Playing with Spaghetti: Vector and Raster Data Models in Depth

1
Playing with SpaghettiVector and Raster Data
Models in Depth

• Talbot J. Brooks
• ASU Dept. of Geography

2
Tonights topics

• Recap of discussion so far
• Big picture overview Raster vs. Vector
• The details Vector data models
• The details Raster data models
• Cardinality an exercise

3
Review you tell me

• What is the difference between vector and raster
  data?
• Basic vector data types
• Examples of raster data
• Computer file structures
• Flat
• Hierarchical
• Network
• Relational

4
RASTER AND VECTOR FORMATS
RASTER Grid-based, Simplify reality VECTOR
Analog map, Cartography
5
DATA MODEL OF RASTER AND VECTOR
REAL WORLD
1 2 3 4 5 6
7 8 9 10
1 2 3 4 5 6 7 8 9 10
GRID RASTER
VECTOR
6
RASTER DATA MODEL

• derive from formulation that real world - it has
  spatial elements and objects fills those elements
• real world is represented with uniform cells
• list of cells is a rectangle
• cell comprises of triangles, hexagon and higher
  complexities
• a cell reports its own true characteristics
• per units cell does not represent an object
• an object is represented by a group of cells

7
Lake
River
Pond
Reality - Hydrography
Lake
River
Pond
Reality overlaid with a grid
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0 No Water Feature 1 Water Body 2 River
1
1
1
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
Resulting raster
Creating a Raster
8
VECTOR DATA MODEL

• derived from the formulation of spatial concepts
  that emphasize on real world objects
• geometry primitives of vector data model are
  point, line and polygon
• objects can be built from these primitives
• object location determined by represented
  location point
• uniqueness of vector data model lies in its
  management and storage of data geometry
  primitives
• spaghetti model
• topology model

9
VECTOR CHARACTERISTICS
POINT X LINE POLYGON
10
RASTER TO VECTOR
RIVER CHANGED FROM RASTER TO VECTOR FORMAT
RIVER THAT HAS BEEN
VECTORISED ORIGINAL RIVER
11
PRO AND CONS OF RASTER MODEL

• pro
• raster data is more affordable
• simple data structure
• very efficient overlay operation
• cons
• topology relationship difficult to implement
• raster data requires large storage
• not all world phenomena related directly with
  raster representation
• raster data mainly is obtained from satellite
  images and scanning

12
PRO AND CONS OF VECTOR MODEL

• pro
• more efficient data storage
• topological encoding more efferent
• suitable for most usage and compatible with data
• good graphic presentation
• cons
• overlay operation not efficient
• complex data structure

13
A look behind the scenes Vector GIS data models

• Spaghetti model
• Topological vector model
• Cardinality (this is gonna hurt!)
• Break

14
The Spaghetti Model

• The spaghetti model is the most simple vector
  data model
• The model is a direct representation of a
  graphical image
• NO explicit topological information

15
Spaghetti Model

• Description direct line for line translation of
  the paper map (often viewed as raw digital data)
• Pros easy to implement, good for fast drawing
• Cons storage and searches are sequential,
  storage of attribute data

16
Spaghetti model
17
Topology

• Branch of mathematics dealing with geometric
  properties
• Geometry of objects remain invariant under
  transformations
• Neighborhood relationships remain the same
• Topology is the distinguishing basis for more
  complicated vector models

18
Topological Vector Model

• Topological data models are provided with
  information that can help us in obtaining
  solutions to common operations in advanced GIS
  analytical techniques.
• This is done by explicitly recording adjacency
  information into the data structure, eliminating
  the need to determine it for multiple operations.
• Each line segment, the basic logical entity in
  topological data structures, begins and ends when
  it either contacts or intersects another line, or
  when there is a change in direction of the line.

19
Topological Vector Model

• Each line has two sets of numbers, a pair of
  coordinates and an associated node number.
• Each line segment has its identification number
  that is used as a pointer to indicate which set
  of nodes represent its beginning and ending.

20
Topological Vector Model

• Polygons also have identification codes that
  relate back to the link numbers. Each link in
  the polygon now is capable of looking left and
  right at the polygon numbers to see which two
  polygons are also stored explicitly, so that even
  this tedious step is eliminated.
• The Topological data model more closely
  approximates how we as map readers identify the
  spatial relationships contained in an analog map
  document.

