Conceptual models of space, data models and representation (data structures)

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Conceptual models of space, data models and
representation (data structures)

• Josef Fürst

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Learning objectives

• In this section you will learn
• how the conceptual perception is already based on
  a model of space and how this conceptual
  perception determines the selection of an
  appropriate data model, and
• how the selection of a particular data model
  influences the appropriate data types to
  represent the phenomena of interest and the
  possible spatial analyses
• Understanding of important geographical data
  structures and their relevance,
• Importance of topology and its utility for
  spatial analysis,
• Relevance and implementation of thematic
  information (attributes)
• Recognition of thematic hierarchies and their
  robust and efficient representation
• Advantages and disadvantages of vector and raster
  data structures

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Outline

• Introduction
• Conceptual models of real world geographical
  phenomena
• Coding the basic data models for input to the
  computer
• Data organisation in vector data structures
• Object oriented data structures
• Data organisation in raster data structures
• Images
• Attributes
• Attributes and topological consistency
• Vector versus raster data structures
• Summary

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Introduction

• Models are created from key features
• What we regard as the respective key
  characteristics and how we build the model,
  depends on our cultural background and the
  purpose of the view.
• A fishermans view of a river is different from
  an engineers view
• Should the Danube be seen as a polyline, a
  waterbody, a trench in the earthss surface or a
  place to live for animals and plants? Is it an
  exactly defined and bounded object or rather
  given by the continuously varying field of the
  river beds elevation?
• Conceptual models of space
• entities
• continuous fields

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Conceptual models of space

• 2 questions
• What is present? ? house, river, ...
• Where is it? ? coordinates
• Entities
• Collection of objects (entities) Definition and
  recognition (house, utility line, forest, river,
  etc.) Properties to describe boundaries and
  position
• continuous fields
• Continuous function of cartesian coordinates in
  2, 3 or 4 (if time is included) dimensions
• The variable is a smooth function, continuously
  varying in space

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Levels of creating a model
Conceptual models ...

• A view of reality the conceptual model.
• Human conceptualization leading to an analogue
  abstraction (analogue model).
• A formalization of the analogue abstraction
  without any conventions or restrictions of
  implementation (spatial data model)
• A representation of the data model that reflects
  how the data are recorded in the computer
  (database model)
• A file structure (physical computational model)
• Accepted axioms and rules for handling the data
• Accepted rules and procedures for displaying and
  presenting spatial data (graphical model)

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From observation to standardized data models
Conceptual models ...
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Entities or continuous field?
Conceptual models ...

• Pragmatic decision, determined by the
  application,
• In administration rather entities, in science
  more often continuous fields
• Examples

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Entities or continuous fields?
Conceptual models ...

• Representation of reality in a data model
  requires 3 steps
• Conceptual model of the world (Entities ? ?
  continuous variation)
• Data model collection of discrete objects ? ?
  smooth continuous field
• Representation
• Entities primitives, combinations of them or
• Fields a) discrete b) differentiable,
  mathematical functions c) non differentiable
  functions
• administration entity model preferred
• sciences, dynamic processes continuous fields
  (mostly raster)

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Geographical data models and geographical data
primitives
Conceptual models ...

• geographical data primitives points, lines,
  polygons (vector model)
• Pixels (raster model)

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Data models of entities
Conceptual models ...

• Vector models
• simple points, lines and polygons
• complex points, lines, polygons and objects
• More complex definitions of points, lines and
  polygons can be used to capture the internal
  structure of an entity functional or
  descriptive.
• E.g. city contains streets, houses and parks,
  each having different functionality and may
  respond differntly to queries or operations.
• Object-oriented systems support a hierarchical
  construction of objects from simple building
  blocks and a framework for description of
  properties as well as behaviour.
• Raster models
• Mainly integer grids with lookup table of
  categories
• Loss of spatial resolution

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Data models of continuous fields
Conceptual models ...

• Vector
• Triangulation (TIN)
• Raster (grid)
• Floating point grids

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Raster or vector model?
Conceptual models ...

• Raster model can also represent points, lines and
  polygons
• Loss of spatial resolution, because location is
  only expressed by multiples of pixel size
• Contour maps Entities or fields?
• e.g soil map

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Data modelling and spatial analysis
Conceptual models ...

• There are links between the selected data model,
  the data types and the possible analyses
• If location and shape of an entity are
  time-invariant and exactly known ? Vector model.
• If attributes are fixed, but the entity may
  change shape but not position (e.g. drying up of
  a lake) ? Raster model
• If attributes can vary, object changes position,
  but not shape ? behaviour can be represented by
  object-oriented models
• If no clear entities can be discerned, then often
  a discretized, continuous field is preferable

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Examples for the use of data models
Conceptual models ...

