UTILISATION OF ARTIFICIAL INTELLIGENCE METHODS AND

NEUROFUZZY ALGORITHMS IN THE PROCESS OF DIGITAL TERRAIN MODEL GENERALISATION

Olszewski R.

Department of Cartography, Warsaw University of Technology, Poland

Abstract Correct generalisation of the DTM is particularly important for supplying Geograohic Information Systems (GIS).

In order to perform reliable spatial analyses it is extremely important that the real locations of characteristic points of key terrain features remain unchanged. Therefore, the process of generalisation should operate as the process of DLM generalisation and not as the cartographic generalisation process. Automation of multiscale DTM modelling, understood in this way, requires utilisation of local filtration methods.

Modification of the method of construction of the hierarchical TIN model has been proposed in the paper, which utilises weighting of model source points, basing on pre-defined structural lines of the terrain relief. Such modification, with simultaneous maintenance of the general idea of the multiscale TIN model, allows for representation of the DTM in the form of a triangular irregular network at the arbitrary level of geometric accuracy.

Utilisation of the �inference engine� in the form of NEURO and FUZZY allows for considerably higher flexibility of the approach to generalisation of spatial data comparing to conventional solutions (CRISP version). The digital application, developed by the author, allows also to maintain significant topological relations between structural lines, which create the �skeleton� of the terrain. Introduction

Issues concerning modelling and presentation of terrain relief are the basic issues of conventional, as well as contemporary cartography. In 1866 E. Sydow defined three basic issues of cartography � calling them �the reefs�:

1. presentation of the spheroidal Earth�s surface on a plane, 2. presentation of terrain relief, 3. cartographic generalisation.

Although these issues were described in the middle of the 19th century, they are still considered as the basic issues of the contemporary cartography. Wide utilisation of digital information stored in spatial databases and common utilisation of GIS analytical tools result in the necessity of re-definition of problems related to terrain relief modelling at various levels of generalisation.

In Poland, intensive works have been performed which concern the development of the idea of SDI (Spatial Data Infrastructure) and integration of spatial data stored in reference databases: the General Geographical Database, the VMap database and the Topographic Database. The Digital Terrain Model is an important component of each of those databases.

The necessity of integration of reference data leads to the necessity of consideration of the idea of an integrated � multiscale reference database (D. Gotlib, A. Iwaniak, R. Olszewski, 2005). Utilisation of the MRDB concept (Mulitiresolution/Multirepresentation Database) seems reasonable in this context.

The existing concept of the development of the Digital Terrain Model (DTM) in the Topographic Database (TDB) assumes that the DTM files will be transferred to cartographic resources in TIN and GRID (with the resolution of 25 m) formats, in sectional division. The currently developed novelty of Technical Guidelines of the DTM component of the TDB database assumes that the terrain relief will be prepared as continuous, vector representation of terrain forms (structural lines, characteristic points, areas of exclusions, height spots etc.). Such way of source data collection allows for

development of procedures of automated selection of structural forms, which are representative for the given level of generalisation of structural forms of the terrain relief. This will also allow for development of the concept of the multiscale (hierarchical) representation of the terrain relief. The concept of multirepresentation digital terrain model is a logical amendment of the idea of multirepresentation topographic database and allows to perform common analyses of all topographic components (A. Makowski, 2004). Besides hierarchicalal approach to terrain relief modelling, in the case of development of the multiscale DTM, the method of source data generalisation is also important. From technological point of view it is possible to perform initial generalisation at the stage of topographic data acquisition, as well as to apply generalisation of the existing models. Due to topographic databases, stored as cartographic resources, consideration of the second concept, seems particularly reasonable.

Supplying medium- and small-scale GIS systems with data, as well as implementation of spatial analyses basing on generalised terrain relief models require detailed definitions of procedures of generalisation of DTM source data. The issues of the terrain relief generalisation (considered as generalisation of a model and not as conventional simplification of contour lines) is a complex issue with respect to concepts and technological solutions. General strategy of DTM generalisation

Generalisation is a method of a model generalisation of data, aiming at achievement of particular objectives. The most important feature of the process of spatial data generalisation is maintenance of the basic structure and the nature of geographic data. According to A. Makowski (2001), generalisation should be considered as an equivalent to the cartographic methods of modelling of reality. W. Ostrowski (2001) formulates similar opinions; he considers the process of cartographic generalisation as an equivalent process to development of the cartographic model, which aims at recognition of selected fragments of the geographic space. Although utilisation of computer-assisted tools is growing, the process of cartographic generalisation cannot be considered as a mechanical procedure of sequential utilisation of deterministic rules; it should be considered as �the process based on understanding� (R. Weibel, 1991). Recognition of the structure of generalised objects requires that cartometric analysis of their shapes, mutual relations and spatial diversification, are performed.

