RASTER-VECTOR CARTOGRAPHIC NUMERIC DATABASE Ureña Cámara, Manuel Antonio (*); Ariza López, Francisco Javier (*) (*) Grupo de Investigación en Ingeniería Cartográfica. Dpto. de Ingeniería Cartográfica, Geodésica y Fotogrametría. Universidad de Jaén. Campus “Las Lagunillas” s/n. 23071. Jaén (Spain). e-mail:
[email protected]. Tel.: +34953212852 e-mail:
[email protected]. Tel: +34953212469
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Abstract
The use of a hybrid raster-vector object oriented model is suggested in order to support generalization processes of urban city blocks taking advantage of the best qualities of the basic raster and vector models. The objects implemented are: pixels and groups of pixels (raster), proximity networks, streets (vector) and lines of sight (collection of vector objects). UML Scheme are shown and also an overview of the processes for deriving each object.
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Introduction
From a conceptual point of view, reality is represented in cartography as an abstraction process. This process can be achieved in two different ways depending on how reality is defined: The representation of the more important phenomena. This is called the vector model. In this model point, lineal and area entities are used to represent the more important features of the world. This model has a continuous representation in space. The sampling of space into zones called cells which are represented by a digital number obtained from an aspect of the world. This is called the raster model. In this model every cell’s digital number is acquired by mean values or samples inside the spatial extension of the cell. The values represent only one quality of the world, either qualitative or quantitative. The raster model is a space-primary data structure (Li and Su 1997). This model samples the world both in space and attribute. It is represented by area surfaces that fill in the world. For example: a B&W digital image is composed of square cells with a digital number that measures the quantity of energy in a specific wavelength. Those reality models are opposed in their conception. Their advantages and disadvantages have been pointed out by many authors (Burrough, Thompson Hansens, etc.), and are derived from their own definitions, for example the vector model can support multiple attributes for each feature, while the raster model needs an image for each attribute. On the other hand, overlaying is a plain operation between cells in a raster data base and a complex operation in a vector model because of the need of intersections calculation and topological rebuilding. However, both models are widely used in cartography, and specifically in generalization. In this area, some examples of the use of the raster model are: Monmonier (1983), Schylberg (1993), Li and Su (1995, 1997), Su, Li and Lodwick (1996, 1996b, 1997, 1998a and 1998b), Su, Li, Lodwick and Müller (1997), etc. Among all the work on the raster model we distinguish the papers of Su, Li and Lodwick whose research is related to mathematical morphology operators. Nevertheless, the majority of generalization studies, examples and applications are based on the vector model. Examples of these: McMaster (1986, 1987 and 1989), Plazanet (1996), Bjørke (1997), Bader (2001), Agent (2000), DynaGEN (from Intergraph Corporation), Lamps2 Generalizer (from Laser-Scan). It can be said that neither model is better than the other, each one having its own strong and weak points. Thus, the Geographical Information System resolves geocomputing processes by applying operators to the most efficient model, and returning data to the original model. Model conversions produce a loss of object shape and precision (Peter and Weibel, 1999), so they must not be used many times and their use should be reduced to critical processes. In this paper we propose a dual model that maintain both raster and vector representation of the same reality. In this way we take advantage of the best qualities models, operation efficiently is improved and loss of information due to model conversions is successfully prevented. Our model goes a little further, giving an interface for other representation models, in advance of future developments. We call this model the Raster-Vector Cartographic Numeric Database (BCNRV from the spanish acronym or RVCND from the english acronym).
This model has been successfully tested on the generalization process of urban city-block maps. The results obtained are explained in the paper “Generalization of urban city-block (built-up areas) maps in raster model” (Ureña and Ariza, 2005), also presented to the 22th International Cartographic Conference. The paper is divided into three sections; the first includes an overview of the model and the second the objects and processes implemented for deriving each one. Finally the main conclusions are presented
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Conceptual Model of Raster-Vector Cartographic Numeric Database (BCNRV).
We propose a model (Ureña, 2004) that uses the object paradigm, as proposed by Buttenfield (1995), where each feature or relevant aspect of a phenomenon is a predefined object. With our model we have achieved the following characteristics: Each relevant phenomenon is an instance of a defined object. Defined objects are sustained by a hierarchy which is represented as a tree where the main object is located at the root. The advantage of this structure is that it supplies a way for classification generalization. There is no graphical representation of objects. They have an original representation that can be defined in the raster or vector model, or in any other possible option. Attributes of phenomena are included in the instances of the objects. These attributes are selected by their mapping importance. The attributes must have a reference to all original valid representations and processes in order to convert these representations and any other one in run-time (not necessarily in design time). In this way a model that maintains both raster and vector representation is proposed: a.
Raster representation model: This structure stores reality based on square cells. It is considered in order to take advantage of efficient raster computations such as morphological operators, Manhattan distances, etc. needed for the development of automatic generalizations processes. Our raster model allows storing multiple data in a unique cell using key values with reference to a table register.
b.
