo which we e ma ked be o e, bu wi h he condi ion ha he ma ked objec s a e adjacen o ano he pixel wi h a di e en colo . Mo eo e , an edge objec ep esen ing he las ma ked pixel is b ough om he en i onmen . Designing a new so wa e ool 383 123 (3) (1, A ij /k, 2), o 1 BiBn,1BjBm. This ule is used o send he edge pixels o he ou pu cell. ( ) iP¼1 (g) oP¼2: 3.2 An o e iew o he compu a ion Rules o ype 1, in a pa allel manne , iden i y he bo de pixels and b ing he edge pixels om he en i onmen . These ules need 4 s eps o ma k all he bo de pixels. F om he second s ep, he ules o ype 2 can be used wi h he i s ules a he same ime. So, in 4 mo e s eps we can b ing om he en i onmen he edge pixels adjacen o wo bo de pixels (as explained abo e). The P sys em can apply he i s wo ypes o ules simul aneously in some con- igu a ions, bu i always applies he same numbe o hese wo ypes o ules because his numbe is gi en by he edge pixels (we conside 4-adjacency). Finally, he hi d ype o ules a e applied in he ollowing s ep on he edge pixels appea ing in he cell. So, wi h one mo e s ep we will ha e all he edge pixels in he ou pu cells. Thus, we need only 9 s eps o ob ain an edge-based segmen a ion o an n9m image. The e o e, we can conclude ha he p oblem o edge-segmen a ion in 2D images is sol ed in cons an ime wi h espec o he numbe o s eps o any compu a ion. 4 A so wa e ool In (Ch is inal e al. 2009), p elimina y segmen a ion esul s we e ob ained using he issue simula o de eloped in Bo ego-Rope o e al. (2007). Such a issue simula o ollows one o he common ea u es o he i s gene a ion o simula o s o cell-like P sys ems, ha is he lack o e iciency in a o o exp essi eness. The e o e, expe i- men s pe o med using his ool we e ex emely slow, and could only use syn he ic images o a mos 30 930 pixels. In o de o pe o m expe imen s wi h bigge images, a new so wa e ool has been de eloped. This so wa e makes possible he ob aining o segmen ed eal images ha ha e been pa i ioned ollowing a memb ane compu ing app oach. Fo op imal e ec i eness and lexibili y, he objec o ien ed C?? p og amming language has been used in he implemen a ion. The so wa e inpu consis s o a digi al 2D image. The image o ma can be any o he mos common as e image o ma s (jpg, png, gi ,…). Such image is p o ided o he P sys em as a se o objec s a ij whe e (i,j) co e s he n9m a ay o pixels and abelongs o C; he se o colo s. A he beginning, he inpu cell con ains objec s a ij codi ying he colo ed pixels om an 2D image (whe e ais he colo alue o he pixel, and i,ji s coo dina es). As an ou pu , he so wa e p o ides a black image (wi h he same o ma as he inpu image), whe e he de ec ed bo de pixels a e whi e. In o he wo ds, pixels belonging o he ou pu cell o he sys em will be conside ed whi e, and p in ed ou in he ou pu image. Some expe imen s and esul s a e shown in Figs. 1,2 and 3. Figu e 1shows a geome ical 340 9340 pic u e oge he wi h he ou pu image o he so wa e. Due o he sha p bounda ies wi hin he image, a p ecise segmen a ion esul is ob ained. In Fig. 2a mo e complex image is Fig. 1 Segmen a ion esul o a 340 9340 pixels image compu ed in 0.105 s Fig. 2 Segmen a ion esul o a 600 9600 CT image o human lungs, compu ed in 0.33 s. On he le , he ini ial image, on he middle he bina ized image, and on he igh he segmen a ion esul 384 D. Dı ´az-Pe nil e al. 123 shown. I is a 600 9600 medical image ha co esponds o compu ed omog aphy (CT) human lungs. In ha case, he so wa e ool needs o p ep ocess he ini ial image be o e segmen i . This ac is due o he simplici y o he segmen a ion algo i hm implemen ed he e, and u u e imp o emen s o i a e planned. In his case, he p ep o- cessing ans o ms an image wi h many g ay le els in o a black and whi e image (middle image in Fig. 2). The ou - pu o he sys em is show on he igh pic u e. The seg- men a ion p ocess ook 0.33 s. A simila example can be seen in Fig. 3. In his case, he image o a oy o size 437 9437 was segmen ed in 0.31 s. 5 Conclusions and u u e wo k Segmen a ion has ea u es which makes i sui able o echniques om Na u al Compu ing. Local solu ion o he pa allelism o he p ocess can be s udied om a heo e ical poin o iew, bu o an e ec i e applica ion o hese echniques o he eal wo ld, i is necessa y o ha e an app op ia e so wa e ool. This pape ep esen s an imp o emen wi h espec o he simula o p esen ed in Bo ego-Rope o e al. (2007). Ou so wa e ool is able o deal wi h images o easonable size and can become a helping ool o he ea men o digi al images, as he wo las examples show. The so wa e can be imp o ed and se e al esea ch lines a e open. One o hem is o s udy he in luence o he ype o adjacency (4 o 8) on he esul . The possibili y o including p ep ocessing ea u es in ou ool be also s udied. As a inal ema k, we will conside o adap his so wa e o a pa allel ha dwa e a chi ec u e and exploi in a ealis ic way he in insic pa allelism o memb ane compu ing me hods. Acknowledgemen s DDP and MAGN acknowledge he suppo o he p ojec s TIN2008-04487-E and TIN-2009-13192 o he Minis e io de Ciencia e Inno acio ´n o Spain and he suppo o he P ojec o Excellence wi h In es igado de Reconocida Valı ´ ao he Jun a de Andalucı ´a, g an P08-TIC-04200. PR and HMA acknowledge he suppo o he p ojec MTM2009-12716 o he Minis e io espan ˜ol de Educacio ´n y Ciencia, he p ojec PO6-TIC-02268 o Excellence o Jun a de Andalucı ´a, and he ‘‘Compu a ional Topology and Applied Ma hema ics’’ PAICYT esea ch g oup FQM-296. Re e ences Abelson H, Allen D, Coo e D, Hanson C, Homsy G J , Knigh TF, Nagpal R, Rauch E, Sussman GJ, Weiss R (2000) Amo phous compu ing. Commun ACM 43(5):74–82 Adleman LM (1994) Molecula compu a ion o solu ions o combi- na o ial p oblems. 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