I would like a way that we can say accurately how complete any area is, without 
relying on other users to have said its complete. Ive come up with a few 
hypotheses and posted them on my blog (http://edwardmjohnson.wordpress.com) of 
ways which we can start to do this. 

    * A complete map will have all of the roads in an area, but we cannot 
obtain stats on the amount of road in every area we may wish to test in 
OpenStreetMap. So an accurate way to predict the length of road in any area 
would be useful. My hypothesis is that the length of road in a given area is 
dependent upon population density. That is to say I expect that urban areas 
will have less road per person than rural areas.

    * For areas where OSM has aerial imagery I would like to compare the 
complexity (ie file size) of the Yahoo! jpeg and the corresponding OSM tiles. 
The hypothesis is that areas with very small aerial jpeg files (because they 
are simply one colour like the sea or vast expanses of desert) will have few if 
any entries on OSM, whereas areas with large file sizes (cities) will have a 
large density of nodes and ways in OSM and therefore large tile size. I do not 
have the technical knowledge to test this so any help would be great.

    * Another hypothesis is that more complete areas of OSM will have a higher 
level of edit activity. If no-one has ever edited an area then it may be 
unlikely that the map is complete there, obviously however there may just be 
nothing there, so this test could be used in conjunction with the Yahoo! 
Imagery test stated before. If we could produce some sort of heat map showing 
which areas are edited most frequently and monitor it over time this could 
certainly show us some interesting trends.

    * This is an attempt to solve the problem of missing roads. I would think 
it unlikely that there would a road which is completely cut off from others, or 
that there would be an entire settlement of roads not connected to rest of the 
country’s road network (as in the Madiera example shown below again). The 
hypothesis is that every road is connected to at least one other road of equal 
or higher classification. So if in OSM there are roads that are not, then maybe 
there are missing roads. This testing may require a lot of calculations and may 
not return that many missing roads. If some one can think of a way to do it 
simpy then I would very much like that input.

Any other ideas of how we can measure completeness statistically?

Ed
http://edwardmjohnson.wordpress.com

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