Maps as Numbers

1
Maps as Numbers

• Front Range Community College
• GIS 101 Spring 2004
• Damon D. Judd

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Objectives

• Understand the nature of GIS data models.
• Recognize technical raster data model issues.
• Identify raster-based GIS applications.
• Identify the principle components of the vector
  data model and arc/node data structure.
• Learn why topology is important.
• Compare and contrast the raster and vector data
  models.
• Learn about GIS data storage and exchange formats
  and spatial data standards.

3
"The good cartographer is both a scientist and an
artist. He must have a thorough knowledge of his
subject and model, the Earth. He must have the
ability to generalize intelligently and to make a
right selection of the features to show. These
are represented by means of lines or colors and
the effective use of lines or colors requires
more than knowledge of the subject - it requires
artistic judgment. Erwin Josephus
Raisz(1893-1968)
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Storing Maps in Digital Form

• GIS requires that maps be represented as numbers.
• The GIS places data into the computers storage
  media in a physical data structure (i.e. files
  and directories).
• Data files can be written in binary or as ASCII
  text.
• Binary is faster to read and smaller, ASCII can
  be read by humans and edited but uses more space.
• Linked attribute data are normally stored in
  tables using a DBMS.

5
Three approaches to handling spatial data within
a GIS

• Raster model
• Array of grid cells
• Vector model
• Points, lines, polygons
• Object-oriented model
• Object classes stored in database tables

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The GIS Data Model

• A logical data model is how data are organized
  for use by the GIS.
• A GIS map is a scaled-down digital representation
  of point, line, area, and volume features.
• GISs have traditionally used either raster or
  vector file structures for storing maps.

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The Raster GIS Data Model
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Def Raster

• Raster - A format for storing, processing, and
  displaying graphic data in which graphic images
  are stored as values for uniform grid cells or
  pixels (picture elements).

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Raster Data Example 1 DEM of Denver Area
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Raster Data Example 2 Satellite Image of Front
Range
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Other Types of Raster (Grid) Data

• Grids
• Elevation (DEM)
• Soils
• Land Cover
• Precipitation
• Geology

• Images
• Satellite Imagery
• Scanned Maps
• Orthophotos
• Scanned Documents
• Radar

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Characteristics of Raster Data

• Rows and Columns of Cells (Array)
• One grid cell is one unit or holds one attribute.
  
• Every cell has a value, even if it is missing
  or Null.
• Value for each cell records type of object or
  condition, or used as index to lookup a value.
• Area of Cell, given as the cell size in ground
  units, equals Spatial Resolution.
• Cells are considered Homogeneous Units.
• Cells do not correspond to spatial entities in
  real world.

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Generic structure for a grid
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Def Pixel

• Pixel - Abbreviation for picture element, the
  smallest indivisible element that makes up an
  image.
• In raster processing, data are represented
  spatially on a matrix of grid cells, which are
  assigned values for image characteristics or
  attributes.
• Pixel Grid Cell for raster imagery.

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The mixed pixel problem

• A pixel containing multiple potential values for
  the ground extent of a grid cell - only one value
  can be assigned.
• Common along the edges of features or where
  features are ill defined.

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Def Spatial Resolution

• Spatial Resolution - The accuracy associated with
  the capture of ground information as reproduced
  in a digital format or graphic display.
• The size of a pixel in ground units.
• Examples 30m, 3 arc-second, 100 ft.

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Examples of Different Spatial Resolutions
30m Landsat
1m Ikonos
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Def Minimum Mapping Unit

• Minimum Mapping Unit - The smallest element we
  can uniquely represent in our data.
• Why do we care? Becomes important in spatial
  analysis operations (e.g. spatial overlay)

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Spatial Analysis - Overlay

• Arithmetic Operations
• Addition
• Subtraction
• Division
• Multiplication

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Spatial Analysis - Overlay

• Logical Operations
• Union (AND)
• Intersection (OR)
• Exclusion (NOT)

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Raster Data - Advantages

• Rasters are faster (support spatial indexing).
• Rasters are easy to understand, easy to read and
  write, and easy to draw on the screen.
• Better for continuous data types (esp. Imagery).
• A grid or raster translates directly onto a
  programming data structure called an array.
• Raster data compression techniques (e.g.
  quadtrees, MrSID) greatly reduce the data storage
  problem.

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Raster Data - Limitations

• Data storage requirements are greater.
• Overlay operations must be performed on every
  cell.
• Sparse data sets require as much processing as
  dense ones.
• Accuracy is dependent on spatial resolution
• Points and lines in raster format have to move to
  a cell center (introduces error).
• Lines can become fat.
• Areas may need separately coded edges (mixed
  pixel problem).
• Each cell can represent only one feature or value.

