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## Definitions |

Geospatial analysis utilizes many of these terms, but many others are drawn from disciplines such as mathematics and statistics. The result that the same terms may mean entirely different things depending on their context and in many cases, on the software provider utilizing them. In most instances terms used in this Guide are defined on the first occasion they are used, but a number warrant defining at this stage. Table 1‑1, below, provides a selection of such terms, utilizing definitions from widely recognized sources where available and appropriate.

Table 1‑1 Selected terminology

Term |
Definition |
---|---|

Adjacency |
The sharing of a common side or boundary by two or more polygons (AGI). Note that adjacency may also apply to features that lie either side of a common boundary where these features are not necessarily polygons |

Arc |
Commonly used to refer to a straight line segment connecting two nodes or vertices of a polyline or polygon. Arcs may include segments or circles, spline functions or other forms of smooth curve. In connection with graphs and networks, arcs may be directed or undirected, and may have other attributes (e.g. cost, capacity etc.) |

Artifact |
A result (observation or set of observations) that appears to show something unusual (e.g. a spike in the surface of a 3D plot) but which is of no significance. Artifacts may be generated by the way in which data have been collected, defined or re-computed (e.g. resolution changing), or as a result of a computational operation (e.g. rounding error or substantive software error). Linear artifacts are sometimes referred to as “ghost lines” |

Aspect |
The direction in which slope is maximized for a selected point on a surface (see also, Gradient and Slope) |

Attribute |
A data item associated with an individual object (record) in a spatial database. Attributes may be explicit, in which case they are typically stored as one or more fields in tables linked to a set of objects, or they may be implicit (sometimes referred to as intrinsic), being either stored but hidden or computed as and when required (e.g. polyline length, polygon centroid). Raster/grid datasets typically have a single explicit attribute (a value) associated with each cell, rather than an attribute table containing as many records as there are cells in the grid |

Azimuth |
The horizontal direction of a vector, measured clockwise in degrees of rotation from the positive Y-axis, for example, degrees on a compass (AGI) |

Azimuthal Projection |
A type of map projection constructed as if a plane were to be placed at a tangent to the Earth's surface and the area to be mapped were projected onto the plane. All points on this projection keep their true compass bearing (AGI) |

(Spatial) Autocorrelation |
The degree of relationship that exists between two or more (spatial) variables, such that when one changes, the other(s) also change. This change can either be in the same direction, which is a positive autocorrelation, or in the opposite direction, which is a negative autocorrelation (AGI). The term autocorrelation is usually applied to ordered datasets, such as those relating to time series or spatial data ordered by distance band. The existence of such a relationship suggests but does not definitely establish causality |

Cartogram |
A cartogram is a form of map in which some variable such as Population Size or Gross National Product typically is substituted for land area. The geometry or space of the map is distorted in order to convey the information of this alternate variable. Cartograms use a variety of approaches to map distortion, including the use of continuous and discrete regions. The term cartogram (or linear cartogram) is also used on occasion to refer to maps that distort distance for particular display purposes, such as the London Underground map |

Choropleth |
A thematic map [i.e. a map showing a theme, such as soil types or rainfall levels] portraying properties of a surface using area symbols such as shading [or color]. Area symbols on a choropleth map usually represent categorized classes of the mapped phenomenon (AGI) |

Conflation |
A term used to describe the process of combining (merging) information from two data sources into a single source, reconciling disparities where possible (e.g. by rubber-sheeting — see below). The term is distinct from concatenation which refers to combinations of data sources (e.g. by overlaying one upon another) but retaining access to their distinct components |

Contiguity |
The topological identification of adjacent polygons by recording the left and right polygons of each arc. Contiguity is not concerned with the exact locations of polygons, only their relative positions. Contiguity data can be stored in a table, matrix or simply as [i.e. in] a list, that can be cross-referenced to the relevant co-ordinate data if required (AGI). |

Curve |
A one-dimensional geometric object stored as a sequence of points, with the subtype of curve specifying the form of interpolation between points. A curve is simple if it does not pass through the same point twice (OGC). A LineString (or polyline — see below) is a subtype of a curve |

Datum |
Strictly speaking, the singular of data. In GIS the word datum usually relates to a reference level (surface) applying on a nationally or internationally defined basis from which elevation is to be calculated. In the context of terrestrial geodesy datum is usually defined by a model of the Earth or section of the Earth, such as WGS84 (see below). The term is also used for horizontal referencing of measurements; see Iliffe and Lott (2008) for full details |

