Chapter 2 Spatial Data

Transcription

1 References - Spatial data structure (classics) Chapter 2 Spatial Data 1. Samet, H. (1990): The Design and Analysis of Spatial Data Structures, Addison-Wesley. 2. Samet, H. (1990): Applications of Spatial Data Structures: Computer Graphics, Image Processing and GIS: Addison-Wesley. References - Spatial data structure 2.1 Introduction 1. Laurini, R. and Thompson, D. (1992): Fundamentals of Spatial Information Systems, Academic Press. 2. Worboys, M. F. (1995): GIS: A Computing Perspective, Taylor and Francis. 3. Rigaux, P., Scholl, M. O., and Voisard, A. (2001): Spatial Databases: With Application to GIS, Morgan Kaufmanns. To do spatial analysis, we need and, 1) a (personal) computer, [hardware] 2) GIS software, [software] 3) spatial data. [contents] Cost 1) Personal computers: not so expensive IBM NetVista A21: 69,280 2) GIS software: reasonable GRASS: 0 (freeware) GeoBasic: 10,000 (academic price) Generally speaking, spatial data are very expensive. If you do not have an adequate knowledge of spatial data, you may pay so much money for inappropriate, or even unnecessary data. 3) Spatial data: still very expensive! Japanese census 2000: 10,000,000 (the whole country) 1

2 2.2 Definition and classification of spatial data The terms 'spatial data', 'GIS data', 'map data', and even 'data' are interchangeable in GIS field. GIS differs from other computer software in that it can treat spatial database. Spatial data differ from other data in that they contain the information about the location of objects. The term 'spatial data' is used in two different ways. In its wider sense, it is equivalent to GIS data and map data. In its narrower sense, however, the term 'spatial data' means only a part of the data that indicates the location of spatial objects. In this case 'spatial data' is used as equivalent to the term 'locational data'. 2.3 Spatial (Locational) data Spatial data (GIS data) Spatial data (Locational data) Raster data Vector data Spatial data are the data that contain information about the location of objects. They are provided not only in digital format but also in analogue format paper maps, directories, etc. Attribute data How do we describe the location of objects? Address system Georeferencing system: the system to indicate the location of spatial objects 1. Address systems 2. Longitude-latitude system 3. Cartesian coordinate systems Block-based system: Japan except Kyoto and some cities 7-3-1, Hongo, Bunkyo-ku, Tokyo , Japan Street-based system: USA, UK, etc Derby Hall, 154 North Oval Mall, Columbus, OH , USA 19 Dunstarn Lane, Leeds, LS16 8EN, UK 2

3 Japanese address system Block-based address system The law on address system in Japan permits both blockbased and street-based systems, either of which each local government can choose as its own address system. Most local governments, however, adopted the blockbased system. 1) The blocks are numbered according to a certain rule. 2) Builldings are then numbered clockwise from a corner of block. The numbering system of blocks and the choice of the starting corner vary among local governments. Figure: Address system of Hiroshima Figure: Address system of Sakai Longitude-latitude system My office is located at E, N. Longitude 135 (degrees) 45 (minutes) 45.7 (seconds) E (east) Latitude 35 (degrees) 42 (minutes) 49.6 (seconds) N (north) This system can be used commonly worldwide, so it is suitable for maps of the world of small scales, say, 1:1,000,000. Figure: Address system of Okagaki (Fukuoka) 3

4 2.3.3 Cartesian coordinate system 1: UTM system UTM: Universal Transverse Mercator grid system The earth s surface is divided by the lattice of longitude 6 degrees and latitude 8 degrees. As a result, we obtain 60 x 22 approximately rectangular subregions. In each subregion, the origin is located at the lower left corner, and the location is described by the XYcoordinates. Figure: Letter addressed by the longitude-latitude system Cartesian coordinate system 2: Japanese system Japan is divided into nineteen subregions. We can refer to a spatial object by the number of the subregion in which the object is located and its Cartesian coordinates given by the origin and XY-axes. This system is better than the UTM system for local georeferencing, because subregions are closer to rectangles; they are less distorted by the projection on a plane. Figure: Japanese cartesian coordinate system Kanto region including Tokyo The ninth coordinate system The origin: E, N (in the north of Noda city) The system covers Tokyo, Fukushima, Tochigi, Ibaraki, Saitama, Chiba, Gunma, and Kanagawa prefectures. The Cartesian coordinate system is used for large scale spatial data such as topographic maps on scale of 1:2,500 and 1:10,000. Figure: the origin of the IX coordinate system 4

