Www.spatialanalysisonline.com Chapter 4 Part C: Queries, Computations & Map Algebra.
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Transcript of Www.spatialanalysisonline.com Chapter 4 Part C: Queries, Computations & Map Algebra.
www.spatialanalysisonline.com
Chapter 4
Part C: Queries, Computations & Map Algebra
3rd edition www.spatialanalysisonline.com 2
Queries, Computations & Map Algebra
Queries Non-spatial queries Spatial queries
SELECT queries/select by location Other SQL-like queries, e.g. Make table Spatial JOIN and RELATE operations
• OGC “Spatial Relations” (See next slide, from 4A)
3rd edition www.spatialanalysisonline.com 3
Method Description
Note: a and b are two geometries (one or more geometric objects or features — points, line objects, polygons, surfaces including their boundaries); I(x) is the interior of x; dim(x) is the dimension of x, or maximum dimension if x is the result of a relational operation
Spatial relations
Equals spatially equal to: a=b
Disjoint spatial disjoint: equivalent to ab=
Intersects spatially intersects: [ab] is equivalent to [not a disjoint(b)]
Touches spatially touches: equivalent to [ab and I(a)I(b)= ]; does not apply if a and b are points
Crosses spatially crosses: equivalent to [dim(I(a)I(b))<max{dim(I(a)),dim(I(b))} and aba and abb]
Within spatially within: within(b) is equivalent to [ab=a and I(a)I(b)]
Contains spatially contains: [a contains(b)] is equivalent to [b within(a)]
Overlaps spatially overlaps: equivalent to [dim(I(a)I(b))=dim(I(a))=dim(I(b)) and aba and abb]
Relate spatially relates, tested by checking for intersections between the interior, boundary and exterior of the two components
OGC OpenGIS Simple Features Specification: Spatial Relations
Queries, Computations & Map Algebra
3rd edition www.spatialanalysisonline.com 4
Queries, Computations & Map Algebra
Simple computations Field level – attribute processing SQL/Query operations – e.g. Make Table Raster layer operations
Basic Map Algebra• Single layer operations: local, focal/neighbourhood,
zonal, global• Multi-layer operations• Raster-vector combined operations• ‘Algebraic’ expressions – e.g. C=(A-B)/(A+B)
3rd edition www.spatialanalysisonline.com 5
Queries, Computations & Map Algebra
Map algebra – local operations, multi-grid
A
B
C'
New rast er
b. G r id resampl ing
A
B
C
New rast er
a. Mat ching gr ids
3rd edition www.spatialanalysisonline.com 6
Queries, Computations & Map Algebra
Map algebra operations – broader view Resolution, orientation and resampling Classification Algebraic and Statistical operations Proximity/landscape metric operations Surface and hydrological analysis operations Transformation and interpolation Filtering
3rd edition www.spatialanalysisonline.com 7
Queries, Computations & Map Algebra
Grid filtering – Linear (weighted average)
Low pass filters, e.g.
High pass filters, e.g.
Kernels - example
aaa
aba
aaa
aaa
aba
aaa
111
141
111
175170124
18818790
20017698
175170124
18816490
20017698 Weighted average as integer
3rd edition www.spatialanalysisonline.com 8
Queries, Computations & Map Algebra
Grid filtering – Linear – common ‘image processing’ functions Sharpening Blurring Edge detection Embossing Gradient operations
3rd edition www.spatialanalysisonline.com 9
Queries, Computations & Map Algebra
Grid filtering – points to note Attribute data range Multi-band image processing Kernel size and shape Single or multi-pass Edge effects User-defined kernels Spatial vs frequency domain filtering
3rd edition www.spatialanalysisonline.com 10
Queries, Computations & Map Algebra
Grid filtering – Non-linear Non-linear local adjustment
Local operation, not based on kernel (weighted average)
Minimum, Maximum, Variance, IQR Median deviation and thresholding Noise reduction
3rd edition www.spatialanalysisonline.com 11
Queries, Computations & Map Algebra
Grid filtering – Erosion and dilation Erosion – pixel removal/alteration Dilation – pixel addition/alteration Kernels and structural elements Source DEM/image Dilation of source Erosion of source
3rd edition www.spatialanalysisonline.com 12
Queries, Computations & Map Algebra
Ratios, indices and normalisation Spatially extensive variables Spatially intensive variables Normalisation of count data
e.g. cars/household, ethnic group counts/1000 population
Common types:• Averages• Proportions/percentages• Densities
3rd edition www.spatialanalysisonline.com 13
Queries, Computations & Map Algebra
Standardisation Direct standardisation
Regional/national comparisons Indirect standardisation
Expected values Excess rates
Statistical standardisation Z-scores Range-based (basic or trimmed)
3rd edition www.spatialanalysisonline.com 14
Queries, Computations & Map Algebra
Ratio computations – some issues Division by 0 and missing data handling Normalisation of ‘normalised data’ Variance instability Divisor selection
Appropriateness Availability/accuracy/timeliness
Rate selection Raw rates, expected rates, rate smoothing
3rd edition www.spatialanalysisonline.com 15
Queries, Computations & Map Algebra
Point density Density: counts/area (n/A) Occupancy: area/counts (A/n) Zone boundaries/area definition Grid counts (cell shape, size, orientation issues) … need for a boundary free approach … develop ideas from univariate statistics
3rd edition www.spatialanalysisonline.com 16
Queries, Computations & Map AlgebraPoint density – kernel methods
Uniform
50:50
Box kernel
Box sum
Box sum
histogram
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Queries, Computations & Map Algebra
Kernel density – Normal kernel function
3rd edition www.spatialanalysisonline.com 18
Queries, Computations & Map Algebra
Kernel density – decisions Functions (finite or infinite) Bandwidth – key criterion (fixed/adaptive) Grid resolution Relative or absolute densities, or ‘probabilities’ Comparison issues
with other density datasets temporal mapped values
3rd edition www.spatialanalysisonline.com 19
Queries, Computations & Map Algebra
Kernel density estimation (KDE) – 2D approach Symmetric functions Finite (e.g. box) or infinite (e.g. Normal) Rotated 1D function 2D function Procedure:
Select function and parameters Specify grid resolution (or extent and number of cols/rows) Apply 2D function to each data point and record value at
every grid intersection Sum grid intersection values and normalise Map resulting grid
3rd edition www.spatialanalysisonline.com 20
Queries, Computations & Map Algebra
2D kernels – single point
Normal kernel (unbounded) Quartic kernel (bounded)
3rd edition www.spatialanalysisonline.com 21
Queries, Computations & Map Algebra
2D mapped kernel density – Lung cancer cases, Quartic kernel and Normal kernel
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Queries, Computations & Map Algebra
3D mapped kernel density – lung cancer cases
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Queries, Computations & Map Algebra
Kernel density – alternative functions Normal (or Gaussian), Quartic (spherical) (Negative) Exponential, Triangular (conic) Uniform (flat), Epanechnikov (paraboloid/quadratic)
Applications Density/probability surface creation/comparisons Case/control analysis Spatio-temporal analysis Hot spot analysis Network analysis (see Okabe et al)
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Queries, Computations & Map Algebra
Cartograms Density adjustment – areas represent population
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Queries, Computations & Map Algebra
Cartograms Density adjustment – alternative approaches
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Queries, Computations & Map Algebra
Line and intersection density Kernel methods applied to linear forms
Route systems (and intersections) Line frequency (number per unit area) Length density (length per unit area) Intersection density (intersections per unit of
length, per unit area)