DEM |
Digital elevation model (a DEM is a particular kind of DTM, see below) |

DTM |
Digital terrain model |

EDM |
Electronic distance measurement |

EDA, ESDA |
Exploratory data analysis/Exploratory spatial data analysis |

Ellipsoid/Spheroid |
An ellipse rotated about its minor axis determines a spheroid (sphere-like object), also known as an ellipsoid of revolution (see also, WGS84) |

Feature |
Frequently used within GIS referring to point, line (including polyline and mathematical functions defining arcs), polygon and sometimes text (annotation) objects (see also, vector) |

Geoid |
An imaginary shape for the Earth defined by mean sea level and its imagined continuation under the continents at the same level of gravitational potential (AGI) |

Geodemographics |
The analysis of people by where they live, in particular by type of neighborhood. Such localized classifications have been shown to be powerful discriminators of consumer behavior and related social and behavioral patterns |

Geospatial |
Referring to location relative to the Earth's surface. "Geospatial" is more precise in many GI contexts than "geographic," because geospatial information is often used in ways that do not involve a graphic representation, or map, of the information. OGC |

Geostatistics |
Statistical methods developed for and applied to geographic data. These statistical methods are required because geographic data do not usually conform to the requirements of standard statistical procedures, due to spatial autocorrelation and other problems associated with spatial data (AGI). The term is widely used to refer to a family of tools used in connection with spatial interpolation (prediction) of (piecewise) continuous datasets and is widely applied in the environmental sciences. Spatial statistics is a term more commonly applied to the analysis of discrete objects (e.g. points, areas) and is particularly associated with the social and health sciences |

Geovisualization |
A family of techniques that provide visualizations of spatial and spatio-temporal datasets, extending from static, 2D maps and cartograms, to representations of 3D using perspective and shading, solid terrain modeling and increasingly extending into dynamic visualization interfaces such as linked windows, digital globes, fly-throughs, animations, virtual reality and immersive systems. Geovisualization is the subject of ongoing research by the International Cartographic Association (ICA), Commission on Geovisualization |

GIS-T |
GIS applied to transportation problems |

GPS/ DGPS |
Global positioning system; Differential global positioning system — DGPS provides improved accuracy over standard GPS by the use of one or more fixed reference stations that provide corrections to GPS data |

Gradient |
Used in spatial analysis with reference to surfaces (scalar fields). Gradient is a vector field comprised of the aspect (direction of maximum slope) and slope computed in this direction (magnitude of rise over run) at each point of the surface. The magnitude of the gradient (the slope or inclination) is sometimes itself referred to as the gradient (see also, Slope and Aspect) |

Graph |
A collection of vertices and edges (links between vertices) constitutes a graph. The mathematical study of the properties of graphs and paths through graphs is known as graph theory |

Heuristic |
A term derived from the same Greek root as Eureka, heuristic refers to procedures for finding solutions to problems that may be difficult or impossible to solve by direct means. In the context of optimization heuristic algorithms are systematic procedures that seek a good or near optimal solution to a well-defined problem, but not one that is necessarily optimal. They are often based on some form of intelligent trial and error or search procedure |

iid |
An abbreviation for “independently and identically distributed”. Used in statistical analysis in connection with the distribution of errors or residuals |

Invariance |
In the context of GIS invariance refers to properties of features that remain unchanged under one or more (spatial) transformations |

Kernel |
Literally, the core or central part of an item. Often used in computer science to refer to the central part of an operating system, the term kernel in geospatial analysis refers to methods (e.g. density modeling, local grid analysis) that involve calculations using a well-defined local neighborhood (block of cells, radially symmetric function) |

Layer |
A collection of geographic entities of the same type (e.g. points, lines or polygons). Grouped layers may combine layers of different geometric types |

Map algebra |
A range of actions applied to the grid cells of one or more maps (or images) often involving filtering and/or algebraic operations. These techniques involve processing one or more raster layers according to simple rules resulting in a new map layer, for example replacing each cell value with some combination of its neighbors’ values, or computing the sum or difference of specific attribute values for each grid cell in two matching raster datasets |

Mashup |
A recently coined term used to describe websites whose content is composed from multiple (often distinct) data sources, such as a mapping service and property price information, constructed using programmable interfaces to these sources (as opposed to simple compositing or embedding) |

MBR/ MER |
Minimum bounding rectangle/Minimum enclosing (or envelope) rectangle (of a feature set) |

Planar/non-planar/planar enforced |
Literally, lying entirely within a plane surface. A polygon set is said to be planar enforced if every point in the set lies in exactly one polygon, or on the boundary between two or more polygons. See also, planar graph. A graph or network with edges crossing (e.g. bridges/underpasses) is non-planar |