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Sources of Raster Image Data

• Satellite data
• LANDSAT (NASA civilian satellite)
• SPOT (French satellite system)
• Space Imaging (Ikonos)
• DigitalGlobe
• Scanned aerial photography
• Digital Orthophotography
• Scanned maps and documents

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Raster GIS Applications

• Integrate images to georeferenced data
• Ex Link scanned drawings to parcel centroids
• Gridded surfaces are important
• Ex Wildfire modeling - compare/analyze
  continuous data such as slope, vegetation,
  precipitation
• Natural resource applications where
• Positional accuracy relaxed
• Large area coverage needed
• Imagery-oriented

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Remote Sensing Integration

• Vector Updating (feature extraction)
• Change Detection
• Land Use/Land Cover analysis
• Anderson Classification Scheme (Anderson, 1976)

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Anderson Classification Scheme (Level 1)

• Land cover can be classified into the following
  types
• Urban and built-up land
• Agricultural land
• Rangeland
• Forest land
• Water
• Wetland
• Barren land
• Tundra
• Perennial snow or ice

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Raster GIS Applications

• Agriculture Precision farming, commodities
  forecasting, global food security analysis, crop
  damage assessments
• Environment Impact assessments, regulatory
  compliance studies
• Natural Resources Natural resource management
  and monitoring
• Exploration Oil and gas exploration and
  monitoring
• Local government Local and regional planning,
  mapping, urban monitoring, change detection
• Utilities Facilities management and monitoring,
  utility corridor assessments, accessibility
  studies
• Infrastructure Transportation network
  assessments, site planning and development
  studies
• International Relief operations support,
  treaty/sanctions verification, regional estimates
  
• National Emergencies Natural disaster
  assessments, emergency evacuation studies
• Insurance Property loss evaluations and risk
  assessments
• Law Litigation support
• Telecommunications Cell siting studies, network
  assessments, corridor planning
• Media Reporting

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Break

• Take a breather

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Vector Data Models

• A vector data model uses points stored by their
  real (earth) coordinates.
• Lines and areas are built from sequences of
  points in order.
• Lines have a direction to the ordering of the
  points.
• Polygons can be built from points or lines.
• Vectors can store information about topology.

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Vector Data Model Primitives

• Points, Nodes
• Lines, Arcs
• Area, Polygons

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Vector Data

• Point single X,Y coordinate pair
• Line series of X,Y coordinate pairs
• Polygon area as a closed loop of X,Y coordinate
  pairs

n2
3
2
A
1
B
n1
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Cartesian Coordinate Systems

• X,Y Coordinate systems
• UTM (Universal Transverse Mercator)
• State Plane Coordinate System
• Geographic Coordinates
• (Xlongitude, Ylatitude)

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Spaghetti Data Model

• Collection of coordinate strings with no
  structure
• Cartesian coordinates stored in data structure
• No spatial relationships stored
• Inefficient data storage technique

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Topological Model

• Topology mathematical method to define spatial
  relationships
• (e.g. adjacency, containment, connectivity)
• Arc-node data model
• Arc a series of points that start and end at a
  node
• Node an intersection point where two or more
  arcs meet

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Additional Vector Terms

• Endpoints the points where a line begins or
  ends (Nodes).
• Vertices the points where a line changes
  direction or is intersected by another line.
• Edges the segments between areas (faces).

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Topology

• Def The spatial relationships between connecting
  or adjacent map features.
• Topological relationships are built from simple
  elements into complex elements.
• Redundant data (coordinates) are eliminated
  because an arc may represent a linear feature,
  part of a boundary of an area feature, or both.

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More Topology

• Topology allows automated error detection and
  elimination.
• Rarely are maps topologically clean when
  digitized or imported.
• A GIS has to be able to build topology from
  unconnected arcs.
• Nodes that are close together are snapped.
• Slivers due to double digitizing and overlay are
  eliminated.

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Topological Vector Data Model

• The topological vector model uses the line (arc)
  as a basic unit.
• Areas (polygons) are built up from arcs.
• The endpoint of a line (arc) is called a node.
  Arc junctions are only at nodes.
• Stored with the arc is the topology (i.e. the
  connecting arcs and left and right polygons).

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Arc/Node Vector Data Structure

• At first, GISs used vector data and cartographic
  spaghetti structures.
• Vector data evolved to the arc/node model in the
  1960s.
• In the arc/node model, an area consist of lines
  and a line consists of points.
• Points, lines, and areas can each be stored in
  their own files, with links between them.
• Topology is supported.

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Basic arc topology
n2
3
2
A
1
B
n1
Topological Arcs File
Arc
From
To
PL
PR
n1x
n1y
n2x
n2y
1
n1
n2
A
B
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14.1
25.2
16.2
Figure 3.5
A topological structure for the arcs.
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Storing Coordinates for Arc/Node Data
13
1 x y
11
e
2 x y
l
i
12
3 x y
F

10
s
2
4 x y
t
7
n
5 x y
i
5
o
POLYGON A
6 x y
P
9
7 x y
4
8 x y
6
1
9 x y
2
10 x y
3
11 x y
8
12 x y
13 x y
1
File of Arcs by Polygon
1,2,3,4,5,6,7
1
A
, Area, Attributes
1,2
1,8,9,10,11,12,13,7
2
Arcs File
Figure 3.4
Arc/Node Map Data Structure with Files.
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Unsnapped Node
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The Bounding Rectangle (Mapextent)
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Topology Matters

• The tolerances controlling snapping, elimination,
  and merging must be considered carefully, because
  they can move features.
• Complete topology makes map overlay feasible.
• Topology is useful in GIS because many spatial
  modeling operations dont require coordinates,
  only topological information.
• Topological data structures dominate GIS software.