Vector representation model: This structure stores reality based on boundary representation (B-rep). The features of this model are point, line and area. It is considered in order to take advantage of efficient vector modelling and computations such as network analysis, topological relations, etc. needed for the development of automatic generalization processes. The vector model allows us to use three dimensional positioning with more precision.
c.
Inherited representation model: This structure only refers to the other representation models in order to store original data.
We call our proposal the Raster-Vector Cartographic Numeric Database (BCNRV), and its conceptual scheme is shown in Figure 1 using Unified Modeling Language (UML) (Quatrani, 1998) representation. Figure 2 shows the relationship model between objects and relations. Both UML diagrams (Figure 1 and Figure 2) show the following characteristics: Each feature of interest of the real world is represented by one instance of BCNRV objects. Relationships between objects are stored as instances of BCNRV objects. In this way all topological relationships are explicitly shown in the model. Each BCNRV object is an isolated representation in its storage. This means that even if a BNCRV object has a vector original representation, it can be shown as a raster representation or by any other implemented option; and conversely, if the original data is raster, a vector representation can be used. Each representation model, both raster and vector, has its own operators and these are independent of attribute operators of the object. These characteristics give us great flexibility for visualization, query and change in the attributes of an instance. Furthermore, this structure provides a mechanism for storing multiple original data representations, with or without different resolutions, and the applicable operators.
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With the specification of this BCNRV model, new forms or models of representation can be developed with no more work than the creation of their interfaces and definitions. Examples of this include simplex representation and triangular irregular network representation. BCNRV Object Class Representation Model
Definition Model Cartographic Object
Vector Operators
Vector Model
Attribute Operators
Generalization Operators
Polygon
Arc
Other Operators
Point/Label
Attribute Table
Raster Operators Generalization Operators Raster Model
Mathematical Morphology Categorization
Pixel
Attribute Model
Other Operators
Attribute Table
Inherit Model
Figure 1. UML conceptual scheme for the BCNRV. Topological Relationships are stored as another BCNRV Object Instance
Instance of BCNRV Object Class (Relationship)
Instance of BCNRV Object Class
Instance of BCNRV Object Class
Figure 2. Example of BCNRV Object instances and their relations (topological and of attributes).
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Example of Application to Urban City Block Maps
In this section we propose the specific application of the BCNRV model developed to supporting generalization processes for urban city-block maps. We have proposed the four features shown in Table 1 in order to model the city space in a proper way for generalizing.
Feature City block/building
Table 1. Calculated features from the image in the enrichment proccess.
Description
More relevant features of a city
Definition
A set of connected pixels with same use (residential, green space, and so on)
Model Raster
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Proximity Network
Street
Lines of sight
Topological relationships between blocks features Streets give the structure of the city. The street network is the dual set of the proximity network when city-blocks are the only features considered of a city. Set of street with a predefined direction. It can be seen as the lines of sight defined by Mackaness (1995)
Different distances between two city blocks or buildings can be considered (Euclidean and Manhattan). Furthermore, stores a pointer to the neighbours of each blocks.
Raster & Vector
Mean axis between two city-blocks.
Vector
Set of aligned streets.
Inherit
All the features shown in Table 1 are extracted from a raster image, even if it is only a binary B&W image (0:background, 1: city-block or building). Of course it would be better if the different uses and importance of city blocks was coded because that would make a further, more specific tuning of procedures possible. Taking as the single starting point an image corresponding to a complete urban map, the proposed method builds automatically all necessary instances and their attributes to include them in a BCNRV application, as is shown in the UML scheme of Figure 3.
Figure 3. UML Diagram of Class Hierarchy developed from original data. The implemented structure that holds the proposed design for the BCNRV is shown in Figure 4 where embedded versions of objects are used.
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Lines of Sight Lines of Sight Attribute Table
Street Zone Image
Interior Distance Image
Node Table
Interior Objects Image
Interior Voronoi Image
Street Attribute Table
Proximity Network Distance Image
Voronoi Polygons Image
Proximity Network Attribute Table
City-Block/Building Objects Image
Objects Attribute Table
Figure 4. Storage structure of features for urban city-block map adapted from BCNRV. The derivation of features and their latter enrichment is a complex task. The flow diagram of this building and enrichment process is shown in Figure 8 and the main steps are: 1.
Determination of city-blocks/buildings and their attributes: An algorithm for detecting continuous objects from the original image is used (example in Figure 5). This algorithm is followed by the calculation of additional attributes of interest (area, perimeter, etc.).
(a)
(b)
(c)
(d)
......
(e)
Figure 5. Evolution of continuous object determination algorithm. (a) – (d) Evolution, blue frame mark pixels used in the search. (e) Evolution of the detected object (each color is a different object).
2.
