How to remove spikes in Polygons with PostGIS

Question

I'm trying to validate the topology of a shapefile. I managed to repair cases of overlap and gaps, but i can't resolve cases of spikes. The image shows one example of this situation.

I used the comand:

SELECT geom,
ST_Buffer(  ST_Buffer(  ST_Buffer(geom,0.00001, 'join=mitre'),-0.00002,                           
'join=mitre'),0.00001, 'join=mitre') AS geom_spike_removed
FROM repaired_polygons;

it works fine to remove the spikes, but changes the original form of the polygon. Comparing area and perimeter before and after, we can see that the perimeter changes because there is no more spikes, and the difference on area it's not absurd, but anyway it changes a little the geometry of the polygons, causing new cases of small overlaps and small gaps.

How can i remove this spikes without changing the original geometry of the polygon? Any suggestions?

Answer 1

Here is a link to my PL/pgSQL function which does exactly what the OP is asking for: removing spikes from polygons and linestrings.

Here you can download it and read the documentation: PostGIS NormalizeGeometry.

---

As suggested in the comments, here is an example:

WITH temp (wkt) AS (
    VALUES
        ('LINESTRING(0 0, 2 2, 0 4, -5 4, 0 4.001, 2 6)'),
        ('POLYGON((0 0, 1 1, 2 1, 3 0.5, 2 -3, 3 0.499, 0 0))')
)
SELECT ST_AsText(normalize_geometry(ST_GeometryFromText(wkt), 0.5, 0.5, 0.005, 0.0001)) 
FROM temp;

-- Output
  LINESTRING(0 0, 2 2, 0 4, 2 6)
  POLYGON((0 0, 1 1, 2 1, 3 0.5 ,0 0))

Before:

After:

Answer 2

Someone may chime in with a more sophisticated, purpose-built solution, but to start I'd try generalizing your polygons. The Visvalingam-Whyatt algorithm is a very intuitive one, especially in this application. If you imagine that each vertex forms a triangle with its neighbors to either side, you call the algorithm by specifying the maximum triangle area that you wish to remove. The other vertices in your polygon will remain untouched.

The Visvalingam-Whyatt algorithm is available in PostGIS 2.2 (docs). You may be able to remove your spikes by calling ST_SimplifyVW with an small tolerance parameter.

You could also try experimenting with ST_SimplifyPreserveTopology (docs), which uses a modified Douglas-Peucker algorithm. The "preserve topology" bit means that it won't introduce self-intersections in your polygon, but it operates on one geometry at a time and may still cause gaps or overlaps between adjacent polygons.