Select ways with circular shape in PostGIS (roundabouts)?

Here's a PostGIS script doing just that: https://github.com/TelenavMapping/useful-postgis-queries/blob/master/sql-queries/detect_possible_roundabouts.sql Enjoy!

Many of us, vector map-makers, do this roundabout recognition, and we do it from the times even before the OSM has been born. There are at least two basic reasons to that:

• to provide more complete and safer turn-by-turn navigation network; and
• when creating the vector scale levels, roundabouts quickly transform to ordinary nodes.

In addition to the answer and comments already provided I would rather add some hints/suggestions based on experience running data-preparation on OSM dumps though the numbers are some months old (I do not register them for every run/OSM dump).

The preparation-tool runs separately on any of the road classes (motorway, trunk, primary, secondary, tertiary, living-street and street) and detects way classes RAC (ways tagged as roundabout) and ORC (the rest or the ordinary roads, not tagged as roundabouts).

Within RAC, we create the roundabout (RA) class (single circular ways or end-to-end connected ways creating circular ways). Now, for the RA class we detect some 5-7 (average/statistical) parameters like the number of edges, the length of the edge, the convexity, the diameter and so on. Finally, within the RAC we detect:

• The safe roundabout (SRA) class (253480 objects for all road classes). These are elements of RA having parameters close to the average values;
• The unsafe roundabout (URA) class (6875), those from RA having at least one parameter far from the average value (outside the tolerance). This unsafe class of RA contains roundabouts wit anomalies as well (with self-crossings, more than one round between the start and end nodes, isolated, having more than one section between two nodes, zig-zag consecutive edges and so on);
• The geo-rec based (GRA) class (708). This are created from the incomplete roundabouts where adding one or two short poly-line sections we create a safe roundabout; finally
• The erroneous objects in RAC (2195). These are ways recognized as ordinary/feeding roads obviously tagged as roundabouts by mistake. This road segments are missing sections in ORC and therefor they are added to the ORC before further processing.
  -Within the ORC we detect circular single ways that closely (perfectly) match the corresponding safe SRA parameters. There were totally 101803 such cases, let us say, ordinary road roundabouts (ORRA).
  -Finally, in a similar way as for GRA we detect some 19547 geo-rec based roundabouts (GORRA) from the ORC class (with high probability also roundabouts).

Within any of the mentioned road types, we merge the described five roundabout classes to a final set of roundabouts. These are the input to further preparation, data generalisation, rooting …

Note that the last two roundabout sets (ORRA and GORRA) contain large number of turning-circles. Visual inspection on a large sample shows that mappers are having dilemma how to tag/upload these kinds of objects. At the same time qualifying turning-circles as roundabouts should not confuse robust line-following/rooting systems.

If interested, some more details can be found from my earlier OSM-dev and OSM-rooting forum discussions/posts here https://drive.google.com/open?id=0B6qGm3k2qWHqRVVXVVFwbVdtN1E