Planar graph |
If a graph can be drawn in the plane (embedded) in such a way as to ensure edges only intersect at points that are vertices then the graph is described as planar |

Pixel/image |
Picture element — a single defined point of an image. Pixels have a “color” attribute whose value will depend on the encoding method used. They are typically either binary (0/1 values), grayscale (effectively a color mapping with values, typically in the integer range [0,255]), or color with values from 0 upwards depending on the number of colors supported. Image files can be regarded as a particular form of raster or grid file |

Polygon |
A closed figure in the plane, typically comprised of an ordered set of connected vertices, v1,v2,…vn-1,vn=v1 where the connections (edges) are provided by straight line segments. If the sequence of edges is not self-crossing it is called a simple polygon. A point is inside a simple polygon if traversing the boundary in a clockwise direction the point is always on the right of the observer. If every pair of points inside a polygon can be joined by a straight line that also lies inside the polygon then the polygon is described as being convex (i.e. the interior is a connected point set). The OGC definition of a polygon is “a planar surface defined by 1 exterior boundary and 0 or more interior boundaries. Each interior boundary defines a hole in the polygon” |

Polyhedral surface |
A Polyhedral surface is a contiguous collection of polygons, which share common boundary segments (OGC). See also, Tesseral/Tessellation |

Polyline |
An ordered set of connected vertices, v1,v2,…vn-1,vn≠v1 where the connections (edges) are provided by straight line segments. The vertex v1 is referred to as the start of the polyline and vn as the end of the polyline. The OGC specification uses the term LineString which it defines as: "a curve with linear interpolation between points. Each consecutive pair of points defines a line segment" |

Raster/grid |
A data model in which geographic features are represented using discrete cells, generally squares, arranged as a (contiguous) rectangular grid. A single grid is essentially the same as a two-dimensional matrix, but is typically referenced from the lower left corner rather than the norm for matrices, which are referenced from the upper left. Raster files may have one or more values (attributes or bands) associated with each cell position or pixel |

Resampling |
1. Procedures for (automatically) adjusting one or more raster datasets to ensure that the grid resolutions of all sets match when carrying out combination operations. Resampling is often performed to match the coarsest resolution of a set of input rasters. Increasing resolution rather than decreasing requires an interpolation procedure such as bicubic spline. 2. The process of reducing image dataset size by representing a group of pixels with a single pixel. Thus, pixel count is lowered, individual pixel size is increased, and overall image geographic extent is retained. Resampled images are “coarse” and have less information than the images from which they are taken. Conversely, this process can also be executed in the reverse (AGI) 3. In a statistical context the term resampling (or re-sampling) is sometimes used to describe the process of selecting a subset of the original data, such that the samples can reasonably be expected to be independent |

Rubber sheeting |
A procedure to adjust the co-ordinates all of the data points in a dataset to allow a more accurate match between known locations and a few data points within the dataset. Rubber sheeting … preserves the interconnectivity or topology, between points and objects through stretching, shrinking or re-orienting their interconnecting lines (AGI). Rubber-sheeting techniques are widely used in the production of Cartograms (op. cit.) |

Slope |
The amount of rise of a surface (change in elevation) divided by the distance over which this rise is computed (the run), along a straight line transect in a specified direction. The run is usually defined as the planar distance, in which case the slope is the tan() function. Unless the surface is flat the slope at a given point on a surface will (typically) have a maximum value in a particular direction (depending on the surface and the way in which the calculations are carried out). This direction is known as the aspect. The vector consisting of the slope and aspect is the gradient of the surface at that point (see also, Gradient and Aspect) |

Spatial econometrics |
A subset of econometric methods that is concerned with spatial aspects present in cross-sectional and space-time observations. These methods focus in particular on two forms of so-called spatial effects in econometric models, referred to as spatial dependence and spatial heterogeneity (Anselin, 1988, 2006) |

Spheroid |
A flattened (oblate) form of a sphere, or ellipse of revolution. The most widely used model of the Earth is that of a spheroid, although the detailed form is slightly different from a true spheroid |

SQL/Structured Query Language |
Within GIS software SQL extensions known as spatial queries are frequently implemented. These support queries that are based on spatial relationships rather than simply attribute values |

Surface |
A 2D geometric object. A simple surface consists of a single ‘patch’ that is associated with one exterior boundary and 0 or more interior boundaries. Simple surfaces in 3D are isomorphic to planar surfaces. Polyhedral surfaces are formed by ‘stitching’ together simple surfaces along their boundaries (OGC). Surfaces may be regarded as scalar fields, i.e. fields with a single value, e.g. elevation or temperature, at every point |