The basic feature of this concept is that two spatial data models and related types of generalisation, are distinguished in the process of data generalisation: cartographic generalisation (display-oriented) and model generalisation (analysis-oriented). Such diversification results from the nature of modelling of spatial data (diversified with respect to objectives of works) (D. Grünreich, 1995). In this approach two stages of works may be distinguished: the digital landscape model � DLM, and the digital cartographic model � DCM. The main DLM database contains real locations of objects and the DCM model contains data which are processed by cartographic edition. The essence of such diversification results from diversification of destination. Data from the DLM model supply geographic information systems, which are focused on spatial analyses, while data from the DCM model supply topographic maps production systems.

Methods of DTM generalisation

Generalisation of the terrain relief model (understood as generalisation of the DTM and not as generalisation of contour drawings) is connected with the utilisation of one of three methods (R. Weibel, 1992):

1. global filtration, 2. local filtration (usually multi-stage filtration), 3. utilisation of heuristic approach.

Global filtration consists of determination - for each DTM point � of the weighted mean value, calculated within a

moving window of a specified size. The number of model points remains constant, only values of particular points are changing. The method is mainly applied for the digital elevation models (GRID) (R. Olszewski, 2003).

Local filtration � generalisation of the model is performed by means of selection of source points. In this approach the

number of points, which determine the model, is decreased (with later possibility of linear model re-composition to the initial spatial resolution values). Points of low importance are eliminated from the source model (usually with the use of iterative methods). The importance of particular points is understood in this case as a vertical difference between the original value and the value interpolated from the model after elimination of the selected point. Selection of parameters of the method should allow for reconstruction of terrain relief forms with sufficient accuracy. This means that all characteristic points (peaks, depressions, passes etc.) must remain in the final DTM.

Heuristic approach is based on the concept of generalisation of structural lines of the terrain. This method may be applied for generalisation of the digital terrain models in TIN and GRID forms. On the contrary to the filtration methods discussed above, he heuristic approach consists of emulation of conventional manual techniques by utilisation of digital operators in the process of interactive co-operation between the operator and the computer system. Generalisation is based on generalisation of the source model of structural lines � SLM (structure line model) by means of utilisation of conventional operators of generalisation: elimination, merging, simplification, etc. of particular structural lines and then, of re-composition of the secondary DTM basing on the resultant SLM.

Hierarchical TIN model

Correct generalisation of the DTM is particularly important for supplying Geograohic Information Systems (GIS). In order to perform reliable spatial analyses it is extremely important that the real locations of characteristic points of key terrain features remain unchanged. Therefore, the process of generalisation should operate as the process of DLM generalisation and not as the cartographic generalisation process. Automation of multiscale DTM modelling, understood in this way, requires utilisation of local filtration methods. Many variations of that method exist. The most interesting ones include the additive method proposed by M. Heller (1990) and the method of hierarchical construction of the TIN model proposed by L. De Floriani (2002) and E. Danovaro (2003).

The method of local filtration in the above discussed, subtractive conventional form is practically applicable for small data files only (due to high complexity of calculations). The similar, additive method, known as the ATM (Adaptive Triangular Mesh), was proposed by M. Heller (1990). Selection of points is based on the importance of particular points for determination of a terrain form. Therefore, it is the information-oriented approach. De Floriani (2002) method of hierarchical construction of a TIN model allows for iterative elimination of points of low importance from the model. The considerable disadvantage of this method is elimination of points basing on the vertical distance criterion only. This does not allow to preserve particular terrain forms. The solution may be in this case utilisation of preliminary analysis of data and determination of particular structural forms. Bigger weights should be assigned to characteristic points than to mass points.

