Neighborhood Operations

Objectives of Lecture:

1. Move from Buffers to Neighborhoods
2. Connect from Surfaces to Neighborhoods
3. Overview of neighborhood combinations (similarity to overlay operations)

1. `immediate neighbors' in grid ['roving window', 3X3 `kernel', etc.]
2. fixed radius of Euclidean distance ('Focal') [with variants, like nested holes, etc.]
3. adjacent objects [topologically connected in vector, eg. next subway stop]

Then (attribute combination), produce an output value by applying a rule that uses the neighboring values.

Examples in textbook (Overheads):

• Holdridge vegetation map in 1 degree cells:
  • Majority filter (most frequent category in neighborhood)
  • Diversity (count of different categories in neighborhood)

Various filters in practical use

• To clean up scanned soil maps (applied just to "noise")
• a routine step in nearly all remote-sensing applications (after a local classification; usually called a Majority Filter or a 3X3 ...) an example project
• Diversity measurment is important for habitat analysis at micro and macro scales (diversity in a wetland | Bat diversity in Washington State )
• detecting aspens in IR photography using max and min filters
• Counting palm trees in 1m space imagery
• edge detectors: (shows a number of distinct rules, applied to shoreline detection)
• edge detection to find roads ( 3X3 LaPlace filter: 4 in center cell, -1 for adjacent cells; detect differences); skip to the Images.

The rules can be grouped by combination method and by level of measurement:

Examples of operations on near neighbors
Level of Measurement	Dominance	Contributory	Interaction
Nominal	Buffer Drop-line aggregation (dissolve)	Voting tabulation majority filter, diversity, etc.	Edge detectors, Explicit combination
Ordinal (at least)	Max/min of neighbors; (example to count palm trees)	Percentile	Profile, drainage
Continuous (aspatial)	Max/min neighbor (population density) (example: Minimum Flying Height: from a max in cell)	Sum/average ; (a population density example using TOTAL; description)	Edge detectors
Continuous attribute with horizontal measures
- Slope	Maximum slope	Best fit plane
- Distance weighting		Smoothing, filters an example of distance filter (Watts Barr; Amazon)	Autocorrelation; hillshading (example) [plus behind the scenes AML to accomplish this...]
- Splines: (see below)			Amazon precipitation; (an animated gif)

Examples of operations on near neighbors. Empty cells seem not to occur in practice.

Of course these operations are sensitive to error: DesMoines flooding, description.

Some additional depth on the surface modelling [Group was at Army Corps of Engineers CERL, then at University of Illinois; Helena seems to be at North Carolina State now...] The page has moved, and most of the movies, but the links are mostly dead (and point back to Illinois!):

• Multidimensional spatial interpolation site (1998)
• Splines have a smoothing factor (animated gif) and a tension parameter (animated gif). These express specific relationships between neighboring values.