CHANGE DETECTION - CELLULAR AUTOMATA METHOD FOR URBAN GROWTH MODELING

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1 CHANGE DETECTION - CELLULAR AUTOMATA METHOD FOR URBAN GROWTH MODELING Sharaf Alkheder, Jun Wang and Jie Shan Geomaics Engineering, School of Civil Engineering, Purdue Universiy 550 Sadium Mall Drive, Wes Lafayee, IN-47907, U.S.A {salkhede, wang31, jshan}@ecn.purdue.edu Commission VII, WG VI/4 KEY WORDS: Urban Growh, Cellular Auomaa, Geneic Algorihm, Dynamic Sysem, Change Deecion ABSTRACT: This paper describes an on-going work on he developmen and implemenaion of cellular auomaa based urban growh modeling using muliemporal saellie imagery. The algorihm is designed o simulae he hisorical growh as a funcion of local neighbourhood srucure of he inpu daa. Transiion rules in he algorihm drive he urban growh over ime. Calibraion is inroduced in he cellular auomaa model. Spaial and emporal calibraion schemes are used o improve he predicion accuracy. Spaially, he model is calibraed on a ownship basis o ake ino accoun he effec of sie specific feaures, while he emporal calibraion is se up o adap he model o he changes in he growh paern over ime. Calibraion provides he opimal values for he ransiion rules o achieve accurae urban growh modeling. The paper discusses a he end a proposed auomaic rule calibraion mehod using geneic algorihm. The aim is o opimize he ransiion rule values. Predicion accuracy is seleced as he finess funcion. A se of srings are used as iniial populaion over which he geneic algorihm runs ill convergence. The cellular auomaa model is esed over ciy Indianapolis, IN, USA o model is urban growh over a period of 30 years. Besides he land use daa derived from he saellie imagery, populaion densiy is used. Resuls indicae good accuracy on a ownship basis for shor erm (5 years) and long erm (11 years) predicion. The model succeeds in adaping o he dynamic growh paern. Geneic algorihm shows promising poenial in he calibraion process. 1. INTRODUCTION Urban growh modeling is geing more aenion as an emerging research area in many disciplines. This comes as a resul of he recen dramaic increase in urban populaion ha increases he pressure on he infrasrucure services. Among all developed urban growh models, cellular auomaa (CA) urban growh models have beer performance in simulaing urban developmen han convenional mahemaical models (Bay and Xie, 1994a). CA simplifies he simulaion of complex sysems (Waldrop, 1992). Is appropriaeness in urban modeling is due o he fac ha he process of urban spread is enirely local in naure (Clarke and Gaydos, 1998). Models based on cellular auomaa are impressive in erms of heir echnological evoluion in connecion o urban applicaions (Yang and Lo, 2003). Developmen of a CA model involves rule definiion and calibraion o produce resuls consisen wih hisorical daa, and fuure predicion wih he same rules (Clarke e al, 1997). Many CA-based urban growh models are repored in he lieraures. Whie and Engelen (1992a; 1992b) CA model involves reducion of space ino square grids. They implemen he defined ransiion rules in recursive form o mach he spaial paern. One of he earlies and mos well-known models in he lieraure is Clarke s e al (1997) CA-based model SLEUTH ha has four major ypes of daa: land cover, slope, ransporaion, and proeced lands. This is rooed in he work of von Neumann (1966), Hagersrand (1967), Tobler (1979) and Wolfram (1994). A se of iniial condiions in SLEUTH is defined by `seed' cells which were deermined by locaing and daing he exen of various selemens idenified from hisorical maps, alases, and oher sources. These seed cells represen he iniial disribuion of urban areas. A se of complex behaviour rules is developed ha involves selecing a locaion randomly, invesigaing he spaial properies of he neighboring cells, and urbanizing he cell based on a se of probabiliies. Despie all he achievemens in CA urban growh modeling, he selecion of he CA ransiion rules remains a research opic (Bay, 1998). CA models are usually designed based on individual preference and applicaion requiremens wih ransiion rules being defined in an ad hoc manner (Li and Yeh, 2003). Furhermore, calibraion of CA models is sill a challenge. Mos of he developed CA models need inensive compuaion o selec he bes parameer values for accurae modeling. The moivaion behind his work is o develop an effecive CAbased urban growh model. Also, developing a calibraion algorihm ha akes ino consideraion spaial and emporal dynamics of urban growh is anoher objecive of his sudy. Geneic algorihm (GA) is inroduced as a heurisic opimizaion echnique for selecing opimal model parameers. 2. STUDY AREA Indianapolis, Indiana, USA is seleced as a case sudy over which he CA model is designed and esed. Indianapolis is locaed in Marion Couny a laiude 39 44' N and longiude of 86 17' W as shown in Figure 1. Represening he main ciy in he sae of Indiana, Indianapolis encouners recognizable acceleraed growh in populaion and urban infrasrucure over he las few decades. The necessiy arises o model he urban growh over ime for beer planning of infrasrucure services.

