Detail, resolution, and scale

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Detail, resolution, and scale

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The surface of the planet is almost infinitely complex, revealing more and more detail the closer one looks. An apparently simple concept such as a coastline turns out to be problematic in practice — should its representation as a polyline include every indentation, every protruding rock, even every grain of sand? It is clearly impossible to build a representation that includes every detail, and in reality decisions must be made about the amount of detail to include. Spatial resolution is the term given to a threshold distance below which the analyst has decided that detail is unnecessary or irrelevant. For example, one might decide to represent a coastline at a spatial resolution of 100m, meaning that all crenelations, indentations, and protuberances that are no wider than 100m are omitted from the representation. In other words, the representation of the phenomenon appears simpler and smoother than it really is.

Cartographers use a somewhat different approach to the omission of detail from maps. A map is said to have a scale or representative fraction, being the ratio of distances on the map to their corresponding distances in the real world. For example, if a map shows Los Angeles and Santa Barbara as 10cm apart, and in reality they are 100km apart as the crow flies, then the map’s scale is 1:1,000,000 (note that in principle, because of projection from a curved to a flat surface, no map’s scale can be exactly uniform although this clearly does not apply to globes). This approach to defining level of detail is problematic, however, if the dataset in question is not on paper. Data that are born digital do not have a representative fraction, and the representative fraction for data displayed on a computer screen depends on the dimensions of the screen. Project onto a larger screen and the representative fraction will change, irrespective of the value shown on the screen. So it is better to use spatial resolution to describe the level of detail of digital data. As a general rule of thumb the spatial resolution of a paper map is roughly 0.5mm at the scale of the map (500m on a 1:1,000,000 map, or 5m on a 1:10,000 map), a figure that takes into account the widths of lines on maps and the cartographic practice of smoothing what is perceived as excessive detail.

When digital map data is displayed decisions have to made, manually and/or automatically, as to how much detail should be displayed, and how feature data should be generalized in order to produce a visually acceptable and meaningful result. This has been the subject of much research, some of which continues to the present day. For a recent book (of collected papers) on this subject, see Mackaness et al. (2007). In a white paper produced by ESRI (1996) they summarized the major generalization operators that they planned to implement at that time, as follows:

Preselection: deciding on which features to include and which to exclude (e.g. major roads only, ignore footpaths etc.)
Elimination: removal of features that are too small/short (below some threshold)
Simplification: simplifying (smoothing, straightening) linear or polygon boundaries whilst retaining their basic form (see also, Section 4.2.4, Line Smoothing and point-weeding)
Aggregation: combining distinct features into a larger composite object (e.g. a cluster of houses into a polygonal ‘urbanized area’)
Collapse: reduction of feature dimensionality, as for example when a town is represented by a point or a broad river by a line
Typification: reduction of the level of detail by replacing multiple objects by a smaller number of the same objects occupying broadly the same locations
Exaggeration: emphasizing important features that might otherwise be removed
Classification and symbolization: grouping together similar features and using different symbology to represent the new arrangement
Conflict resolution (displacement): identifying and resolving feature conflicts (e.g. overlaps, labeling), and
Refinement: altering feature geometry and alignment to improve aethestics