Lecture 13Neighborhoods and Neighborhood Operations

Learning Objectives

13.1 Describe the spatial component of neighborhoods for raster and vector structured spaces.How do neighborhoods relate to surfaces?

13.2 What rules are used to combine attribute data values?

13.3 How does a cross-reference framework consisting of levels of data measurement and combination rules help us understand computing with neighborhood attribute data values?

13.1 Describe the spatial component of neighborhoods for raster and vector structured spaces. How do neighborhoods relate to surfaces?

A buffer spreads a distance measurement (zone) outwards to include more space. Thisoperation makes a new data layerthat can be used in subsequent overlay analysis.
Buffers are the simplest kind of neighborhood operation, neighborhoods are often defined by Euclidean distance, but could be defined using topology, e.g. with adjacency. With Euclidean distance, the attribute data of the center spatial object is moved outward,dominating its neighbors; but can be extended to other attribute treatments.

Surfaces have properties such as slope composed of gradient & azimuth that are estimated based upon neighboring data values. This process is a special case of neighborhood operations as well.
Exploring GISChapter 7 presents a scheme for these operations, using the same groupings of procedures found in overlay operations.
First is the spatial part. Assemble the neighboring data values using geometry or topology. Note problems on edge of layer, where special considerations are made.
Near neighbors = ‘immediate’ + ‘focal’ (to approximate an incremental step)

  1. `immediate neighbors' in grid using a roving 3X3 filter
  2. fixed radius of Euclidean distance ('focal') with variants, like nested holes, etc.
  3. adjacent objects, e.g. topologically connected such as next transit stop

`Extended' neighbors beyond the local are addressed in chapter 8.

Neighborhood distance relationships in a raster grid structured space

- Figure 7.7shows grid distances and cell counts at ‘standard cell distance’.

- Spatial neighborhood component is developed in increments of “next to” (adjacency component of topology).

- every cell has a neighborhood based on these ‘next to’ relationships

Neighborhood distance relationships in a vector structured space

- Multitude of computations using points, polylines, and areas.

- The spatial neighborhood component can be computed based on distance (geometry) or derived by “next to”(adjacency component of topology).

The attribute part…

13.2 What rules are used to combine attribute data values?

Dominance – one data value is “better” or “worse” than all the others in the neighborhood, and only that data value will be used to compute the output data value

Contributory – all data values from the neighborhood are used as input to compute the output data value, e.g. mean, median, or mode

Interaction –selected data values from a neighborhood are used as input based on a defined relationship, and together they are used to compute the output data value(s)

13.3 How does a cross-reference framework consisting of levels of data measurement and combination rules help us understand computing with neighborhood attribute data values?

Remember that we have already established the spatial neighbor aspect.

Attribute combination produces an output data value by applying a rule that uses neighboring data values. The rules can be grouped by a combination rule and by level of measurement (Exploring GIS Table 7-1 Operations on Near Neighbors):

Table 7-1 Examples of operations on near neighbors
Level of Measurement / Dominance / Contributory / Interaction
Nominal / Buffer
Drop-line aggregation (dissolve) / Voting tabulation:
majority filter (fig 7.8); proportion (fig 7.9); diversity (fig 7.10) / Flow is convergent or divergent
Ordinal (at least) / Max or min of neighbors / Percentile / Profile curvature, flow slowed or accelerated
Interval or ratio:
Continuous– no spatial component / Max or min / Sum, average(density) / Edge detectors
Interval or ratio:
Continuous–with spatial component / Slope and Distance weighting are the two types below
- Slope / Maximum slope / Best fit plane showing gradientin degrees / None usually
- Distance weighting / None usually / Smoothing, filter, min/max filter / Hillshading, Autocorrelation

Expanding upon the descriptionspresented in Table 7-1:

  • Nominal data measurement using contributory rule - Holdridge vegetation mapin .5 degree (Lon,Lat) cells(nominal level, contributory rule):
  • Majority filter (most frequent category in neighborhood) Figure 7-8
  • Proportion ratio (amount of total) Figure 7-9
  • Diversity (count of different categories in neighborhood)Figure 7-10Diversity measurement is important for habitat analysis at micro and macro scales
  • Flow is divergent orconvergent (interaction rule)
  • Ordinal data measurement using interaction rule (ordinal level, interaction rule)
  • Drainageprofile curvatureshowing accelerated or slowed flow
  • Continuous (aspatial is no spatial component) interval measurement using contributory rule
  • Populationdensity – computed based on population within grid cell, thus no near-neighbor (neighborhood) component.
  • Continuous with horizontal measure
  • Slope gradient data measurement using contributory rule
  • Best fit plane showinggradient (steepness) in terms of degree
  • Distance weighting using contributory rule – filtering/smoothing
  • Infrared photography using max and min filters
  • Distance weighting using interaction rule
  • hillshading – angle of sun above horizon and slope to compute shadows

Many examples presented by Helen Mitsova’s work at North Carolina State University