Focal Operation

7. Focal Operation#

7.1. Focal Operations#

  • Operations:

    • Local, focal and global operations based on the spatial scope of neighborhood

    • Neighborhood relation operations

  • 3 kinds of mapping/analysis units:

    • Cells

    • Raster zones

    • Features

Mapping Units

Neighborhood Relation: Local

Neighborhood Relation: Focal

Neighborhood Relation: Global

Cells

Local

Focal

Global

Raster zones

Local

Features (vectors)

Local

7.2. Topics#

  • Focal operations with raster map

    • Moving-window, distance/direction based, irregular weighted neighborhoods

  • Focal operations with vector map

    • Buffer

  • Domain-based focal neighborhoods

    • Watershed

  • Types of focal operations

7.3. Focal Operations#

  • Compute for each output MU with the neighbors of its focal neighborhood

  • Cells, raster zones, vector features as MUs

  • Data manipulation within MU’s focal neighborhood

7.4. Focal Neighborhood#

  • A set of locations that has a certain relationship with a MU

    • Beyond the MU itself (vs local neighborhood)

  • Represents interactional relationship between a MU and other locations

    • Exchange of matter, energy, and information

  • The MU is also referred to as the neighborhood focus

  • The related locations are referred to as the neighbors

7.5. Characterizing Focal Neighborhoods#

  • Two ways to characterize focal neighborhoods:

    • Based on distance and direction

      • Moving-window (raster), Buffer (vector/raster)

    • Based on domain knowledge/processes

      • Watershed, viewshed, network, etc.

7.6. Moving-Window Neighborhoods#

  • Neighborhood defined by a “window” of a specific shape and size

  • The window “moves” from cell to cell

  • Neighborhood is same for all cells (relative to the focus)

  • Types:

    • Square (3x3, 5x5, etc.)

    • Circle

    • Plus (rook’s case)

7.7. Focal Statistics#

  • Calculate a statistic for the values within the moving window

  • Common statistics:

    • FocalSum: Total value (e.g., total biomass)

    • FocalMean: Average value (smoothing)

    • FocalMax/FocalMin: Range or edge detection

    • FocalVariety: Number of unique values (diversity)

7.8. Examples of Moving-Window Operations#

  • Smoothing: Use FocalMean to reduce noise in data

  • Edge Detection: Use FocalMax - FocalMin to find where values change rapidly

  • Focal Variety: Useful for identifying boundaries between different land cover types

7.9. Morphology/Shape Analysis#

  • Use Focal operations to analyze the shape of features

  • Erosion: Using FocalMinimum on a binary map

    • Removes outer layer of pixels

  • Expansion/Dilation: Using FocalMaximum on a binary map

    • Adds an outer layer of pixels

7.10. Morphology/Shape Analysis (cont.)#

  • Inner Boundaries: Identify cells that are part of the feature but touch the background

  • Outer Boundaries: Identify background cells that touch the feature

  • Combined boundaries provide detailed structural analysis

7.11. Distance/Direction-Based Neighborhoods#

  • Neighborhood defined by specific distance and directional parameters

  • Neighborhoods in ArcGIS:

    • Rectangle, circle, annulus (donut), or wedge (a slice of a circle)

7.12. Finding Appropriate Wind Farm Sites#

  • Selection criteria:

    • Wind speed: Higher elevation generally equals higher speed (Elevation >= 1000m)

    • Aspect: Facing the prevailing wind direction

    • Wind exposure: Not blocked by nearby hills in the prevailing wind direction

  • Data needed:

    • Prevailing wind direction (e.g., 225° to 315°)

    • Digital Elevation Model (DEM)

  • Wedge neighborhood: Used to check for obstructions in the specific wind direction

7.13. Types of Focal Operations#

  • Simple Focal Operations: Neighborhood is predefined (shape/size)

    • Example: Moving window

  • Irregular/Weighted Focal Operations: Neighbors have different “weights” or importance

    • Example: Gravity model, Kernel density estimation

  • Process-based Focal Operations: Neighborhood is defined by a physical process

    • Example: Watershed (defined by terrain/gravity)

7.14. Irregular Weighted Neighborhood#

  • Neighborhood and weights are defined by a matrix

    • 0s indicate a location is not a neighbor

    • Other values represent weight (neighbor relation property)

  • Matrix can be stored as a neighborhood text file

    • Kernel file in ArcGIS

  • All cells use the same neighborhood structure

  • Operation: Weighted Summary

    • Get the neighbor value from the input map

    • Summarize (weight * value)

7.15. Weighted Moving-Average (Smoothing)#

  • Weights are inversely proportional to distance

  • The weight for the focus MU is typically the largest

  • Used to reduce noise while preserving more detail than a simple mean

7.16. Kernel Density Estimation (KDE)#

  • Neighborhood is a circle with a radius (bandwidth)

  • Weights are defined by a continuous kernel function

    • Weight is highest at the center and decreases to zero at the boundary

  • Operations:

    1. Calculate weighted value for each neighbor (Weight * Value)

    2. Sum all weighted values

    3. Normalize (optional)

7.17. Process-Based Focal Neighborhoods#

  • Neighborhood is defined by a physical or social process

  • Examples:

    • Watershed: Neighborhood defined by terrain and gravity (flow of water)

    • Viewshed: Neighborhood defined by line-of-sight and topography

    • Service Area: Neighborhood defined by travel time on a road network

7.18. Watershed as a Focal Neighborhood#

  • A watershed is a neighborhood where all locations drain to a common outlet (focus)

  • Interaction: Water, sediment, and pollutants move from neighbors to the focus

  • Neighborhood is irregular and varies from location to location

7.19. Types of Focal Operations (Based on Output)#

  • Three types of focal operations based on what the output value represents:

    1. Characterize focal neighborhood

    2. Compare focus MU and its neighbors

    3. Predict attribute at the focus MU

7.20. Type 1: Characterize Focal Neighborhood#

  • The output value summarizes the attributes within the neighborhood

  • Focal Statistics:

    • FocalSum: Total amount

    • FocalMean: Average intensity/density

    • FocalMax/FocalMin: Extremes

    • FocalVariety: Diversity/Heterogeneity

    • FocalMajority: Dominant type

7.21. Type 2: Compare Focus MU and Neighbors#

  • The output value represents the relationship or contrast between the focus and its surrounding area

  • Operations:

    • ContrastLocation: Distance to specific neighbors

    • ContrastValue: Difference between focus value and neighborhood mean

    • FocalPercentage: Percentage of neighbors with values equal to the focus

    • FocalPercentile: Percentage of neighbors with values less than the focus

7.22. ContrastValue Operation Examples#

  • FocalPercentage:

    • Measures the homogeneity of the focus relative to its neighbors

  • FocalPercentile:

    • Identifies if a focus MU is a local peak (high percentile) or local pit (low percentile)

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