2 Figure 3. Year 2000 census rac map and populaion densiy The Euclidean disance from each census rac cenroid o he ciy cener is compued. This process is repeaed for all racs so ha a able of populaion densiies versus disance is prepared. Populaion densiies for census racs wihin specified disance from ciy cener are averaged o reduce he variabiliy in daa. For example, an average populaion densiy for all census racs wihin 2 km is calculaed hen anoher average densiy is calculaed for racs wihin 2-4 km and so forh. An exponenial funcion is fied represening populaion densiy as a funcion of disance from he ciy cenre: B* DISTANCE POPULATION DENSITY = Ae (1) Figure 1. Ciy of Indianapolis, Indiana, USA (US Census Bureau) Model parameers A and B are calculaed for year 2000 as shown in Figure 4. This exponenial model is used o calculae he populaion densiy for each pixel in he imagery based on is disance form ciy cener for year DATA PREPARATION This secion describes he inpu daa processing scheme. Five hisorical TM images (1973, 1982, 1987, 1992 and 2003) are colleced over he sudy area (Figure 2). These images are recified and regisered o he same projecion of UTM NAD1983 o fi each oher spaially. Seven classes of ineres are idenified in he images: waer, road, commercial, fores area, residenial areas, pasure and row crops. Residenial and commercial classes represen urban class. The overall classificaion accuracy for all classified images is above 93%. Populaion densiy(1/km2) y = e x R 2 = Disance from ciy cener (KM) Figure 4. Year 2000 populaion densiy Figure 2. Hisorical TM images over Indianapolis Populaion densiy is used as anoher inpu for he CA model algorihm. Populaion census rac maps for year 1990 and 2000 over Indianapolis are colleced. The populaion densiies are compued for all census racs by dividing heir populaions by he rac areas. Figure 3 shows he census rac map (lef) and he calculaed populaion densiy for each census rac (righ). To model he populaion, he cenroid (Xc,Yc) for each census rac is calculaed. The same procedure is repeaed for year 1990 o find is exponenial populaion model wih A and B parameers. The change in model parameers over he 10 years (from 1990 o 2000) is used o calculae he yearly rae of change in A and B parameers. The updaed parameers (A and B values ha changed year by year) are used o calculae populaion densiy grids for each year from 1973 o 2003 maching he same size of he inpu imagery. These grids are used as CA daa inpus for he purpose of running he model over hisorical growh period. 4. CELLULAR AUTMATA URBAN MODELING This secion discusses in deail he design of he CA urban growh modeling. The design phases include: ransiion rule definiion, calibraion mehod and evaluaion sraegy for he model. Calibraion modules for accurae modeling over he hisorical saellie imagery o adap he urban paern are discussed in deails.

3 4.1 CA Algorihm Design The design of he CA algorihm consiss of defining he ransiion rules ha conrol he urban growh, calibraing hese rules, and evaluaing he resuls for predicion purpose. Figure 5 presens a flowchar ha describes he CA algorihm srucure. CA ransiion rules driving he urban growh are programmed in ArcGIS hrough Visual Basic for Applicaions (VBA). The oldes hisorical classified TM image (1973) is used as inpu o he CA model over which he ransiion rules are applied o model he urban growh saring from his ime epoch. A polygon shapefile represening he ownships in he sudy area is overlaid over he inpu image (Figure 6). A oal of 24 ownships in he area are idenified. Figure 6. Township map of Indianapolis Figure 5. Flowchar of CA algorihm design Transiion rules definiion is he mos imporan phase in CA model design since hey ranslae he effec of inpu daa on he urban process simulaion. So an accurae and realisic definiion of he rules is needed. The CA algorihm design sars wih defining he ransiion rules ha drive he urban growh over ime. They are designed as a funcion of land use effec on urban process, growh consrains and populaion densiy. The ransiion rules are defined over he 3x3 neighbourhood of a pixel o minimize he number of inpu variables o he model. The rules idenify he neighbourhood