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Topological Data Spatial Operations

• Contiguity spatial relationship of adjacency
• i.e., stand of coniferous trees adjacent to
  deciduous trees
• Connectivity interconnected pathways or
  networks
• i.e., street networks, water networks

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Contiguity

• Zoning
• Residential
• Commercial
• Industrial
• Parks, open space, greenbelts

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Connectivity - Shortest Path
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Connectivity Quickest Path
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TIN Triangulated Irregular Network

• Topologic vector data structure for 3-D surfaces.
• Common in some GIS and many CAD packages.
• More efficient than a grid.

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More on TINs

• Volumes (surfaces) are structured with the TIN
  model, including edge and/or triangle topology.
• TINs use an optimal Delaunay triangulation of a
  set of irregularly distributed points.
• TIN surfaces honor the original data values at
  the nodes of triangles.
• TINs are popular in CAD and surveying packages,
  and for supporting engineering design and volume
  calculations.

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Vector Data Formats

• Vector formats use either page definition
  languages or preserve ground coordinates.
• Page languages are HPGL, PostScript, and Autocad
  DXF.
• True vector GIS data formats are DLG (digital
  line graph) and TIGER (census), which has
  topology.

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More Data Formats
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Arc/Info Coverages

• The coverage is the vector data storage format in
  Arc/Info.
• It represents a single set of geographic objects
  such as roads, parcels, soil units, or wells in a
  given area.
• A coverage supports the georelational model - it
  contains both the spatial (location) and
  attribute (descriptive) data for geographic
  features.
• It uses the INFO database format to store
  attribute tables and has been replaced in ArcGIS
  8.x by the geodatabase.

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ArcView Shapefiles

• Shapefiles are a simple, non-topological format
  for storing the geometric location and attribute
  information of geographic features.
• A shapefile is one of the spatial data formats
  that you can work with in ArcView (v3.x and
  v8.x).
• The shapefile format defines the geometry and
  attributes of geographically-referenced features
  in as many as five files with specific file
  extensions that should be stored in the same
  project workspace.

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ESRI Geodatabase

• Geodatabases contain feature classes and tables.
• Feature classes can be organized into a feature
  dataset they can also exist independently in the
  geodatabase.
• Feature classes store geographic features
  represented as points, lines, or polygons, and
  their attributes they can also store annotation
  and dimensions.
• All feature classes in a feature dataset share
  the same coordinate system.
• Geodatabase tables may contain additional
  attributes for a feature class or geographic
  information such as addresses or x,y,z
  coordinates.

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Geodatabase Relationships

• Objects in a geodatabase can be related to each
  other.
• To explicitly define the relationships between
  objects in a geodatabase, you must create a
  relationship class.
• Relationships let you use attributes stored in a
  related object to symbolize, label, or query a
  feature class.
• Feature classes in a feature dataset can be
  organized into a geometric network. The network
  combines line and point feature classes to model
  the linear network and maintains topological
  relationships between its feature classes.

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Object-Oriented GIS

• Databases that support objects has been a major
  development in the software world.
• Object-oriented databases represent the future of
  GIS data models.
• The first object model GIS was Smallworld (now GE
  Smallworld).

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Data Exchange Formats

• Most GISs support many formats and use one data
  structure.
• If a GIS supports many data structures, changing
  structures becomes the users responsibility.
• Data also are often exchanged or transferred
  between different GIS packages and computer
  systems.
• Example data exchange formats include
• DXF (AutoCad drawing exchange format)
• SDTS (Spatial Data Transfer Standard)
• .E00 Arc/Info coverage export

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Raster GIS Data Formats

• Most digital images are raster
• Orthophoto (TIF, MrSID)
• Satellite Image (BIL, BIP, MrSID, ECW)
• Geo-referenced Scanned image (e.g. DRG)
• TIF, GIF, JPEG commonly accepted raster formats
• Encapsulated PostScript (EPS), CGM, BMP are
  raster formats that are not geo-referenced.
• DEMs (Digital Elevation Models) are true raster
  data formats.

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GIS Data Exchange

• Data exchange by translation can lead to
  significant errors in attributes and in geometry.
• In the USA, SDTS was evolved to facilitate data
  transfer.
• SDTS became a federal standard (FIPS 173) in
  1992.
• SDTS contains a terminology, a set of references,
  a list of features, a transfer mechanism, and an
  accuracy standard.
• DLG, DEM, and TIGER data are available in SDTS
  format.
• Other standards efforts include those from FGDC,
  OGC, ISO, the Tri-Service Spatial Data Standards
  (SDSFIE), and other international standards.

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Data Exchange -- Bottom line

• Understand what the data formats and metadata are
  and know what your GIS package accepts.
• To exchange data between systems you must know
• What coordinates your data are in.
• What map projection(s) your data are in.
• What datum was used to capture the data.
• What units the data are in.