Local Operations

6. Local Operations#

6.1. Map Compute Framework#

  • Three kinds of analysis/mapping units (MUs) in maps

    • Cells, raster zones, features

  • Four kinds of operations

    • Local, focal, and global operations (based on spatial scope)

    • Neighborhood relation operations

Mapping Units

Neighborhood Relation: Local

Neighborhood Relation: Focal

Neighborhood Relation: Global

Cells

Local

Focal

Global

Raster zones

Local

Features (vectors)

Local

6.2. Topics#

  • Local operations

    • Cells and vector features as mapping units

    • Output/analysis MU itself is and defines the neighborhood

  • Application examples

    • NDWI and mNDWI

    • Composite image

    • Create rainfall map using elevation map

6.3. Local Operations#

  • Compute a new map where the value for each MU on the output map is a function of one or more values at the same MU on the input map(s)

  • General form: \(Value_{new} = f(Value_{in1}, Value_{in2}, ...)\)

  • Output map MUs are the same as (or defined by) the input MUs

6.4. Local Operations in Practice#

  • Reclassify (e.g., fungus diffusion exercise)

  • Turn precipitation table into a map (using weather station points)

  • Map overlay (Intersect, Union, Erase, etc.)

  • Field calculator (Vector) / Raster calculator (Raster)

6.5. Types of Local Operations#

  • Local operations with one input map

    • \(Value_{new} = f(Value_{in})\)

  • Local operations with multiple input maps

    • \(Value_{new} = f(Value_{in1}, Value_{in2}, ...)\)

6.6. Local Operations: One Input Map#

  • Arithmetic and logical operations

    • \(Map + 10\)

    • \(Map > 100\) (Boolean output)

  • Reclassification

    • Grouping values into new categories

    • Example: Land cover types to “Suitable/Unsuitable”

6.7. Local Operations: Multiple Input Maps#

  • Cell-by-cell or feature-by-feature combination

  • Mathematical combinations

    • \(Map_A + Map_B\)

    • \((Map_{NIR} - Map_{Red}) / (Map_{NIR} + Map_{Red})\) (NDVI)

  • Overlay (Vertical Integration)

6.8. NDWI and mNDWI Example#

  • Normalized Difference Water Index (NDWI)

    • \(NDWI = (Green - NIR) / (Green + NIR)\)

  • Modified NDWI (mNDWI)

    • \(mNDWI = (Green - SWIR) / (Green + SWIR)\)

  • Uses local operations to enhance water features in satellite imagery

6.9. Composite Image#

  • Combining multiple single-band raster maps into a single multi-band map

  • Each band represents a different wavelength of light

  • A local operation where the output is a multi-valued map

6.10. Creating Rainfall Map using Elevation#

  • Relationship: \(Rainfall = f(Elevation)\)

  • If a mathematical model exists (e.g., regression: \(R = 0.5 \times Elev + 100\)), it can be applied as a local operation to the elevation map

6.11. Local Operations with Vector Features#

  • Calculating new attributes based on existing ones

  • Example: Population Density = Population / Area

  • Area is a geometric attribute of the MU itself

6.12. Effective Local Neighborhood#

  • In a local operation, the “neighborhood” is the MU itself

  • The operation only looks at the data within that specific unit to produce an output for that same unit

6.13. Characterizing Effective Local Neighborhood#

  • Sometimes the output value depends on the geometry of the MU or the distribution of features within it

  • Local Stats: Min, Max, Mean, Sum within the MU

  • Examples:

    • LocalSum: Sum of points within a polygon (e.g., total population in a city)

    • LocalCount: Number of points within a polygon (e.g., number of crimes in a district)

6.14. Summarize Data Toolset in ArcGIS#

  • Aggregate Points: Local operation using polygon MUs to count points within them

  • Summarize Within: Local operation calculating statistics for features within a boundary (polygon/rectangle)

6.15. Two Types of Local Operations Summary#

  • Type 1: Output MUs are the same as input MUs (Standard Map Algebra)

  • Type 2: Characterize effective local neighborhood where output MUs may be different from the input MUs (e.g., points to polygons)

Feature Type

Geometry attribute

Point

Count

Line

Length

Polygon

Area, Perimeter
Contents