needed for he esed cell o urbanize. The growh consrains should reflec he conservaion sraegy adoped in he sudy area for cerain land uses. For example, conservaion of cerain species of naural resources can be aken ino consideraion hrough rules definiion sage. Waer resources proecion hrough discouraging urban growh nearby hese sies o reserve hem over ime is anoher example of consrained rules design. The fuure sae of a pixel (Equaion 2) a ime (+1) from saring ime () depends on hree facors: - Curren sae of he es pixel. - Curren saes of is neighbourhood pixels - Transiion rules ha drive he urban growh over ime. +1 S ( ) = ( f S ( ), S ( ), ransiion _ rules) α α τ (2) where S +1 ( α ) = es pixel fuure sae a ime epoch +1. S ( α ) = es pixel curren sae a ime epoch. S ( τ ) = neighbourhood pixels saes se. Dividing he sudy area on a ownship basis will ake ino consideraion he effec of sie specific feaures in each ownship on he urban growh. The same CA ransiion rules are defined for each ownship, however, wih differen rule values. Calibraion in he nex secion will discuss finding he opimal rule values for each ownship. 4.2 CA Model Calibraion Once he CA ransiion rules are idenified and iniialized for each ownship, he model runs from 1973 ill The year 1982 image represens he firs ground ruh being used for calibraion. For each ownship, he modeling accuracy is calculaed as a raio beween he simulaed and real urban growh daa (Equaion 3) for simulaed 1982 image. Over/underesimaion concep is inroduced o represen how comparable is he simulaed resul o he real one. This indicaes how ransiion rules defined on a ownship basis succeed in modeling he real amoun of urban growh given he predefined condiions. Calibraion in his work is mean o find he bes se of rule values specific o each ownship for realisic urban growh modeling. Simulaed urban class Accurracy = 100% (3) real urban class Calibraion aims o define he bes se of CA rules based on which he model run o mach as close as possible he simulaed resuls wih he ground ruh images. To achieve his purpose, wo calibraion schemes are inroduced in his algorihm: spaial and emporal calibraions. In spaial calibraion module, he CA ransiion rules a a given ime (=1982 in our case) are

4 modified spaially over he 2D grid space. This is done hrough uning he values of each rule se on a ownship basis o mach he urban dynamics for each ownship wih is sie specific feaures. This allows he model o ake he variabiliy in he spaial urban growh paern ino accouns for realisic modeling. If he ownship rules resul in higher growh levels (overesimaed), hey are modified o reduce he urban growh a his ownship. For he underesimaion case, he rule values of he ownship under consideraion are uned o increase he amoun of urban growh o mach he real one. So, he spaial calibraion aims o find he bes se of rule values ha fi a given ownship k according o is geographical locaion: X(k), inpu daa parameers: C(k) and is over/underesimaion case: OAE (k) as shown in Equaion 4. Townships close o each oher in erm of geographical locaion and having similar urban growh characerisics (e.g. same developmen level over ime) are associaed wih he same rule values. The overall calibraion over he enire es image a ime epoch is obained hrough performing he same spaial calibraion by aking he average of all ownships as shown in Equaion 5. Once he rule values are modified spaially, he model runs again from 1973 o 1982, he modeling accuracy is evaluaed for each ownship and rules are calibraed once again as illusraed above. This loop coninues ill he defined convergence crierion is me (Equaion 6). In our work convergence crierion of 100%±10% accuracy is used. The rule values afer convergence will be used for he nex ime period modeling. The model will be calibraed a he nex ground ruh image o ake ino consideraion he emporal effec. where SC epoch, = f ( X ( k), C( k), OAE( k)) (4) 24 epoch, = epoch, l= 1 OC SC ( l) FC { Converge( Loop( OCepoch ) } epoch,, (5) = (6) SC = spaial calibraion a ime epoch. epoch, OC = over all calibraion a ime epoch. epoch, FC = final calibraion a ime epoch. epoch, The final calibraed rules a 1982 are used o run he model ill he nex