5 If the location of spatial objects are given by the coordinates, we can easily visualize the data in GIS. However, if the location is given only by its address, the data cannot be directly handled in GIS. In such a case we have to convert the address into its XYcoordinates such as longitude-latitude coordinates. This process is called 'geocoding'. Figure: Geocoding system at CSIS ( Figure: Application of geocoding Figure: Distribution of Chinese noodle restaurants 2.4 Attribute data Attribute data are the information about spatial objects except spatial (locational) information. A parcel: Spatial data: address, coordinates, Attribute data: area, perimeter, land use, name of owner, the number of residents, Figure: Map showing the location of a restaurant 5

6 2.5 Raster data In GIS, spatial and attribute data are linked with each other by the identification number. Spatial data ID Longitude Latitude E N Attribute data ID Name Age Sex Yukio Sadahiro 35 Male Raster data use space-filling congruent figures to represent spatial phenomena in digital format. They are also called lattice data or grid data. In Japan they are called mesh data, which is a Japanese- English term. Terminology Raster, cell: the minimum spatial unit to represent spatial phenomena Lattice: the spatial structure given by the set of cells Grid: a square or a rectangular lattice Resolution: the number of cells per unit area or length Figure: A paper map (land use map) Figure: Overlay of a square lattice Figure: Raster data of land use 6

7 Assignment of attibutes Cell shape Assignment of attribute data is based on a certain rule. For example, a cell is assigned an attribute value 1. that covers the maximum area of the cell, 2. that is given at the centroid (gravity center) of the cell, 3. that represents all the attribute values of the cell, say, the average value. The cell of raster data 1. has to fill out the infinite plane by its copies, 2. should be a simple figure because of computational tractability, 3. can be a square, a rectangle, a triangle, a regular hexagon. There are numerous cell shapes available, but we usually use a square cell. Figure: An equilateral triangular lattice Figure: A lattice of a regular hexagon Cell size The cell should be as small as computational environment permits, because smaller cells can describe the shape of spatial objects in more detail. On the other hand, small cell size (high resolution) requires more space for data storage and faster processors for data manipulation. Figure: Raster data of a higher resolution 7

8 How should we determine the cell size? It depends on the balance between the resolution you need to represent spatial objects and your computational environment (CPU clock, capacity of storage devices, etc.). Rule of thumb: Side length of the cell should be smaller than the diameter of the smallest spatial object to be recorded. Figure: Raster data of a lower resolution diameter circumcircle 2.6 Data structure of raster data Simple structure {(1, 1): 48}, {(1, 2): 48}, {(1, 3): 48}, {(1, 4): 48}, {(1, 5): 48}, {(1, 6): 48}, {(2, 1): 238}, {(2, 2): 238}, {(2, 3): 238}, {(2, 4): 240}, {(2, 5): 240}, {(2, 6): 240}, {(3, 1): 240}, {(3, 2): 240}, {(3, 3): 240}, {(3, 4): 240}, {(3, 5): 240}, {(3, 6): 240}, {(4, 1): 103}, {(4, 2): 103}, {(4, 3): 103}, {(4, 4): 115}, {(4, 5): 115}, {(4, 6): 168}, {(5, 1): 103}, {(5, 2): 103}, {(5, 3): 103}, {(5, 4): 19}, {(5, 5): 19}, {(5, 6): 19} This structure is easy to understand and its implementation is straightforward, but it requires much space for data storage An improved structure Chain-code structure Coordinates of the origin: (0,0) Cell size: 1m x 1m Cell count: 5 x 6 The 1 st row: {48, 48, 60, 60, 60, 60} The 2 nd row: {238, 238, 238, 240, 240, 240} The 3 rd row: {240, 240, 240, 240, 240, 240} The 4 th row: {103, 103, 103, 115, 115, 168} The 5 th row: {103, 103, 103, 19, 19, 19} Coordinates of the origin: (0,0) Cell size: 1m x 1m Cell count: 5 x 6 The 1 st row: {(48, 2), (60, 4)} The 2 nd row: {(238, 2), (240, 3)} The 3 rd row: {(240, 6)} The 4 th row: {(103, 3), (115, 2), (168, 1)} The 5 th row: {(103, 3), (19,3)} This structure is also easy to understand and it requires less space for data storage This structure can store the data effectively if many cells have the same attribute value. In the worst case, however, it requires twice as much space as the simple method

9 2.6.4 Hierarchical raster data structure A set of raster data of different (hierarchical) resolutions It permits fast visualization and search of spatial data. A typical data strusture is the quadtree structure Figure: Hierarchical raster data structure (numerical data) Figure: Hierarchical raster data structure (numerical data) Figure: Hierarchical raster data structure (categorical data) 2.7 Examples of raster data Figure: Hierarchical raster data structure (categorical data) 9

