Neighbourhood operations

NEIGHBORHOOD OPERATIONS 

Neighborhood operations, also called proximity analyses, consider the characteristics of neighboring areas around a specific location.  These functions either modify existing features or create new feature layers, which are influenced, to some degree, by the distance from existing features.  All GIS programs provide some neighborhood analyses, which include buffering, interpolation, Theissen polygons, and various topographic functions.

Buffering
Buffering creates physical zones around features.  These “buffers” are usually based on specific straight-line distances from selected features common to both raster and vector systems, are created around point, line, or polygon features.  The resulting buffers are placed in an output polygon feature layer.  Once complete, buffer layers are used to determine which features (in other layers) occur either within or outside the buffers (spatial queries), to perform overlay, or to measure the area of the buffer zone.  They are the most used neighborhood operation.

Interpolation
Interpolation is a method of predicting or estimating pixel values at unsampled locations based on the known values of neighboring pixels.  Since it is impractical to take measurements at all locations across the study area due to money, time, legal, and physical constraints, interpolation is required between known pixel values (sampled locations).  With interpolation, a continuous surface like elevation, temperature, and soil characteristics can be created.  Because of its continuous nature, interpolation is only available within raster-based systems.
There are many different types of interpolation:

1. Linear interpolation, the simplest form, assumes that the value change over distance from recorded pixels is uniform.  This interpolation method is not always appropriate, so there are other methods like
2. Fixed-radius Local Averaging
3. Inverse Distance Weighted
4. Trend Surface
5. Splines and
6. Kriging.  

All of these interpolation methods look at the values of the recorded pixels to generate the value of the pixels that fall in between.  The methods differ in how they weigh the recorded attributes and in the number of observations used for each method.  No method is accurate in every situation.


Theissen polygons (voronoi or proximal polygons)
Theissen polygons are boundaries created around points within a point layer.  The resultant polygons form around each of the points, and they delineate territories around which any location inside the polygon is closer to the internal point (that created it) than to any other point in the layer.  Attributes associated with each point are assigned to the resultant polygon.  It is a vector and raster process.

Topographic Functions
Topographic functions use Digital Elevation Models (DEMs) to illustrate the lay of the land.  DEMs are raster layers containing elevation data in each pixel.  From these values, you produce output layers to portray slope (inclination), aspect (direction), and hillshading.  These topographic functions are typical neighborhood processes; each pixel in the resultant layer is a product of its own elevation value as well as those of its surrounding neighbors.

Slope layers exhibit the incline or steepness of the land.  It is the change in elevation over a defined distance.
Aspect is the compass direction in which a slope faces.  From north, it is usually expressed clockwise from 0 to 360 degrees.
Hillshading, which is cartographically called shaded relief, is a lighting effect which mimics the sun to highlight hills and valleys.  Some areas appear to be illuminated while others lie in shadows.

These functions are raster processes, most can be mimicked in a vector environment by Triangulated Irregular Networks (TIN).  In addition, topographic functions can derive vector isolines (contours).

Neighborhood functions operate on the neighboring features of a given feature or set of features.
Search functions allow the retrieval of features that fall within a given search window (rectangle, circle, or polygon).

Line-in-polygon and point-in-polygon functions determine whether a given linear or point feature is located within a given polygon, or they report the polygon(s) that a given point or line are contained in.

Topographic functions compute the slope or aspect from a given digital representation of the terrain (digital terrain model or DTM).
Interpolation functions predict unknown values using the known values at neighboring locations.
Contour generation functions calculate contours as a set of lines that connect points with the same attribute value. Examples are points with the same elevation (contours), depth (bathymetric contours), barometric pressure (isobars), or temperature (isothermal lines).