ground ruh image 1987 o perform emporal calibraion. The goal behind he emporal calibraion is o recalibrae he model so ha he model can adap he urban growh paern over ime (Equaion 7). This way any growh variaion over ime relaed o new policy or new infrasrucure plans can be learned by he model and he modeling resuls become more realisic. The emporal calibraion module is a funcion of changes in spaial calibraion resuls beween wo epochs and +1, growh change, and accuracy. TC = (,, ) (, 1) f FC + (, + 1) UG Accuracy where (7) TC = emporal calibraion beween epochs (, + 1) and +1. FC = changes in spaial calibraion resuls (, + 1) beween epochs and +1. UG = urban growh change beween and +1. The same spaial calibraion process a 1982 is repeaed a 1987 ground ruh ill convergence. The final calibraed rule values a 1987 are used o predic he urban growh a 1992 for shor erm predicion of 5 years (Figure 7a). The firs es image a 1992 is used o validae he model hrough evaluaing he predicion resuls a 1992 on a ownship basis. Table 1 summarizes he predicion resuls accuracies for year The rules are calibraed spaially again a 1992 o perform long erm predicion of 11 years from 1992 ill 2003 (Figure 7b) ha are validaed using he es image a Table 1 shows he predicion accuracy for prediced image a Resuls and Discussion The predicion resuls of 1992 and 2003 show good accuracy on he ownship basis and on he average scale. Accuracy for shor erm predicion (1992) is higher as comparing wih long erm predicion inerval (2003). The improvemen in he accuracy over space for each ownship is noiceable as a resul of he spaial calibraion module. Temporal calibraion also helps improve he predicion accuracy resuls over ime. The spaial calibraion a specific ime epoch succeeds in reducing he variabiliy in modeling accuracy beween ownships hrough maching each ownship ransiion rules wih is sie specific feaures. Spaial and emporal calibraions succeed in capuring he urban growh paern over space and ime based on real growh facors. Hisorical saellie imagery fis he spaial and emporal naure of he developed CA urban growh model. I provides imporan informaion inpu o he model. 4.4 Evaluaion and Analysis Predicion accuracy for each ownship is used as a basis for rule calibraion. Over/under esimaion principle is implemened. If a se of rules for a paricular ownship produces underesimaed resuls, his mean he growh rae is small and hence he rules are modified o increase he urban growh. For overesimaion, he rules are modified o reduce he urban growh amoun. The ransiion rules for a ownship are repeaedly calibraed ill he convergence crierion is me. The ground ruh imagery provides he reference for calibraion process. Table 1 resuls indicae good spaial predicion accuracy ranging for year 1992 beween 78.32% (underesimae) for ownship 17 up o % (overesimae) for ownship 1. The range for year 2003 is beween 67.78% and %. The average accuracies for 1992 and 2003 are 98.35% and 94.57%, respecively. Higher accuracies achieved for shor erm predicion (1992) as compared o long erm (2003). The spaial variabiliy beween ownships predicion resuls afer calibraion is small for boh (1992 and 2003) predicions. This indicaes he effec of spaial calibraion in maching each ownship wih is realisic urban growh paern hrough calibraing is rules o fi such paern. Visually, calibraion on a ownship basis succeeds in preserving he urban paern over space where emporal calibraion preserves is dynamical changes over ime. Rule values resuls a he end of he calibraion process indicae some similariy beween ownships. These ownships are close o each oher geographically and wih similar urban growh characerisics. 5. TRANSITION RULE CALIBRATION This secion inroduces briefly an ongoing sudy on using geneics algorihm (GA) o auomae he spaial and emporal rule calibraions. GA as a heurisic opimizaion echnique can work over he search space o find he mos suiable soluion. GA improves he efficiency of rule calibraion o selec he bes se of rule values for accurae modeling. GA is firs inroduced by Holland (1975) as compuer programs o mimic he evoluionary processes in naure. GA manipulaes a se of feasible soluions o find an opimal soluion.

