A COMBINED AUTOMATED GENERALIZATION MODEL OF SPATIAL ACTIVE OBJECTS

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1 A COMBINED AUTOMATED GENERALIZATION MODEL OF SPATIAL ACTIVE OBJECTS J. Joubran Abu Daoud, Y. Doytsher Faculty of Cvl and Envronmental Engneerng Department of Transportaton and Geo-Informaton Engneerng Technon- Israel Insttute of Technology, 3000 Hafa, Israel (jacquele, Commsson IV, WG IV/3 KEY WORDS: Generalzaton, Cartography, GIS, Automaton, Analyss, Data Mnng, ABSTRACT: Automatng the map generalzaton process has tradtonally been a major focus of research n cartography and GIS envronment. Many algorthms and models have been developed over the past three decades, startng wth the lne smplfcaton algorthms and endng wth Clarty the new envronment employng AGENTS, JAVA, XML and Topology. Although automaton of cartographc generalzaton has been a feld of extensve research, a method of usable holstc understandng generalzaton s stll lackng. The model for combned generalzaton descrbed n ths paper, s ntended to ntate a method that understands and descrbes the acton and behavour of actve objects n the map generalzaton process. The paper focuses on the object propertes analyss n order to determne the power of each object n any gven map, and the nteractons between these powers. These nteractons produce "forces" that act on the objects and control ther behavour accordng to the cartographc constrants. 1. INTRODUCTION Cartographc generalzaton ams at smplfyng the representaton of cartographc data to sut the scale and purpose of the map. Although automaton of cartographc generalzaton has been a feld of extensve research (Muller et al 1995, Webel & Jones 1998, Rchardson & Mackaness 1999, and many others), there s stll a lack of a usable holstc understandng generalzaton method. Successful mplementaton of a generalzaton process s supposed to produce a good map that satsfes the cartographc requrements, rules and constrants. Recently several methods have been developed based on constrants and rules defnton (Raus & Plazanet 1996, Harre 1999, Sester 000, Raus 000, Harre 003). However, t s clear that more research on the defnton and the formulaton of the rules and the constrants to be used s needed. The man ssue of the generalzaton process s to determne where the conflcts are and how to solve them wthout creatng new conflcts. The objects n the map must not be treated n solaton, and the combned generalzaton should model the relatonshp between the objects and the way they affect each other. Several authors (Ware & Jones 1998, Sajakosk & Klpelanen 1999, Sester 000) have already suggested such holstc process; however, no soluton has been presented for the mplementaton of the complete generalzaton process n a sngle contnuous step. The research descrbed n ths paper examnes behavour of the map objects and the nteractons between them n order to understand the generalzaton process. The developed model defnes several parameters that determne for each object a "power" n the map, and set rules to control the mutual nteracton forces between these powers n order to compromse between the constrants and solve the competton between the objects on the lmted map area at a reduced scale. The parameters are dependent on the object propertes (area, type, stffness, and shape) on the one hand, and the area propertes (densty, empty area surroundng an object, the map target, and the map scale) on the other. Each object acts accordng to ts power, computed as a functon of ts propertes and these parameters. Interactons between map objects are expressed by actons of the forces constructed around the cartographc constrants and affected by several parameters dependng on the propertes of the surroundng objects. The combned generalzaton model takes nto consderaton the surroundng objects and defnes ther propertes, such as dstance, type, densty and topology. As a result, the surroundng objects affect and cause the weak objects to change ther shape or place. The mplementaton of ths new method requres: (1) determnaton of quanttes and thresholds of each parameter, () defnton of the rules and the constrants of each force acton, and fnally (3) translaton of the results nto one or more of the generalzaton operators - dsplacement, aggregaton, selecton, and enlargement. Due to the lmted scope of ths artcle, we wll dscuss the nteracton among objects belongng to only one layer, buldngs. Ths paper wll present the new combned generalzaton method of cartographc generalzaton, ts mplementaton, tests on a real data subset, and the results acheved.. CARTOGRAPHIC OBJECTS AND THEIR PROPERTIES The objects n the map are treated accordng to ther propertes, ther type, and what they represent. The cartographc map generalzaton at a requred scale s a process of competton

