1 / 26

Understanding Spatial Queries, Computations, and Map Algebra Techniques

This resource covers essential topics in spatial analysis, including non-spatial and spatial queries, SQL-like operations, and OpenGIS specifications. It delves into computations at the field level, map algebra, and filtering techniques. Readers will learn about local, focal, zonal, and multi-layer operations, as well as non-linear adjustments and transformations. The text also addresses issues like boundary-free approaches and the importance of kernel density estimation (KDE) for spatial data representation, emphasizing their practical applications in landscape and hydrological analysis.

hallam
Télécharger la présentation

Understanding Spatial Queries, Computations, and Map Algebra Techniques

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Chapter 4 Part C: Queries, Computations & Map Algebra 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) www.spatialanalysisonline.com

  3. Queries, Computations & Map Algebra • OGC OpenGIS Simple Features Specification: Spatial Relations 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) www.spatialanalysisonline.com

  5. Queries, Computations & Map Algebra • Map algebra – local operations, multi-grid 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 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 Weighted average as integer www.spatialanalysisonline.com

  8. Queries, Computations & Map Algebra • Grid filtering – Linear – common ‘image processing’ functions • Sharpening • Blurring • Edge detection • Embossing • Gradient operations 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 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 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 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 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) 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 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 www.spatialanalysisonline.com

  16. Queries, Computations & Map Algebra • Point density – kernel methods Uniform 50:50 Box kernel Box sum Box sum histogram www.spatialanalysisonline.com

  17. Queries, Computations & Map Algebra • Kernel density – Normal kernel function 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 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 www.spatialanalysisonline.com

  20. Queries, Computations & Map Algebra • 2D kernels – single point Normal kernel (unbounded) Quartic kernel (bounded) www.spatialanalysisonline.com

  21. Queries, Computations & Map Algebra • 2D mapped kernel density – Lung cancer cases, Quartic kernel and Normal kernel www.spatialanalysisonline.com

  22. Queries, Computations & Map Algebra • 3D mapped kernel density – lung cancer cases www.spatialanalysisonline.com

  23. 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) www.spatialanalysisonline.com

  24. Queries, Computations & Map Algebra • Cartograms • Density adjustment – areas represent population www.spatialanalysisonline.com

  25. Queries, Computations & Map Algebra • Cartograms • Density adjustment – alternative approaches www.spatialanalysisonline.com

  26. 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) www.spatialanalysisonline.com

More Related