PathOverlap: Compute the proportion overlap of two paths.
In stmueller/pathmapping: Compute Deviation and Correspondence Between Spatial Paths

PathOverlap

R Documentation

Compute the proportion overlap of two paths.

Description

This computes the proportion of the two paths that are mapped onto one another. The outcome is a number between 0 and 1.0, measuring how much of each path corresponds to a non-endpoint of the other map. This does not by itself measure path similarity, because two paths that are highly dissimilar that happen to start and end at similar spots would have a value close to 1.0. This is sensitive to 'partial' paths. If on path is a sub-path of the other, then it should measure the average of the proportion of path1 that is in path2 and the proportion of path2 that is in path1.

Usage

PathOverlap(mapping,costfn=Cost_Area)

Arguments

`mapping`	`mapping` is the output of `CreateMap()`.
`costfn`	`costfn` is the cost function to use

Details

PathOverlap works with a basic mapping and computes 'minimal' mappings, both left-biased and right-biased, to arrive at two best mappings (those involving the least distance between corresponding points). These will typically be identical, but there are non-degenerate cases where they can differ.

Once this mapping is arrived at, the algorithm identifies the core of the mapping–the central segment of both paths that are mapped onto the core of the other path, by identifying the segments of each path (on both ends) that are mapped onto the endpoint of the other path. For each path, the length of its core is subtracted from the total length of the path, and these two values are averaged together for the returned proportion value.

The result of this can be used to weigh distance between paths in terms of overall path similarity. A reasonable measure of path similarity might be the (area between paths) / (average length of two paths) / overlap, so that two paths with low overlap get their total distance inflated by that proportion.

Value

Return value is a number between 0 and 1. Values below 0.5 are difficult, because the average overlap of the two paths is found. Thus, even if one path has 0 overlap, the other is likely to have an overlap near 1.0, resulting in an average of 0.5.