21
Topological Vector Model
22
How do we preserve topology ina computer
database?

• What are we storing?
• Points, lines, polygons
• What do we need to preserve?
• Neighborhood relationships between these objects
• Terminology
• point, link, node, polygon

23
Terminology

• Point x, y coordinate identifying a geographic
  location
• Link (line, arc) an ordered set of points with a
  node at the beginning and end of it
• Node the beginning and end of link (often
  defined where 3 or more lines connect)
• Polygon two or more links connected at the
  nodes, contains a point inside to identify the
  polygons attributes

24
Nevada
Utah
California
Arizona
25
Identify the polygons
26
Create the polygon attribute table (PAT)
27
Identify the nodes
28
Node table
29
Identify the links (arcs, lines)
30
Simplify this
31
Create the topology!
32
Nodes First
33
Nodes First
34
Polygons
35
Polygons
36
Identify the points
37
Link List
38
Point Coordinates
39
Putting it all together
40
Putting it all together
41
Putting it all together
42
Putting it all together
43
Putting it all together
44
Cardinality

• Cardinality is the relationship between spatial
  objects, attributes, or spatial objects and
  attributes.
• This relationship may be defined as
• 11
• 1many
• manymany

45
Cardinality

• We can use cardinality to establish relationships
  and rules among objects and attributes
• This becomes the basis for modeling how data is
  arranged within a GIS - especially one that uses
  vector data.

46
Cardinality contd

• Entity-entity relationships are described by
  cardinality which may be
• One to one. A FOREST can have only one MANAGER
  and a MANAGER can have only one FOREST
• Many to one. Many FACILITIES may be contained
  within one FOREST
• Many to Many. The relationship water_supply may
  have many entries and may be connected to many
  entries FACILITIES, FOREST, etc

47
Cardinality contd

• The same concept applies to space
• A bathroom is located within a house (11)
• Many homes are within a town (many1)
• Many people are within many homes (manymany)

48
Diagram Characteristics

• Boxes represent entities
• Ovals represent attributes
• Diamonds represent relationships
• Note how cardinality is depicted
• Key attributes are underlined
• Multi-valued attributes are in double ovals

49
Entity-Relationship (ER) Diagrams A Conceptual
Model
50
Exercise work in pairs 10 minutes

• Create a simple ER diagram for your neighborhood
• Pick a feature that matches each geometry type
  (point, line). For example
• For points, you might pick fire hydrants and lamp
  posts
• For lines, you might pick streets and water mains
• For polygons, pick parcels or zip codes

51
Break time!
52
Raster data
53
What type of data?

• Continuous data
• Examples elevation, temperature
• Square grid tessellation also called raster

54
Raster Models (tessellation)
55
Raster
Data values are stored in rows and columns
56
Two types

• Scanned Map images
• Digital Raster Graphic
• Other maps
• Tessellation Models
• Square Grid Tessellation
• Hexagon Tessellation

57
Scanned Maps

• Scanned map as a photograph
• The value of each cell represents the color on
  the map needs to be interpreted the way a
  paper/analog map is interpreted

58
Digital Raster Graphic (DRG)
There is typically another file linked with the
DRG, so that the geographic position of the
graphic is known
59
MapQuest
60
Maps or Images??
61
Summary of scanned maps

• Have the characteristics of an analog map in that
  the location information and the attributes are
  stored as a visual product
• No queries can be made based on the database

62
Tessellation Models

• Location-based spatial data model process of
  dividing an area into smaller, contiguous tiles
  with no gaps between them
• Types
• regular and irregular
• Uses continuous surfaces
• Pros easy to implement and manipulate
• Cons high data storage, output not cartographic
  quality

63
Spatial and Attribute Data

• Combined in a single file
• Unlike the scanned maps, they can be searched

64
Tessellation Models

• Regular

Most common
Rarely used
65
Tessellation models
Regular grid
66
Data

• Rows and columns containing the attribute value
  associated with each data layer
• The row/column location of the data value
  represents the spatial position
• Exact geographic position is typically
  established with header information before the
  rows and columns of data
• Also need knowledge of what the values represent
  (e.g., elevation in meters) typically part of
  the metadata