Derivation of the proximity network, or topology, between city-blocks/buildings: After determining the main objects the relationships between them are derived, as well as all distances between pairs of neighbouring objects.
3.
Determination of the street network: The street axis is the arc between two point intersections of three or more blocks.
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(a) (b) Figure 6. Example of street calculation, each color represents the Voronoi region of each city-block/building. (a) Intersection of 3 or more regions, the street intersections. (b) Intersection of 2 regions, the street arcs. 4.
Construction of lines of sight: In order to determine lines of sight several aligned street arcs are joined using an angular criterion in the same way as that defined by Mackaness (1995). After this process the data is enriched by calculating all of the Alpha Analysis characteristics (Hillier and Hanson, 1984 from Mackaness 1995). The other attributes are inherited from street arcs.
(a)
(b)
Figure 7. Multiple lines of sight including non-linear elements (a) and non-aligned elements (b). Different brightness represents different objects. 1/25000 Scale Map City-Block/Building Entity Determination
Attributes
Proximity Net Entity Street Entity
Tolerances: - Maximum distance of urban envelope. - Maximum number of pixels per crossing.
Determination
Perimeter fitting
Tolerances: Maximum angle between street (rad)
Attributes
Lines of Sight Entity Determination Attributes Route Connectivity
Figure 8. Enrichment proccess followed for calculation of BCNRV (feature process version)1.
1
Route Connectivity: The number of times a line of sight is crossed in the route between any two given points in a city.
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Parameters of Object Calculation (area, perimeter, ...)
Object Calcultation
Object Image
1/25000 scale Map
City-block/Building Feature Topological Calculation, Distance Calculation
Street Feature (calculated attributes)
Shape Adjustment of Street Feature
Parameters of Street Calculation (lenght, width, ..) Lines of Sight Calculation
Street Feature
Removing of street intersection versus city-blocks/buildings
Tolerances: Maximum angle between streets
Lines of Sight Feature
Proximity Network Feature Mean axis between nearer objects
Tolerances: - Maximum closer distance - Maximum pixels per intersection
Parameters of Lines of Sight Calculation (Depth, control, ...)
Lines of Sight with Route Connectivity
Enriched Lines of Sight Distance Cacultation through Lines of Sight Network
Figure 9. Enrichment process for calculation of BCNRV (dataflow version). The complete process, as previously described, is guided by three parameters that allow fine tuning to users needs. These parameters are: Maximum angle between streets: This parameter controls the automatic construction of the lines of sight giving a threshold for the alignment criterion and the joining or non-joining decision for two arcs. Maximum closer distance: This parameter sets the maximum distance between two blocks in order to be considered automatically the same urban zone. Maximum number of pixels per intersection: The maximum number of pixels allowed in an individual intersection between multiple regions. Among the three parameters results show that the order of importance is: maximum closer distance, maximum angle between streets, and minimum number of intersections, because the first defines zones in the city and the second defines the lines of sight. Our experiments show that in both parameters the sensitivity to changes is low. Nevertheless, experimental results indicate that the maximum angle between streets should be near to 20º and maximum closer distance near 50 m. After all instances corresponding to a concrete map have been created, generalization can be applied to them by means of raster and vector operators included in the BCNRV. We have developed a generalization engine (see Ureña and Ariza, 2005b for more detail) that can be used interactively and in batch mode to achieve a generalized map. The process has been developed and applied to several urban maps at scale 1/25000 (this can be seen in the work of Ureña and Ariza, 2005a). Original vector data were converted into image maps with resolution of 0.1 mm and classified to represent multiple uses of city land. Later, we process all the maps as explained in Ureña and Ariza (2005b). There are three differences between this generalization process and others carried out: 1.
The use of raster and vector data in one data structure which generalises different parts of built-up areas.
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2. 3.
The verification with visual analysis (polling people not related to the process) and automatic assessing measures. The use of a high number of built-up areas which evidences the liability of the results (9 cities).
Generalization results can be reviewed in Ureña and Ariza (2005b), but an example of a generalized map is shown in Figure 10.
(a)
(b) Figure 10. Example of generalization results using BCNRV, different brightness represents a different instance of city-block. (a) Original Data. (b) Generalized Data.
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Conclusions
In this work we propose a new conceptual model. The main characteristic of this model is its advantage in handling different representation models (raster, vector or others) for each feature. This new model isolates each representation from the others and implements interfaces between all the representations. This characteristic allows the use of all vector and raster operators thus improving the possibilities of available generalization procedures. The model is suggested in order to support generalization processes of urban city blocks taking advantage of the best qualities of the basic raster and vector models. Implemented objects are: pixels and groups of pixels (raster), proximity networks and streets (vector) and lines of sight (collection of vector objects), because these are very similar to those
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used by a cartographer. A complete procedure for supporting automatic city maps generalization has been developed and implemented using the proposed model. The basis of the method is an enrichment and object-building process.
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References
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