• Water bodies
• Changing water levels in lakes, reservoirs or
  rivers can change their size, shape and position
• During flood events, rivers can change their path
  (breakthrough of meanders, new reaches) ? change
  of geometry and topology!
• Continuous fields in hydrological models
• Continuous fields in GIS only spatially
  discretized (TIN, raster)
• Dimension of time not represented

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Representation (data structures)

• Data models are independent of a specific
  implementation in a GIS. Also analogue maps are
  based on models of the area.
• digital coding of the information, in several
  stages from the data model, data structures, data
  types up to their binary representation
• We need efficient data structures, that
• represent the selected data models completely and
  unambiguously,
• are robust,
• efficiently support the desired analyses and
• use storage space economically.

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Coding the basic data models for input to the
computer
Data structures ...

• discrete primitives of geographical data to
  create entities as well as continuous fields
• Representation of position, relationships and
  attributes of different types
• Points, lines and polygons are the spatial
  primitives in a vector model, pixels in raster
  models.
• Spatial relationships between entities are
  defined by topology

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Data organisation in vector data structures
Data structures ...

• Vector-based geographical databases are composing
  a complex theme of several layers, each of which
  combines a certain class of phenomena.
• E.g. hydrological map rivers, lakes, observation
  sites, land use, etc., each in a separate layer
• Layer (Coverage) consists of entities of one
  type, with relationships, different attributes
• Layers are handled independently from each other
• E.g. data structure does not force a gauge to be
  on the river bank
• Vector-GIS use implicit relations (tables) for
  storage
• Software packages use different structures.

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Points
Data organisation in vector data structures...

• Position of points is defined by a single pair of
  coordinates (X, Y)
• Additional info type of point, attributes
• Layer of point entities created from simple table
• E.g. event theme in ArcView

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Lines
Data organisation in vector data structures...

• Sequence of (X, Y) coordinate pairs and
  connecting straight lines or curves

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Networks
Data organisation in vector data structures...

• Information about connectivity with other line
  entities to represent street networks, utilities,
  rivers
• topological information in the data structures ?
  connectivity tables
• Topological terms node and arc
• arc-node topology

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Polygons
Data organisation in vector data structures...

• Shape, neighbours, hierarchy
• simple polygons sequence of x,y coordinate pairs
• Border lines between polygons are digitized and
  stored twice. Error gaps, overlaps
• No information on neighbourhood.
• islands only graphically represented.
• Difficult to validate

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Polygons
Data organisation in vector data structures...

• Polygons by arc-node-topology
• Underlying principle free of redundancy

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The shape file format (1)
Data organisation in vector data structures...

• ESRI file based format for vector datasets
• Proprietary, but open documentation ? industry
  standard
• A shapefile consists of several files with
  different extensions, e.g. myshapes.shp,
  myshapes.dbf,
• A shape files holds only one type of entities
  points OR lines OR polygons
• myshapes.shp the geometry in binary format
• myshapes.dbf the attributes, in dBase IV format
• myshapes.shx a spatial index
• Optional
• myshapes.sbx index for joins
• myshapes.prj the projection
• Myshapes.shp.xml Metadata for shapefile

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The shape file format (2)
Data organisation in vector data structures...

• Open source libraries to read and write
• No arc-node-topology!
• 3D lines possible (but not widely supported!)
• For details, see http//www.esri.com/library/whit
  epapers/pdfs/shapefile.pdf

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Triangulation of continuous fields
Data organisation in vector data structures...

• Node list and triangle list
• Optimal TIN by Delaunay criteria

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Object oriented data structures
Data structures ...

• Object oriented systems encapsulate data objects
  together with methods applicable to them. Access
  to objects is only done by the methods defined
  for them
• Data structures get a defined behaviour
• Hydrant should delete itself, when the last
  pipe connecting it to the network is removed.
• inheritance
• Structural object orientation capability, to
  create composed objects (Arc Hydro)
• Behavioural object orientation behaviour of data
  types with specifically defined functions and
  procedures
• CASE-Tools (Computer Aided Software Engineering)
  for design and implementation

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Object oriented data structures
Data structures ...

• UML (unified modeling language) diagram of a part
  of a geodatabase

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Object oriented data structures
Data structures ...

• Arc HydroFramework

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Data organisation in raster data structures
Data structures ...

• Raster resembles photo
• 3 ways to interprete a pixel
• classification a range of values is allocated to
  certain objects (gray pixels are roads, blue
  pixels are water surfaces,...).
• measure the value intensity of a colour,
  concentration, etc.
• relative height over reference height.

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Raster data structure
Data organisation in raster data structures

• Position is represented by discrete cells
• Types of raster maps
• Nominal data like land use (forest, grassland,
  farmland, ...)
• Continuous values, concentration, light intensity
• relative measures like elevation.