It has been assumed in performed investigations that in the process of construction of the hierarchical structure of the DTM, structural lines of the terrain relief should be determined and appropriate numerical weights should be assigned to those lines. In the process of the model generalisation, the importance of the nature of points (mass or structural of the specified order) is equal to the importance of its vertical significance. Therefore, the proposed method is a kind of combination of the local filtration and heuristic approach.

It has been assumed that, for the construction of the hierarchical (multiscale) DTM based on generalisation of important

morphological forms, correct determination of structural lines, which create �a topographic skeleton� of the area, is particularly important. Those lines were determined basing on direct surveys, on existing topographic maps, as well as basing on analysis of TIN and GRID models. The objective of performed investigations were the analysis whether it could be possible to automatically determine structural lines of the terrain basing on irregular (or regular) source data, which does not contain any additional information of structural forms. regular GRID structure Many algorithms of determination of structural lines of the terrain relief, basing on a regular model, exist (J. P. Wilson, J. C. Gallant 2000). The commonly of them are: D8 (deterministic eight node), Rho8 (random eight node) and DEMON (Digital Elevation MOdel Networks) (M. C. Costa-Cabral, S. J. Burges 1994). The majority of them consist of the advanced analysis of accumulation of potential surface run-off. This procedure may slightly differ depending on the applied GIS tool; however, obtained results are usually comparable. The modified D8 algorithm, implemented for the GM Grid 5.2 module, being a functional extension of the Intergraph GeoMedia Professional package, was applied for performed investigations. irregular TIN structure Many methods of determination of structural lines of the terrain relief, basing on analysis of TIN models (triangular irregular network), exist. One of the most interesting solutions was proposed by L. De Floriani, P. Magillo (2002) and Danovaro, P. Magillo, M. Mesmoudi (2003) as the method of hierarchical construction of the digital terrain model of the terrain relief. In theory, this approach allows to consider the morphological structure of the modelled surface. The most important feature of this method is the fully automatic determination of structural lines of the terrain relief basing on a set of distributed points. The algorithm is based on the, so-called, Morse-Smale Theory (S. Smale, 1960), developed by the authors from its original forms, corresponding to description of continuous and differentiable surfaces to modelling of structures composed of finite elements. The proposed decomposition of a statistical surface (Morse-Smale decomposition) allows for determination of �stable� and �unstable� areas. The multistage method of �area development� is used for

determination of such areas. Overlaying of stable and unstable areas allows for determination of structural lines of the analysed statistical surface (in particular case, the digital terrain model) (E. Danovaro, L. De Floriani, P. Magillo, M. Mesmoudi, E. Puppo (2003).

In performed investigations, which aimed at determination of structural lines of test sites, topographic maps, digital terrain models, GeoMedia Grid software and own digital application based on the algorithm of E. Danovaro, P. Magillo, M. Mesmoudi (2003) were used. Direct assumption of Morse-Smale structures has its consequences in the field of automation of the generalisation process of the digital terrain model, based on generalisation of skeleton lines.

Fig. 1. Determination of structural lines (Tatra Mountains) Comparing the system of skeleton lines for the fragment of Tatra Mountains (Fig. 1) obtained by means of four various methods: manual plotting basing on a topographic map (Fig. 1c), with the use of Morse-Smale decomposition (Fig. 1d) and with the use of GRID structure analysis for two different initial parameters (Fig. 1e,f), the following conclusions may be drawn:

� The system of skeleton lines obtained basing on Morse-Smale decomposition differs from the image of manually plotted skeleton lines more than the image obtained by means of the Grid software,

� Selection of parameters (the threshold number of pixels considered for the analysis) in GeoMedia Grid software highly influences the level of details of the obtained image of skeleton lines.

Therefore, performed investigations prove that the necessity to acquire structural lines of the terrain in the process of direct surveys should be considered as justified, for example by means of utilisation of photogrammetric techniques at the stage of acquisition of source data for the TDB database. Basing on the �terrain skeleton� determined in this way, it is possible to correctly generalise the terrain relief model, maintaining at the same time the important topological relations. In such an approach the basic terrain structure (structural lines) is determined at the stage of processing of survey data and not basing on analysis, performed in the postprocessing mode.