5 a. Resul of year 1992 predicion (5 years) Table 1. Year 1992 and 2003 predicion resuls Township# Accuracy(%), Accuracy(%), Average Sd. Dev. b. Resul of year 2003 predicion (11 years) Figure 7. Cellular auomaa predicion resuls GA s is able o find he global opimum soluion. The following seps describe he design of he proposed GA-based ransiion rule calibraion. Sep 1: Iniial GA populaion generaion In his sep, 30 ses of rule values are randomly generaed as an iniial populaion for each ownship over which GA module will work. Each rule value se is coded as a binary sring. A sring is designed as a combinaion of he rule values. Three rules are idenified o be opimized using GA: Rule1: The number of neighbourhood residenial pixels, in he possible range of [0-8] ineger values or in corresponding binary coding [0000 o 1000]. Rule2: The number of neighbourhood commercial pixels, in he possible range of [0-8] ineger values or in corresponding binary coding [0000 o 1000]. Rule3: The populaion densiy hreshold, coninuous values represening he cu-off of populaion densiy a a pixel. This rule is scaled by muliplying is value by 10 in he range of [020] possible values or in binary coding [00000 o 10100]. All he rules are combined o form one binary sring. Sep 2: Finess funcion idenificaion Finess funcion evaluaes he performance of each sring. The predicion accuracy is used as he finess funcion Sep 3: GA selecion operaion Rank selecion procedure is used in his work. All he srings are ordered based on heir finess values in descending order and he sring wih highes finess value is given rank 30 hen he second one 29 ill lowes finess value wih rank 1. Rank is divided by he summaion of all he ranks and he probabiliy of selecion for each sring in nex generaion is idenified. Sep 4: GA crossover and muaion parameers design The crossover probabiliy is seleced o be 80%, 24 srings are seleced for crossover, while he oher 6 (he bes 6 in erms of finess values) are copied direcly o he new generaion (his process is known in GA as Eliism). Eliism can rapidly increase he performance of GA, because i prevens a loss of he bes soluion. A muaion rae of 1% is used. Once he crossover and muaion is done, he new generaion of 30 srings is already produced. The nex sep is o run he CA model using he new srings o evaluae heir new finess values. Sep 5: Running he GA-CA model All he seps from 1 o 4 are repeaed ill convergence. GA model works again over he newly creaed 30 srings and a new generaion of 30 srings is produced and he loop coninues. This coninues unil he convergence crierion is me. The final oupu is he opimized CA rule values for each ownship ha model he emporal urban growh. The model is run over he images from 1973 ill 1982 o calibrae is ransiion rules. The final resuls (Figure 8 and Table 2) indicae saisfacory resuls as compared o he crisp CA mehod. 6. CONCLUDING REMARKS This work explores he poenial of implemening he cellular auomaa o model he hisorical urban growh over Indianapolis. The main goal is o design he model as a funcion

6 of local neighbourhood srucure o minimize he inpu daa o he model. Saellie imagery represens he medium over which he model works. One imporan issue our model akes ino accoun is he calibraion process. Two modules are inroduced namely, spaial and emporal calibraions. Spaial calibraion fis he model on a ownship basis o is sie specific feaure while he emporal calibraion adaps i o he urban growh dynamic change over ime. This shows a noiceable effec on producing a good spaial mach beween he real and simulaed image daa. On he oher hand, geneic algorihm is inroduced o enhance he CA calibraion process. GA makes he calibraion process more efficien hrough manipulaing a se of feasible soluions in he search space o find an opimal soluion. This will reduce he search space for he opimal rules values on a ownship basis. REFERENCES Bay, M., and Xie, Y., 1994a. From cells o ciies. Environmen and Planning, B21, pp Bay, M., Urban evoluion on he deskop: simulaion wih he use of exended cellular auomaa. Environmen and Planning A, 30, pp Clarke, K. C., Hoppen, S., and Gaydos, L., A selfmodifying cellular auomaon model of hisorical urbanizaion in he San Francisco Bay area. Environmen and planning B, 24, pp Clarke, K. C., and Gaydos, L. J., Loose-coupling a cellular auomaon model and GIS: long-erm urban growh predicion for San Francisco and Washingon/Balimore. Inernaional Journal of Geographical Informaion Sciences, 12, pp Hagersrand, T., Innovaion Diffusion as a Spaial Process (Universiy of Chicago Press, Chicago, IL). Holland, J.H., Adapaion in Naural and Arificial Sysems, Univ. of Michigan Press, Ann Arbor, MI. Li, X., and Yeh, A. G. O., Error propagaion and model uncerainies of cellular auomaa in urban simulaion wih GIS. In: 7h Inernaional Conference on GeoCompuaion, 8-10 Sepember 2003, Universiy of Souhampon, Souhampon, UK (GeoCompuaion CD-ROM). Figure 8. GA-CA calibraed image for year 1982 Table 2. GA-CA calibraed resuls for year 1982 Township# Urban Pixel # Accuracy(%) % % % % % % % % % % % % % % % % % % % % % % % % Average 87.63% Sd. Dev 13.73% Tobler, W., Cellular geography, in Philosophy. In: Geography Eds S Gale, G Olsson (D Reidel, Dordrech), pp von Neumann, J., Theory of Self-Reproducing Auomaa. Universiy of Illinois Press, Illinois. Edied and compleed by A. W. Burks. Waldrop, M., Complexiy: The Emerging Science a he Edge of Order and Chaos (New York: Simon and Schuser). Wolfram, S., Cellular auomaa. In: Cellular Auomaa and Complexiy: Colleced Papers (Addison Wesley, Seven Wolfram, Reading, MA). Yang, X., and Lo, C. P., Modelling urban growh and landscape changes in he Alana meropolian area. Inernaional Journal of Geographical Informaion Science, 17, pp