Tesseral/Tessellation |
A gridded representation of a plane surface into disjoint polygons. These polygons are normally either square (raster), triangular (TIN — see below), or hexagonal. These models can be built into hierarchical structures, and have a range of algorithms available to navigate through them. A (regular or irregular) 2D tessellation involves the subdivision of a 2-dimensional plane into polygonal tiles (polyhedral blocks) that completely cover a plane (AGI). The term lattice is sometimes used to describe the complete division of the plane into regular or irregular disjoint polygons. More generally the subdivision of the plane may be achieved using arcs that are not necessarily straight lines |

TIN |
Triangulated irregular network. A form of the tesseral model based on triangles. The vertices of the triangles form irregularly spaced nodes. Unlike the grid, the TIN allows dense information in complex areas, and sparse information in simpler or more homogeneous areas. The TIN dataset includes topological relationships between points and their neighboring triangles. Each sample point has an X,Y co-ordinate and a surface, or Z-Value. These points are connected by edges to form a set of non-overlapping triangles used to represent the surface. TINs are also called irregular triangular mesh or irregular triangular surface models (AGI) |

Topology |
The relative location of geographic phenomena independent of their exact position. In digital data, topological relationships such as connectivity, adjacency and relative position are usually expressed as relationships between nodes, links and polygons. For example, the topology of a line includes its from- and to-nodes, and its left and right polygons (AGI). In mathematics, a property is said to be topological if it survives stretching and distorting of space |

Transformation 1. Map |
Map transformation: A computational process of converting an image or map from one coordinate system to another. Transformation … typically involves rotation and scaling of grid cells, and thus requires resampling of values (AGI) |

Transformation 2. Affine |
Affine transformation: When a map is digitized, the X and Y coordinates are initially held in digitizer measurements. To make these X,Y pairs useful they must be converted to a real world coordinate system. The affine transformation is a combination of linear transformations that converts digitizer coordinates into Cartesian coordinates. The basic property of an affine transformation is that parallel lines remain parallel (AGI, with modifications). The principal affine transformations are contraction, expansion, dilation, reflection, rotation, shear and translation |

Transformation 3. Data |
Data transformation (see also, subsection 6.7.1): A mathematical procedure (usually a one-to-one mapping or function) applied to an initial dataset to produce a result dataset. An example might be the transformation of a set of sampled values {xi} using the log() function, to create the set {log(xi)}. Affine and map transformations are examples of mathematical transformations applied to coordinate datasets. Note that operations on transformed data, e.g. checking whether a value is within 10% of a target value, is not equivalent to the same operation on untransformed data, even after back transformation |

Transformation 4. Back |
Back transformation: If a set of sampled values {xi} has been transformed by a one-to-one mapping function f() into the set {f(xi)}, and f() has a one-to-one inverse mapping function f-1(), then the process of computing f-1{f(xi)}={xi} is known as back transformation. Example f()=ln() and f-1=exp() |

Vector |
1. Within GIS the term vector refers to data that are comprised of lines or arcs, defined by beginning and end points, which meet at nodes. The locations of these nodes and the topological structure are usually stored explicitly. Features are defined by their boundaries only and curved lines are represented as a series of connecting arcs. Vector storage involves the storage of explicit topology, which raises overheads, however it only stores those points which define a feature and all space outside these features is “non-existent” (AGI) 2. In mathematics the term refers to a directed line, i.e. a line with a defined origin, direction and orientation. The same term is used to refer to a single column or row of a matrix, in which case it is denoted by a bold letter, usually in lower case |

Viewshed |
Regions of visibility observable from one or more observation points. Typically a viewshed will be defined by the numerical or color coding of a raster image, indicating whether the (target) cell can be seen from (or probably seen from) the (source) observation points. By definition a cell that can be viewed from a specific observation point is inter-visible with that point (each location can see the other). Viewsheds are usually determined for optically defined visibility within a maximum range |

WGS84 |
World Geodetic System, 1984 version. This models the Earth as a spheroid with major axis 6378.137 kms and flattening factor of 1:298.257, i.e. roughly 0.3% flatter at the poles than a perfect sphere. One of a number of such global models |

Note: Where cited, references are drawn from the Association for Geographic Information (AGI), and the Open Geospatial Consortium (OGC). Square bracketed text denotes insertion by the present authors into these definitions. For OGC definitions see: Open Geospatial Consortium Inc (2006) in References section