Investigations

The proposed concept of iterative elimination of points from the source model combines elements of the local filtration and heuristic approach. The basis for further analysis is division of source points of the model into structural and mass points, which is performed determination of structural lines of the terrain. In the process of generalisation points are eliminated basing on common evaluation of several criteria: their vertical significance (which is locally determined), density, and � for structural points � also the weight of a structural line and the local sinusoity of those lines. Selection of significance of particular factors is fully parameterised, what allows arbitrary assigning of weighting coefficients.

Besides elimination of points, maintenance of significant topological relations between structural lines, which create �the skeleton� of the area, is also important.

Implementation of such objectives required that own, digital application was developed, which allowed for development of the hierarchical TIN model by means of iterative elimination of points, basing on parameterised weighting coefficients, with maintenance of topology of the terrain relief. The author has developed programming libraries, which allow for parameterisation of weighting coefficients by means of three techniques: the conventional (crisp) and so-called, artificial intelligence methods based on machine learning: neuro inference engine, fuzzy inference engine.

Fig. 2. DTM generalisation (source data, source DTM, neuro generalisation, fuzzy generalisation)

Nowadays, the algorithmic approach may be considered as the dominating tendency in the field of generalisation. It

consists of utilisation of strict, parameterised procedures of utilisation of elementary generalisation operators: simplification, aggregation, filtration etc. Results of utilisation of artificial intelligence and cognitive modelling in the process of generalisation of spatial data, are also very promising. On the contrary to expert systems, well known since the eighties of the 20th century, which utilise IF-THEN deterministic rules, the essence of the discussed approach is connected with the use of machine learning (ML) processes (L. Meng, 1998). The technology of the ML algorithms utilisation is defined as data mining. In practice, it consists of searching for specified regularities in large databases (as, for example, specification of leading attribute groups or representative reduction of data volumes). The discussed methods are cognitive modelling tools which allow to perform data reduction, but, first of all, they allow for explanation of complexity of the systems, which are modelled. The discussed approach relies upon utilisation of the wide meaning of fuzziness in the course of specification of decision rules for data generalisation systems. The performed investigations prove that utilisation of the fuzzy or neuro approach allows for more flexible determination of weighting coefficients, which characterise the significance of particular points. They also point that the importance of maintenance of topology is equal to the importance of the process of iterative reduction of the number of points of the terrain relief model.

Conclusions

Generalisation of the digital terrain model is an important issue, both with respect to the topographic database generalisation, as well as to supplying geographic information systems with data. The basic feature of generalisation of the terrain relief model should be the maintenance of its structure (the morphological skeleton). Simple algorithms of the DTM generalisation, such as conversion of TIN models to the regular GRID structure of the specified spatial resolution and utilisation of global filtration allow for relatively low reduction of the level of complexity of the source model.

Correct generalisation of the digital terrain model requires interactive co-operations with the computer system (the strategy of enhanced intelligence) or utilisation of local filtration algorithms, which allow for representative selection of points from the source model. The concept of construction of the multiscale (hierarchical) TIN model also seems to be an interesting solution. Such a model may have a monoscale representation at an arbitrary, user-defined level of generalisation, with maintenance of the relief structure, which is significant for this level. Within performed research works, the method of construction of the multiscale TIN model, in its original approach proposed by De Floriani (2002) was analysed in details; it was stated that the, so-called- decomposition of Morse-Smale terrain structure does not preserve all significant

morphometric features of the real landscape. The authors of the concept of the �extended Morse-Smale decomposition� L. De Floriani (2002), (E. Danovaro, L. De Floriani, P. Magillo, M. Mesmoudi, E. Puppo 2003) state, that generalisation of automatically determined structural lines allows for hierarchical generalisation of the DTM, which maintains significant topological relations. Performed investigations have not confirmed that assumption. It seems that � if the DTM generalisation (or its hierarchical construction), performed by means of generalisation of structural lines, may be considered as justified, the automation of the process of determination of those lines does not lead to expected results. Thus, the necessity to acquire structural lines of the terrain surface in the process of direct surveys (such as utilisation of photogrammetric techniques at the stage of acquisition of source data for the topographic database) should be considered as justified. Basing on the �skeleton of the terrain� determined in that way, it is possibly to correctly generalise the terrain relief model, with maintenance of significant topological relations.

