Delineating Regions

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Delineating Regions
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Regions

• Regions are identical areas or share common
  characteristics
• Regions could be locations serviced by single
  points or areas (e.g. Villages depend on Towns
  for services)
• Regions is a group of cells that have the same
  attribute value
• Regions can be a temporary set of cells taken
  from vector polygons
• Regions can have distinct or vague boundaries
• Not all regions are physical boundaries

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World GDP per Capita, 2000 (US)
Not Available
Less than 2,000
2,000 to 5,000
5,000 to 12,000
12,000 to 20,000
More than 20,000
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World Crude Oil Production, 2001 (in 1,000
barrels per day)
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World Petroleum Consumption, 2001 (in 1,000
barrels per day)
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Mode of Territorial Occupation by Transport
Networks
Overlap
Air corridor
Rail
No service
Road
Cellular coverage
Maritime corridor
Vaguely defined
Without definition
Clearly defined
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The Optimal Shape of a Market Area
A
B
10 km
E
C
D
20 km
17 km
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Non-Isotropic Conditions and the Shape of Market
Areas
Isotropic Condition
Non-Isotropic Conditions
Modified Market Areas
Low
Average
High
Road
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Reillys Law
Mab
29.1 km
45.9 km
a
b
75 km
100,000
250,000
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Reillys Law and Market Areas
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b
e
30 km
35
35 km
a
55
15 km
20
d
30 km
15
c
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Techniques in analysing regions

• Logical operations
• Feature extraction, merging.
• Proximity analysis
• Buffers, distance comparisons, Thiessen.
• Boundary operations
• Clip, erase, update, split, append.
• Spatial joins
• Point-in-polygon, line-in-polygon,
  polygon-in-polygon.

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Proximity Analysis

• The term proximity analysis can mean any
  procedure that performs neighborhood, vicinity,
  or distance analysis.
• The basic framework for proximity analysis
  includes several types of spatial relationship
  questions.

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Nearest Feature

• Calculating distance between features or finding
  the nearest features are very useful GIS
  operations, especially when database attributes
  can be incorporated.
• Near is a generic GIS proximity analysis
  procedure that determines the shortest distance
  from one feature or features to a set of others.

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Spider Diagrams

• Spider diagrams are special operations that
  compute (and show) point-to-point multiple
  distances.
• They draw lines from each feature or location to
  its nearest source.

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Spatial Operations

• Two of the most important spatial operations are
  centroids and thiessen polygons.
• Centroids associate the size and shape of lines
  or polygon features, whereas the Thiessen
  operation expands points into polygons.

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Centroids

• Lines and polygons can be represented by their
  center points, called centroids.
• The spatial centers are computed and a single
  point replaces the feature.
• All attributes are transferred to the centroids
  database.
• Center points usually are the mean X and Y
  coordinates.
• Centroids can have several applications. First is
  the utility of knowing the geometric center of a
  polygon in addition, centroids can simplify an
  area of mixed-size and mixed-shape polygon to a
  more efficient visual and database structure.

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Thiessen Polygons

• The opposite of centroids are equal areas around
  points, termed Thiessen polygons (also called
  proximal polygons).
• They are the territories of points. The program
  extends each points area until it meets the next
  one coming from a neighbor point or until it runs
  into a theme edge. The boundaries are an equal
  distance (or halfway) between two points.

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Theissen (Voronoi) polygons

• Each point is credited with the region of
  points closer to it than to any other point

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Dulaunay Triangulation

• By testing adjacent regions of the Voronoi
  diagram, interesting questions can be answered.

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Proximity Analysis
Point distance
Buffer
Near
Thiessen
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Thiessen (Voronoi) Polygonsand Delaunay Triangles
Thiessen Polygons (or proximal regions or
proximity polygons)

• Polygons generated from a point layer such that
  any location within a polygon is closer to the
  enclosed point than to a point within any other
  polygon
• They divide the space between the points as
  evenly as possible
• Used for market area delimitation, rain gauge
  area assignment, contouring via Delaunay
  triangles (DTs), etc.
• Elevation, slope and aspect of triangle
  calculated from heights of its three corners
• DTs are as near equiangular as possible and
  longest side is as short as possible, thus
  minimizes distances for interpolation

Delaunay Triangles
Thiessen neighbors of point A share a common
boundary. Delauney triangles are formed by
joining point to its Thiessen neighbors.
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Districting elementary school attendance zones
grouped to form junior high zones.
Regionalization census tracts grouped into
neighborhoods
Classification cities categorized as central
city or suburbs soils classified as igneous,
sedimentary, metamorphic
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Voronoi queries

• Where is the nearest facility, e.g. fire house,
  hospital, restaurant?
• Which is the second best facility?
• What is the largest empty region (to put new
  store, or toxic dump)

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is nearest to

• point/point- which clinic is closest to
  thevillage?
• point/line- which road is nearestto the village
• same with other combinations of spatial features

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is nearest toThiessen polygons
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Polygon overlay
Hospital CatchmentAreas
Districts
Overlay
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Point in polygon
even number of intersections point is
outside odd number of intersections point is
inside
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Areal weighting

• If 30 of district d overlaps with hospital zone
  z, then zone z will also receive 30 of district
  ds population
• Areas of overlap derived from a polygon overlay
  operation
• Assumes that districts have constant densities

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Operations on raster layers

• cell by cell operations (local)
• neighborhood operations (focal)
• operations that consider entire layer (global)
• region-specific operations (zonal)
• descriptive operations

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Local operations

• New layer is a functionof two or more
  inputlayers
• Output value for eachcell is a function ofthe
  values of the corresponding cells in the input
  layers
• Neighboring or distant cells have no effect

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Raster map overlay

• Output cell value is the result of an arithmetic
  operation on the input layers
• e.g., if a and b are input layers and c is an
  output layer,c a bc a b..
• Also any kind of function such as average, sum,
  min, max, std. dev.

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Raster map overlay

• These operations are often termed map algebra
• Important to consider measurement of input data
  layers e.g., it makes no sense- to divide soil
  class a by land use class b- or to add
  population density in layer a to the agroclimatic
  class in layer b

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Neighborhood operations (focal)

• Output cell value isa function of a groupof
  neighboring cellsin the input raster
• Operations could be- average (zonalmean)- sum
  (zonalsum)- variance (zonalvar)

input
output
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Other focal operations

• SlopeSteepness of slope in elevation
  layerComputed by comparing cell elevation with
  neighboring valuesMeasured as the angle from
  horizontal

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Distance

• Output cell values are the distances from an
  originating cell or point

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Buffer

• Can be thought of as spreading a feature by a
  given distance

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Buffer

• Buffer around streams carrying water-borne
  diseases to estimate population at risk
• Noise buffer around a road
• Buffer around habitat of a threatened species
• Extent of buffers can be modified using -
  barriers e.g., physical features- friction
  e.g., cost of travel

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Readings on the topics
Chapter 14 in Longley et al. (2005) pp.
333-336 Chapter 5 in Burrough-McDonnell (1998)
pp. 98-102, 113-121
Exam questions
What is a region? Illustrate two techniques to
analyse regions. Use sketches to illustrate the
techniques.