2 among the objects over the map area. Each object has ts own power as a functon of ts propertes, the surroundng objects, map scale, and map type. Ths power controls the behavor of the object n the generalzaton process n accordance wth the cartographc rules..1 Basc Object Parameter The basc parameter n the generalzaton process s the object area at the scale of the new map. The object symbol has ts locaton, ts dmenson, and ts relatve mportance among other objects, accordng to the map type. The same objects may be of dfferent relatve mportance when plotted on dfferent maps for dfferent uses.. Shape Analyss Methods Many cartographc objects represented on large scale maps can be consdered to be geometrc objects n the form of polygons or closed polylnes. These geometrc objects could be descrbed by the set of shape parameters, consstng of, but not lmted to, numercal values and topologcal descrptors (Guenko & Doytsher 003). The shape analyss methods themselves could be formally classfed by certan parameters. There are two major groups of shape analyss methods: boundary technques (external analyss) and global technques (nternal analyss). These methods are applcable to dfferent representatons of the same object. Ths paper, however, focuses on the objects as polygons n vector format, derved from GIS databases...1 Major Geometrc Shape Parameters The followng major parameters can be used to descrbe the shape of geometrc objects n polygon form: area, permeter, centrod, major axes and angle, elongaton, compactness, soldty and convexty (Guenko & Doytsher 003). The frst fve parameters could be calculated usng moments. Usng moments for shape descrpton was ntated by (Hu, 196), who proved that moment based shape descrpton s nformaton preservng. Ths study concentrates on the second moment, the moment of nerta that can be used to determne the prncpal axes of the shape. Moment nerta can be computed n respect to the object shape by ts vertces or by ts edges. Usng the length of the edges of a polygon rather than ts vertces s preferable as t s ndependent of the number and densty of vertces and s a functon of the polygon shape only (Doytsher 1979). Thus, the moment nerta computed hereafter s based on edges, wth weghts proportonal to ther lengths. Therefore, the moment for the two major axes n ths study s calculated as follows: (1) Ixx ( y y ) dx A c dx y1 y, y, dx x 1 x also provde useful and mportant nformaton about the object s shape (Guenko & Doytsher 003). These parameters are calculated as follows: 4 Area (3) compactness, permeter sqrt( dx dy ) permeter ( 4).3 Spatal Analyss soldty area convexarae One of the well-known methods of spatal data analyss s spatal data mnng; a feld dealng wth producng new spatal data from exstng data. Data mnng s facltated by utlzng shapes or propertes whch are not explctly expressed n the orgnal databases, and s performed wthout changng them (Kang 1997). Databases kept n GI systems consttute a vald potental for data mnng due to the vast and dversfed data stored n them. In ths study spatal data analyss s attaned by mplementaton of the Delaunay Trangulaton and Rngs analyss. Both methods allow producng large quanttes of nformaton about the data, densty and shape, even though no prevous explct knowledge exsted regardng these propertes..3.1 Delaunay Trangulaton Generally, trangulaton of a planmetrc surface s the method of dvdng the surface nto a fnte number of trangles. Ths method s the key tool for handlng problems requrng solutons based on area dvson accordng to the prncples of fnte element theory. There are number of methods for performng trangulaton, of whch the Delaunay trangulaton s preferred for cartographc purposes, snce t supples trangles wth the shortest edges. At the frst stage, a constraned Delaunay trangulaton s performed n order to nclude the polygons or lne edges, descrbng the objects as part of trangle edges. The trangles n the trangulated surface are dvded nto two groups: 1) trangles contaned wthn objects, and ) trangles stretched between objects n the ntermedate space (Joubran & Gabay 000). It s the edges of the second group trangles, or ther area that serve as an ndcator of data densty n the regon surroundng a gven object. The area of the empty trangles surroundng each object and the average length of ther edges determne ts densty and the surroundng free area. The surroundng objects between whch and a gven object these trangles are stretched, affect the object s densty and behavor, and are therefore defned n ths study as "neghbor objects". () Iyy ( x x ) dy A c dy x1 x, x, dy y 1 y In order to obtan effectve nformaton on the shape of the object, the rato between the moments s also calculated (rato between the larger and the smaller moments). When the numercal value of the rato s close to 1, t ndcates that the shape s approxmately a square, and t s more stable than a prolonged shape (wth a numercal rato fgure much hgher than 1). Other parameters lke compactness and soldty, can Fgure 1. Sample of Delaunay trangulaton - surroundng trangles stretched between an object and ts neghbors

.3. Rng Analyss Spatal analyss of the surroundng area of each object s performed by dvdng the area nto rngs around the mnmal crcumscrbng rectangle (Doytsher 1988).