10 2.7.1 Aerial photographs Remotely sensed data (RS images) Name Resolution NOAA/AVHRR-3 (USA) 1km Landsat-5/TM (USA) 30m JERS-1/OPS (Japan) 18*24m SPOT/HRV-P (France) 10m IRS-C3 (India) 6m IKONOS (USA) 1m 10m 3m 1m Figure: RS images of various resolutions Figure: RS images of various resolutions Figure: An artificial satellite Figure: Orbits of artificial satellites 10

11 Figure: The direction of a camera Figure: Landsat TM images Figure: Original RS image and landcover data Figure: Images before and after flooding Figure: Florida hurricane Figure: Florida hurricane 11

12 Figure: Mosquito extermination Figure: Mosquito extermination Figure: Mosquito extermination Figure: High-resolution RS image Figure: high-resolution RS image Figure: high-resolution RS image 12

13 Figure: Artificial satellite Figure: Artificial satellite Figure: Taking a picture Figure: Miyako (Iwate prefecture) Japanese census data (mesh data) Lattice of the 1 st order: cells with one degree width and forty seconds height Lattice of the 2 nd order: each 1 st order cell is divided into eight by eight cells. Lattice of the 3 rd order: each 2 nd order cell is divided into ten by ten cells. Figure: Sapporo 13

14 The 3 rd order cells are almost squares of side 1km. In urban areas, lattice of the 4 th order is available, where the 3 rd order cells are divided into two by two smaller cells (squares of side 500m). Census data contain a lot of attribute data such as population classified by age class, occupation, etc., number of households, number of employees, average commuter time, Suuchi-chizu 50m They are one of the most fundamental spatial data used in urban planning. They have been created from 1970, every five years, so they are suitable for analyzing the change of urban structures. Digital elevation model (DEM) of resolution 50m Provided by National Geological Agency It costs only 7,500 yen! However, they are very costly (about 10,000,000 yen for the whole country). Who can afford them? 2.8 Vector data Spatial objects represented by vector data Vector data describe spatial objects by a set (chain) of XY-coordinates. They are suitable when the shape of spatial objects should be preserved in GIS. In urban planning, vector format is used for representing urban infrastructures such as traffic roads and railroads as well as residential lots and buildings. 0-dimensional spatial objects: Point, node, vertex 1-dimensional spatial objects: Line, arc, link 2-dimensional spatial objects: Polygon Point data Line data Polygon data 14

15 Figure: A paper map (land use map) Figure: Vector data of land use 2.9 Data structure of vector data Whole polygon structure Polygon I (1, 0), (4, 2), (3, 4), (1, 5) Color: Red Polygon II (4, 2), (9, 3), (8, 5), (6, 6), (3, 4) Color: Green Polygon III (5, 1), (10, 1), (9, 3), (4, 2) Color: Blue 5 0 I II III I II III 5 10 Cartographic spaghetti The whole polygon structure stores all the coordinates of polygons explicitly. Many nodes appear more than once in spatial database. Overlap This leads to 1) inefficiency of data storage, 2) inconsistency between neighboring polygons. Gap Lines are tangled with each other. 15

16 2.9.2 Arc-node structure The whole polygon structure does not have explicit information about adjacency between polygons. It lacks the topological information about polygons. Thefore, we cannot tell neighboring polygons directly from the data. We need a computational algorithm to test whether two polygons are neighboring. 4 1 D K C 3 B I 2 E A 5 9 II J H III F 8 I 7 G 6 1: 2: 3: 4: 5: 6: 7: 8: 9: Node (1, 0) (4, 2) (3, 4) (1, 5) (5, 1) (10, 1) (9, 3) (8, 5) (6, 6) A: B: C: D: E: F: G: H: I: J: K: Arc (1, 2) (2, 3) (3, 4) (4, 1) (2, 5) (5, 6) (6, 7) (2, 7) (7, 8) (8, 9) (9, 3) Polygon I: (A, B, C, D) II: (H, I, J, K, B) III: (E, F, G, H) 4 1 D C I A 3 B K 2 E 5 II 9 Color: Red Color: Green Color: Blue J H III F 8 I 7 G 6 The arc-node structure has topological information about polygons explicitly, so we can easily find neighboring polygons of a certain polygon. However, the arc-node structure Is rather complicated, and its construction needs more time than that of the whole polygon structure Examples of vector data in Japan In usual, spatial data structure is hidden from GIS users. However, in creating new spatial data and exporting spatial data from GIS, we have to be careful of their structure. 1. Suuchi-chizu 2500 (Spatial Data Infrastructure) 2. CMS: Census Mapping System 3. Zenrin Z-MAP 4. Shobunsha Mapple 5. Sumitomo-denko Digital Road Map 6. Tokyo Urban Mapping System 16