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Raster data structure
Data organisation in raster data structures

• Entities also in raster model
• Cell size determines resolution cell size max.
  50 of smallest recognized object

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Raster data structure
Data organisation in raster data structures

• Topology described implicitly by raster
• Cell raster point raster

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Images
Data structures ...

• Pictures can be used as map displays (e.g.
  satellite image, orthophoto) or also as attribute
  information (e.g. pictures of the measuring
  instruments linked to the measuring points on a
  measuring point map, photo of the houses in the
  information system of a real estate agent).

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Storage of images
Images

• Similar to raster maps, with some specific
  properties
• Pixel (from picture element)
• Economical storage
• 1, 8, 24 or 32 bit for coding of a colour value
• Number of bits per pixel colour depth
• monochrome, grayscale, RGB, CMY, CMYK
• Use of a lookup table

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Georeferencing of images
Images

• Depending on the orientation of the coordinate
  system, objects equal in nature are represented
  differently in the raster model
• If distortions of image are small (flat terrain)
  ?georeferencing by affine projection with gt 4
  ground control points (polynomial
  transformation).
• Pixel are re-computed by interpolation or areal
  averaging, according to the type of variable ?
  loss of information

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Storing vector and raster data in DBMS
Data structures ...

• Efficient access to large volumes of data with
  complex relationships
• B-Trees
• R-Trees
• Use of DBMS
• Geo-relational model
• Hybrid concept geometry data in vendor-specific
  binary format, attributes in RDBMS (INFO, ORACLE,
  INGRES, INFORMIX, MS ACCESS)
• Storage of attribute data independently from
  spatial data
• extension, updating, deletion of attribute data
  do not influence spatial data
• Commercial RDBMS ensure use of latest
  developments and standardisation
• Use of standard query language like SQL

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Attribute information

• Geoinformation is based on two main elements
• Geometry and topology (Question Where?) and
• Thematic information (attributes) (Question
  What?).
• Approach via thematic maps
• Analogy of transparencies

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Attribute information in a raster model
Attribute information

• Geometry and topology determined by definition of
  the raster (origin, resolution)
• Attribute information is additional dimension
• Spatial query, thematic query, and combined query

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Thematic information in vector models
Attribute information

• A theme is assigned to each topological object
  (node, edge, polygon) by one or more attributes
  (often tied to a label point)
• MN relationship between different thematic
  layers ? resolve into n units with 1M
  relationship

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Thematic attributes
Attribute information

• thematic attributes quantitatively classify
  objects, e.g., a land parcel is attributed by ID,
  area, prize, owner, address, etc.
• Logically organized in tables
• A key-field uniquely relates attributes and
  topological objects
• required and optional attributes
• computed attributes (area, length)
• Hierarchical inheritance of attributes in
  object-oriented systems

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Thematic information and topological consistency
Topological consistency ...

• Consistency of data is one of the most important
  criteria of an information system. It must be
  warranted when new data are added as well as
  after updates

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Thematic information and topological consistency
Topological consistency ...

• Topology-rules in ArcGIS 8.3
• Polygons

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Thematic information and topological consistency
Topological consistency ...

• Topology-rules in ArcGIS 8.3
• Lines

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Thematic information and topological consistency
Topological consistency ...

• Topology-rules in ArcGIS 8.3
• Points

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Vector versus raster data structures

• Decision depends on classes of represented
  objects
• Linear phenomena are better handled in vector
  models
• Raster model has advantages with areal data
• If high positional accuracy is important, rasters
  need too much storage
• Applications define the criteria
• Coordinate transformation is easy in vector
  models
• Coordinate transformation is more difficult for
  raster models, because input pixel generally do
  not have only a single output pixel ?
  irreversible process

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Data exchange, standardization

• De-facto-standards for exchange of geometry and
  attribute information
• Topology is not so common
• Meta data
• national, European and international standards
• OpenGIS Consortium (OGC) Interoperability of
  GIS

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Summary

• Data structures should represent spatial
  phenomena completely and clearly and support
  efficient analysis
• Discrete primitives for entities and continuous
  fields
• Topology Relationship between entities. Arc-node
  topology supports connectivity, definition of
  areas and connectivity
• Vector-GIS generally implement a layer concept
  with basic elements of points, lines, networks or
  polygons
• TIN is a vector data structure for continuous
  fields
• Object oriented data structures encapsulate data
  objects together with methods for their behavour.

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Summary

• Raster data structures generally grid of square
  cells, aligned with coordinate axes
• Images are special raster data sets with high
  resolution
• Thematic attributes describe what an object is
  (semantics)
• DBMS for robust storage of geo-data
• Adherence to national and international standards
  for exchange of geo-data between different
  systems and institutions