We thus started wth the rng closest to the mnmum rectangle crcumscrbng the object. The effect of each rng on the densty determnaton s calculated as follows: Fgure 4.

Rng analyss by 4 dfferent sdes It was found that the wdth of the rngs should be defned as dentcal to the cartographc tolerance based on the scale of the desred map.

3 .3. Rng Analyss Spatal analyss of the surroundng area of each object s performed by dvdng the area nto rngs around the mnmal crcumscrbng rectangle (Doytsher 1988). The rng analyss method s based on gvng a larger weght to rngs closer to the object. It descrbes the effect of surroundng objects and the mportance of the dstance between them. We thus started wth the rng closest to the mnmum rectangle crcumscrbng the object. The effect of each rng on the densty determnaton s calculated as follows: Fgure 4. Sde analyss Each object and ts mnmum crcumscrbng rectangle s analyzed as demonstrated n Fgure 5. Fgure. Rng analyss method (5) Densty AW rng _ area W Fgure 5. Rng analyss by 4 dfferent sdes It was found that the wdth of the rngs should be defned as dentcal to the cartographc tolerance based on the scale of the desred map. The number of the rngs s a functon of the rngs wdth and the area of the surroundng free regon for each object. Where: A s the area of the objects contaned n the rng W s the weght of a certan rng Ths equaton, when used n the example below, produces the requred results, where objects n the mddle of a gven area have hgher densty values than objects on the boundares of ths gven area. Rngs _ area object _ area object _ free _ surroundn _ area Rngs _ area ( ab * Rngs _ number * rngs _ wdth)^ ab ( a b) / (6) Rngs _ number Rngs _ area ab It was found by several experments wth a satsfactory result that accordng to ths equaton the number of requred rngs around each object s almost the same. Thus, more or less the same weght was assgned to each of the rngs surroundng the dfferent objects. a1 Rngs _ number (7) a n 1 frst rng weght a a j 1 n j Fgure 3. Densty values of set of buldngs In order to be more precse about the way the objects are scattered n a gven rng, the rngs were dvded nto four parts wth the free area and the mnmum dstance between other object are calculated n each part. The followng examples demonstrate the need for such sub-analyss method: 3. METHOD OF PERFORMANCE Several requrements must be fulflled n the generalzaton process. A possble framework for automatc generalzaton s to formulate these requrements as constrants and let them control the process (Beard, 1991). The major dfference between rules and constrants s that the rules state what s to be done and constrants state what results should be obtaned (Harre, 003). Snce t s dffcult to formalze the

generalzaton process n the form of rules, several authors have proposed and used constrants n the generalzaton process (e.g. Brassel & Webel 1988, Ruas & Plazanet 1996, Harre 1999, Ruas 000).