Modification of the method of construction of the hierarchical TIN model has been proposed in the paper, which utilises weighting of model source points, basing on pre-defined structural lines of the terrain relief. In this approach, the basic structure of the terrain (structural lines) is determined at the stage of processing of survey data and not basing on the analyses performed in the postprocessing mode. Such modification, with simultaneous maintenance of the general idea of the multiscale TIN model, allows for representation of the DTM in the form of a triangular irregular network at the arbitrary level of geometric accuracy. This method of terrain relief generalisation is compliant with a concept of generalisation of spatial data, represented by the DLM database model.

Utilisation of the �calculation engine� or �inference engine� in the form of NEURO and FUZZY allows for considerably higher flexibility of the approach to generalisation of spatial data comparing to conventional solutions (CRISP version). The digital application, developed by the author, allows to maintain significant topological relations between structural lines, which create the �skeleton� of the terrain. Similarly to CRISP version, both �calculation engines�, neuro and fuzzy, may be implemented in any GIS environment, such as ArcGIS, GeoMedia or MapInfo.

REFERENCES

1. Costa-Cabral M. C., Burges S. J., 1994, Digital elevation model networks (DEMON): a model of flow over hillslopes for computation of contributing and dispersal areas, in: �Water Resources Research�, 30, 1681-1692.

2. Danovaro E., De Floriani L., Magillo P., Mesmoudi M.M., Puppo E., 2003, Morphology-Driven Simplification and Multiresolution Modeling of Terrains, Proceedings ACM-GIS 2003 - The 11th International Symposium on Advances in Geographic Information Systems, E. Hoel and P. Rigaux (Eds.), ACM Press, pp. 63-70, www.disi.unige.it/person/DeflorianiL/publications.html

3. De Floriani L., Magillo P., 2002, Multiresolution Mesh Representation: Models and Data Structures, In Multiresolution in Geometric Modelling, M.Floater and A.Iske and E.Quak editors, Springer-Verlag, pp. 363-418, www.disi.unige.it/person/DeflorianiL/publications.html

4. Grünreich D., 1995, Development of Computer-Assisted Generalization on the Basis of Cartographic Model Theory, In: GIS and Generalization - Methodology and Practice, pages 47-55, London, Great Britain, Taylor & Francis

5. Heller M., 1990, Triangulation Algorithms for Adaptive Terrain Modeling, Symposium on Spatial Data Handling, Zurich, vol. 1, pp. 163-174

6. Makowski A., 2001, Na obrze¿ach cybernetyki, in: �Mapa w systemach komputerowych�, Materiaùy XXVIII Ogólnopolskiej Konferencji Kartograficznej, Szczecin

7. Meng L., 1998, Project report on "Strategies on Automatic Generalization of Geographic Data" - Stage 2: Cognitive modeling of cartographic generalization, http://www.lrz-muenchen.de/~t583101/WWW/content/aboutus/meng.htm

8. Olszewski R., 2003, Cartographic modelling of statistic surface with the use of non-linear neural networks, XXI International Cartographic Conference, Durban

9. Ostrowski W., 2001, Typy generalizacji kartograficznej z punktu widzenia semiotyki, in: �Metody kartograficzne a mo¿liwo�ci systemów komputerowych�, Uniwersytet Warszawski

10. Smale S., 1960, Morse inequalities for dynamical system, in: Bulletin of American Mathematical Society, 66: 43-49 11. Weibel R., 1991, Amplified intelligence and rule-base systems, in: �Map generalization: making rules for knowledge

representation�, Red.: B. Buttenfield, R. McMaster, Longman, London 12. Weibel R., 1992, Models and Experiments for Adaptive Computer-Assisted Terrain Generalization, Cartography and

Geographic Information Systems, vol. 19, no. 3

13. Wilson J. P., Gallant J. C., 2000, Terrain Analysis, New York, John Wiley & Sons.

14. Wytyczne Techniczne, Baza Danych Topograficznych, 2003, Warszawa, Gùówny Urz¹d Geodezji i Kartografii.

Robert Olszewski (r.olszewski@gik.pw.edu.pl) He is currently researcher and teacher at the Department of Cartography, Warsaw University of Technology. Since 1995 he has been active in Cartography and GIS. He completed his PhD (2001), with a thesis about fractal geometry and analyses. His research interest involves: � spatial data mining, � cartographic generalization, � fuzzy sets and systems, � neural networks, � cellular automata, � fractal geometry.