17 Suuchi-chizu 2500 (Spatial Data Infrastructure) Suuchi-chizu 2500 (Spatial Data Infrastructure) is a basic micro-scale vector dataset in Japan, which is provided by National Geological Agency. It is based on the topographic paper maps of scale 2,500. Contents: road network, railroads, blocks, etc.. Coverage area: urban areas in Japan Price: 7,500 for a rectangular region of 1.5km x 2.5km Figure: Suuchi-chizu CMS: Census Mapping System Census data are available in either raster or vector format. CMS provides Japanese census data in vector format aggregated within 'Shi-ku-cho-son' units. Contents: number of households, employees, etc.. Coverage area: whole area of Japan Price: 10,000,000 for the whole country Figure: Census Mapping System Zenrin Z-MAP Similar to Suuchi-chizu 2500, Zenrin Z-MAP is also a micro-scale vector dataset based on a 2,500 scale paper maps. Contents: buildings, railroads, blocks, etc.. Coverage area: most urban areas in Japan Price: 2,500,000 for Tokyo 23-ku area Figure: Zenrin Z-MAP 17

18 Shobunsha Mapple Shobunsha Mapple is another micro-scale vector dataset provided by a private company. Contents: buildings, railroads, blocks, etc.. Coverage area: Tokyo 23-ku area Price: about 2,000,000 for Tokyo 23-ku area Figure: Shobunsha Mapple Sumitomo-denko Digital Road Map Sumitomo-denko road network data is the data developed for carnavigation systems. It is therefore microscale, detailed data, and updated monthly (!). Contents: buildings, railroads, blocks, etc.. Coverage area: the whole area of Japan Price: 1,500,000 for the whole country Figure: Sumitomo-denko Digital Road Map Tokyo Urban Mapping System Attribute data Tokyo Urban Mapping System is vector data developed for urban planning. It is based on the topographic paper maps of scale 2,500. Contents: landuse, buildings, zoning system, etc.. Coverage area: the whole area of Tokyo Price: not for sale (not open to public) Spatial data are usually provided with attribute data such as landuse, population, and phone number. In addition to spatial data, various attribute data (often called 'statistical data') are also available. If they contain an attribute that can be used as an identification code, say, ID number or name of administrative unit, they can be linked to spatial data. 18

19 To search the data you need, you had better access a website called a 'clearinghouse'. Clearinghouse provides us the information about the data, that is, 'metadata': There are also 'spatial' data clearinghouses in Japan:. Data are aggregated within Cho-cho-moku units Election data in 1996 and 2000 Data are aggregated within Oaza units. Car ownership data in 2000 Data include the address of stores. NTT telephone directory 'Townpage' (commercial facilities) Data include the address of individuals. NTT telephone directory 'Hellopage' (individuals) Data are aggregated within Shi-ku-cho-son units. Statistical datasets 'Statpack' provided by Seitosha 19

20 2.11 Comparison of raster and vector formats Choice of data format Shape description Data volume Raster data Not precise Small Vector data Precise Large Please keep in mind that it is easy to convert vector data into raster data, Processing speed Complexity Fast Simple Slow Complex but the reverse is quite difficult and practically impossible. Construction cost Low High Data updating Easy Not easy Data analysis Easy Difficult 2.12 Other types of spatial data In early years of GIS, application programs could treat only raster data, because of the slow processing speed of CPU, small volume of storage devices, etc. However, since mid 90 s, vector data have increasingly become available because of the rapid improvement of computer ability. Continuous surfaces (TIN) Uncertain (fuzzy) spatial data Representation of accuracy Fractal spatial objects 3-dimensional spatial objects Spatiotemporal objects (moving objects, ) Homework Q.2.1 (10 pts) Homework Q.2.2 (20pts) Find spatial data of your home country/region/city available on GIS and report their properties such as contents, data format, price, etc.. Represent the polygon data below by the arc-node structure (indicate the coordinates of node i as (x i, y i )) A R 2 3 B C D I Q E 5 8 J II G F 6 IV H O V P 12 T M K VI 7 9 III N L S

21 Homework Q.2.2 (Cntd.) Describe a procedure for enumerating the polygons surrounding the polygon IV. II III I IV V VI 21