4 generalzaton process n the form of rules, several authors have proposed and used constrants n the generalzaton process (e.g. Brassel & Webel 1988, Ruas & Plazanet 1996, Harre 1999, Ruas 000). In ths study, the generalzaton process s controlled by the power of objects. These powers have been determned and thus affect and act accordng to the process rules. The forces that are "developed" n each object as a result of the powers acton are translated accordng to ts value and drecton to sut the generalzaton operator n respect to the process constrants. 3.1 Object Power Determnaton An analogy to the nteracton among a large number of objects can be found n electrc feld theory. In an electrc feld each object acts accordng to ts power, affects ts neghbors and s n turn affected by them. In ths study, t s suggested to mplement the electrc feld theory, assumng that the map generalzaton process wll be based on powers of the map s features affectng each other. The power s determned as a functon of the object s propertes, locaton, and the surroundng area and objects. The acton of the power acton controls the object s behavor, thus t has to be calculated carefully, takng nto account all affectng elements. Object Propertes The am of ths research s to establsh a model for a combned generalzaton, where the powers are calculated and determned n order to be able to hghlght the dfferent qualtes of each ndvdual object. The area s a very mportant element n such a process; snce a bgger object has a hgher power value. Dfferent objects have dfferent factors under the cartographc rules (e.g., trees mght be moved easer than buldngs). Accordng to the map type each object has ts relatve mportance value (e.g. n a tourst map hotels wll be more hghlghted than prvate houses). In a smlar manner, hgh buldngs should be "stronger" than low buldngs, and the process prefers not to change ther shape or move ther locaton. Square buldngs should be "stronger" than rectangular or elongated ones. In analogy to the electrc feld theory, the power contaned n each object wll be calculated as a functon of the followng object propertes: Area Surroundng an Object The area surroundng an object affects ts behavor as well. Objects can be located n a dense urban area, or "solated" n a rural area. Objects wth a hgher densty value resultng from more objects n the surroundng area should be "stronger" beng practcally unable to change ther shape or moved from ther locaton. The values of all these elements were chosen n proporton to the expected power (larger values vs. larger power), and therefore, the power can be calculated as follows: ( 10) power area * shape * heght * elastc * Im por tan ce * densty 3. Forces between Objects The forces between neghborng objects express the nteracton between them. Returnng to the electrc feld theory, each object has ts "electrc charge", and attracton or rejecton forces control ther movements. When adoptng the same behavor or nteracton model, the forces between the objects n the map are computed as follows: (11) Force a, b G *( P R P ) a a, b The force between two objects s a drect functon of the dfference between both powers. Thus, the same style and power objects won t affect each other. However, there s an nverse functon expressng the dstance between the objects and ther effect, wth close objects havng a stronger effect. 3..1Mnmal Dstance between Neghborng Objects It was determned that the approach should be to calculate the dstance between objects as the mnmal dstance between the convex hulls crcumscrbng the objects as shown n Fgure 6. b 1. Area: calculated at the scale of the map (sze of the plotted object or ts plotted symbol).. Shape: calculated as a functon of the compactness, soldty, and second axes moment rato: soldty * compactness (8) Ishape rato max( I xx, I yy ) (9) rato mn( I, I xx yy) 3. Heght: a normalzed value, gven to D objects lke roads, and sngle story houses. The value s ncreased for multstory buldngs. 4. Type: an elastc value for each object descrbng ts "materal" accordng cartographc rules and map content. 5. Importance n the map: normalzed values accordng to the map type. Fgure 6. Mnmum dstance between convex hulls 3.. Drecton of Forces between Objects The crtcal zones n a map are located where there s mnmum dstance between neghborng objects, especally f that dstance causes a spatal conflct. The goal of the combned

generalzaton process s to ncrease the dstance between objects by movng the weaker objects.

affectng the weaker object. 3.3 Implementng Actons of Forces The actons of forces on each object control and determne ts behavor.

Alternatvely, based on the type of the object and ts surroundng objects, the object wll be clustered wth them f they are all of the same type and endowed wth more or less the same power level.

5 generalzaton process s to ncrease the dstance between objects by movng the weaker objects. In order to acheve ths goal, the forces actng from the mass center of the object towards the mnmal dstance need to be calculated, wth the drecton of the force ssung from the stronger object and affectng the weaker object. 3.3 Implementng Actons of Forces The actons of forces on each object control and determne ts behavor. A mddle object wth many forces from surroundng objects s under hgher rsk of beng deleted f the surroundng objects are much stronger. Alternatvely, based on the type of the object and ts surroundng objects, the object wll be clustered wth them f they are all of the same type and endowed wth more or less the same power level. A spatal conflct s resolved by dsplacng the weaker object n accordance wth the value and the drecton of the unfed force affectng t. 4. RESULTS Fgure 8. Number of calculated rngs Thus, each object has ts power value calculated as a functon of the densty derved from the rngs analyss, and shape parameters. The values of the powers are presented n Fgure 9, as a "colored scheme". In ths chapter the suggested method s demonstrated on a group of polygonal enttes. A map of buldngs n a certan area s gven, each buldng s descrbed as a closed polygon composed of a known number of vertces. The numerc parameters for each object are calculated the area of the polygon, ts permeter and ts compactness. A convex hull crcumscrbng the polygon, and the mnmal rectangle crcumscrbng the convex hull are computed. The determnaton of prncpal axes enables computng the polygon soldty and thus the orentaton of the surroundng rngs for the fttng rngs analyss. A constraned Delaunay Trangulaton s appled by forcng the buldng edges to become part of the trangle edges formed by the trangulaton, as depcted n Fgure 7. Fgure 9. Powers values of buldngs Interacton between the buldng powers produces and s expressed by forces as shown n Fgure 10. Large numercal values of forces evolvng between close objects are a warnng of potental spatal conflct. Fgure 7. Constraned Delaunay trangulaton The free surroundng area for each object was calculated as the sum of the area of the trangles stretched between a gven object and surroundng objects n the ntermedate space. The surroundng objects connected to the free area of the gven object are defned as ts "affectng neghbors". Tolerance may be calculated accordng to the desred map scale and rngs analyss. The wdth of the rngs s equal to the tolerance value and the number of rngs s calculated as a functon of rng wdth, object area and ts free surroundng area. As depcted n Fgure 8, the number of rngs needed for the dfferent buldngs of the gven set as shown n the hstogram, s about the same for all buldngs. Fgure 10. A force solvng spatal conflct The fnal results are derved from translatng the acton of forces to the sutable generalzaton operator accordng to the value of the balance of forces and ts drecton as follows (Fgure 11):

