Session 4: rasters

1
Session 4 rasters
2
Philosophical background

• On 2D space we may have fields or objects
• fields have value everywhere
• objects have a location and a geometry
• Vector geodata is typically better in
  representing objects
• but can as easily be used for fields (see
  tessellations)
• Raster geodata is typically better in
  representing fields than objects
• but can be used for objects too

3
raster algebra

• a f(b,c,d,...)
• a, b, c, d, etc. are rasters (map layers) or
  scalars
• f is a function
• note operators, such as and can also be
  represented as functions, for example abc can
  be written as asum(b,c)

4
data types

• In general, raster data type is either Integer or
  Real (can also be Complex)
• In Integer valued rasters, the value typically
  denotes a land cover class etc. but can also be a
  numeric value
• In Real valued rasters, the value typically is an
  interpolated value, for example an average for
  the area of the cell, or value of the field at
  the center point of the cell, etc.
• Real-life rasters have 8 bit ints, 32 or 64 bit
  floats etc.

5
nodata value and masks

• a special nodata value may be used to denote
  areas from which there is no data or where the
  value is undefined
• nodata value usually has to be coded as some
  selected value in the datatype of the raster, for
  example 9999 or 9999.0
• a mask raster may also be used to focus on a
  specific area

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assumptions

• typically rasters should be somehow overlayable
• same cellsize
• same coordinate systems
• same bounding box
• can define that value is nodata outside the
  bounding box
• from now on, assume complete overlayability

7
types of functions

• arithmetics ,-,,/,...
• sum of two rasters is a new raster where the cell
  value is the sum of values of the same cell of
  the operands
• the result is a new raster
• note sum may be used also for example for the
  total sum of cell values, then the result is a
  scalar

8
other functions

• special functions log, exp, sin, cos, ...
• logical operations and, or, not, ...
• defined for boolean values (usually integer
  0false and 1true)
• information functions histogram, average,
  variance, .
• spatial functions

9
Tomlins categories

• local (sometimes also called global)
• operation is done independently for all cells in
  the raster(s), looking at one cell at a time
• focal
• instead of one cell, the operation looks at the
  cell and its neighbourhood (kernel, focus)
• zonal
• the operation looks at all cells which have the
  same value and are connected

10
spatial functions, a categorization

• distance functions
• result is real valued raster
• area of influence functions
• result is boolean raster
• zonal functions
• result is an associative table
• interpolation functions
• result is real valued raster
• geophysical functions
• other

11
distance functions

• the distance from all locations to some locations
• distance may be defined in many ways geometric,
  travel time, hydrological path (hillslope), cost,
  

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area of influence

• from distance raster by using a logical operation
• with some spread function
• groundwater
• air pollution
• noise

13
zonal functions

• input is two rasters
• division of the space into zones
• values
• result is a table of average, variance, sum, etc.
  of the values at each zone

14
interpolation

• value at each location is computed somehow from
  values at known locations
• nearest neighbor
• kriging
• ..

15
geophysical functions

• typically from DEM (digital elevation model)
• slope, aspect, curvature, .
• flow directions -gt stream network, catchments

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other

• image manipulation

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Extensions to raster algebra

• temporal raster algebra
• Mennis et al Cartography and Geographic
  Information Science, Vol. 32, No. 1, 2005, pp.
  17-32
• three dimensional raster algebra
• Karssenberg and De Jong International Journal of
  Geographical Information Science Vol. 19, No. 5,
  May 2005, 559579

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raster in gtk-gis
open
libral raster Created every time the map is
updated. cellsize by screen
new
Independent in-memory libral raster. cellsize by
data
clip
open
GDAL managed link to a possibly huge raster on
disk. cellsize by data
rasterize
OGR link to vector data