67
Rows and Columns
68
Geographic Position
origin
orientation
size of each cell
69
Sample data
70
Each cell has a value
71
Data File
Origin (x,y) Ymax (x,y) Row,col Cell size
72
Tessellation models
Hexagonal mesh
Primary advantage over square grid tessellation
is distance measurements. Important in
applications that need to spread distances evenly
- e.g., spread of forest fires
73
Distance between adjacent cells?
Example modeling the spread of a fire from one
cell to the next adjacent cell.
74
Distance measurements between cells is the same
in the hexagon model
75
Where do we get raster data? Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• DRG
• Converted into a tessellation database
• Interpolating data from points

76
One satellite data

• Example Landsat Thematic Mapper (TM) data from
  USGS

77
(No Transcript)
78
(No Transcript)
79
Multispectral

• Multispectral meaning that each cell has more
  than one value (different sections of the
  electromagnetic spectrum) associated with it
  (these are called bands)

80
Bands and Resolution

• Fixed spatial resolution (either 30 meters or 120
  meters) depending on the band

Landsats 4-5 Wavelength (micrometers) Resolution
(meters) Band 1 0.45-0.52 30 Band 2
0.52-0.60 30 Band 3 0.63-0.69 30 Band
4 0.76-0.90 30 Band 5 1.55-1.75 30
Band 6 10.40-12.50 120 Band 7 2.08-2.35
30
81
What can we do with the bands?

• Band 1 penetrates water for bathymetric mapping
  along coastal areas and is useful for
  soil-vegetation differentiation and for
  distinguishing forest types.
• Band 2 detects green reflectance from healthy
  vegetation, and
• Band 3 is designed for detecting chlorophyll
  absorption in vegetation.
• Band 4 data is ideal for detecting near-IR
  reflectance peaks in healthy green vegetation and
  for detecting water-land interfaces.
• The two mid-IR red bands on (bands 5 and 7) are
  useful for vegetation and soil moisture studies
  and for discriminating between rock and mineral
  types.
• The thermal-IR band on (band 6) is designed to
  assist in thermal mapping, and is used for soil
  moisture and vegetation studies.

82
False color

• Bands 4, 3, and 2 can be combined to make
  false-color composite images where band 4
  represents the red, band 3 represents the green,
  and band 2 represents the blue portions of the
  electromagnetic spectrum. This combination makes
  vegetation appear as shades of red, brighter reds
  indicating more vigorously growing vegetation.
  Soils with no or sparse vegetation range from
  white (sands) to greens or browns depending on
  moisture and organic matter content. Water bodies
  will appear blue. Deep, clear water appears dark
  blue to black in color, while sediment-laden or
  shallow waters appear lighter in color. Urban
  areas appear blue-gray in color. Clouds and snow
  appear bright white. Clouds and snow are usually
  distinguishable from each other by the shadows
  associated with clouds

83
False Color Example
84
False Color example
85
False Color example
86
With the same data (NDVI)
Normalized difference vegetation index
87
Where do we get raster data? Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• DRG
• Converted into a tessellation database
• Interpolating data from points

88
Second source for raster data

• Data that are in another format (either vector or
  paper map) and need to be converted to a raster
  format

89
Land use in vector format
To convert it, we need to decide what size each
cell needs to be. How do we decide? Minimum
mapping unit and spatial resolution.
90
Sort the database
91
Minimum mapping unit
92
Better
This would give us a 2 m cell size
93
Default settings
94
Resulting data
95
Resulting data
755 (default)
96
200 meters
97
100 meters
98
10 meters
99
(No Transcript)
100
(No Transcript)
101
(No Transcript)
102
Which is best?
vector
100 meter
10 meter
103
Area and database size comparisons
104
Three conversion from a paper map

• Scanning can convert to a DRG or into a square
  grid or hexagon database
• Same rules apply as with vector scanning best
  approach is to trace to mylar, then scan
• (my personal experience it is easier to vector
  digitize, then use software to convert to raster
  format)

Note with scanning you can create either a DRG
or a tessellation database
105
Database size can be a problem Compaction
Run length encoding
106
In some cases, there is very little you can do
107
Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• Interpolating data from points