6 Guenko G., Doytsher Y., 003. GIS Data for Supportng Feature Extracton from Hgh Resoluton Aeral and Satellte Images. Journal of Surveyng Engneerng ASCE. Clusterng Harre, L., 003. Weght settng and Qualty Assessment n smultaneous Graphc Generalzaton. The Cartographc Journal, Vol. 40 No. 3, pp Harre, L., The Constrant Method for Solvng Spatal Conflcts n Cartographc Generalzaton. Cartography and Geographc Informaton System, Vol. 6, No. 1, pp Fgure 11. Forces & generalzaton operators 5. DISCUSSIONS AND FUTURE WORK The method presented here for a new model of combned generalzaton, makes use of spatal data mnng to understand the propertes of objects and of topology n order to determne ther behavor n the generalzaton process. The algorthm examnes the generalzaton process from a new standpont that vews the map as a stage n area warfare. Each object has ts power and the forces control the object s fnal poston. Experment results on a lmted level ndcated mplementaton of the method on objects belongng to a sngle layer of buldngs. Addtonal work s stll requred. A more thorough nvestgaton of object behavor n the generalzaton process requres addng addtonal layers of objects, handlng lnear objects concurrently wth polygonal objects, and dealng wth the topologcal relatonshp between the dfferent layers. REFERENCES Deleton Dsplacement Trees Shape changng Hu, M. k., 196. Vsual Pattern Recognton by Moment Invarants. IRE Trans. Inf. Theory, 8, Joubran, J., and Gabay, Y., 000. A Method for Constructon of D Hull for Generalzed Cartographc Representaton. Proceedngs 9 th Congress of ISPRS, Amsterdam, Netherlands, PP Muller, J.C., Webel, R., Lagrange, J.P., Sagle, F., Genralzaton: State of the art and ssues. In: GIS and Generalzaton: methodology and practce, J.C. Muller, J.P. Lagrange and R. Webel eds., Taylor and Francs, Pp Ruas, A., 000. The Role of Meso Objects for Generalzaton. Proceedngs of the 9 th Spatal Data Handlng Symposum, Bejng, Pp. 3b. 50-3b. 63. Ruas, A., and Plazent, C. 1996, Strateges for Automated Generalzaton. Advances n GIS Research, SDH 96, pp Rchardson, D. E., Mackaness, A. W., Computatonal Processes for Map Generalzaton.(Introducton). Cartography and Geographcal Informaton System, Vol. 6, No. 1, pp Sarjakosk, T., Klpelane, T., Holstc Cartographc Generalzaton by Least Adjustment for Large Data sets, In: Proceedng ICA, Internatonal Cartographc n Canada, Sesson 39-D, Index 08, pp Sester, M., 000. Generalzaton Based on Least Square Adjustment. Internatonal Archves of Photogrammetry and Remote Sensng, Vol., Part B4. Amsterdam, pp Ware, J. M., Jones, C. B., Conflct Reducton n Map Generalzaton Usng Iteratve Improvement. GeoInformatca, Vol., No. 4, pp: Webel, R., Jones, C. B., Computatonal Perspectve on Map Generalzaton. GeoInformatca, Vol., No. 4, pp: Brassel, K. E., and Webel, R A Revew and Conceptual Framework of Automated Map Generalzaton. Intennatonal Journal of Geographcal Informaton Systems, Vol., pp Doytsher Y., Methods and Software for Creatng Data- Bases for Town Plannng Compatble for Mn-Computers, 7th European Symposum - Urban Data Management, Hague, The Netherlands.

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