mjhjmtu

Does anyone know of a routine/function or transformer that would identify if a polygon is not fully enclosed/surrounded by other polygons?

The polygons have no gaps or slivers between them so if a certain section of polygon is not attached to another polygon then these are the ones I want to keep.

I am happy to use any of PostGIS/FME/QGIS I just cannot seem to find a function or transformer that would do it.

EDIT

I have added a picture to help explain:

I am after the purple polygons and ignore the yellow ones as they are not fully enclosed by other squares

I have an answer that should be logically correct but the SQL part is not complete. The idea is based on intersections of adjacent polygons. The intesections are either lines if polygons share segment(s), or points if polygons meet at one vertex.

The first step is to compute the intersection of one polygon and the union of all the polygons on the layer, except the selected polygon.

The intersection of polygon 1 and union of all the rest is a multilinestring with two members. The intersection of polygon 6 and anything else but polygon 6 consists of four linestrings members which are connected.

The second step is to try if it is possible to build a new polygon from the intersections. For the connected lines from polygon 6 it is possible but not for the two linestrings from polygon 1.

This is the SQL that I used for testing.

select ST_MakePolygon(ST_LineMerge(c.intersection)) from 
(select 
ST_Intersection(sub_a.a,sub_b.b) as intersection from
(select ST_Union("GEOMETRY") as a from outline_test where gid!=6) as sub_a,
(select "GEOMETRY" as b from outline_test where gid=6) as sub_b) as c;

With gid=1 the result is an error:

ERROR: lwpoly_from_lwlines: shell must have at least 4 points

and with gid=2:

ERROR: lwpoly_from_lwlines: shell must be closed

Another approach: The polygons you want to find have 1-dimensional intersection (lines) with the outer ring of the whole area as an union. If polygon is only touching the outer boundary the intersection is a point with dimension=0, and polygons which are totally inside to not intersect as all (so they are disjoint).

So you can select the features with ST_Dimension=1 from SQL query like

select outline_test.gid,ST_Dimension
(ST_Intersection(outline_test."GEOMETRY",sub_a.geometry))
from 
(select ST_ExteriorRing(ST_Union("GEOMETRY")) as geometry from outline_test)
as sub_a, outline_test;

The query does not make difference between "touches" and "disjoint" as documented in https://postgis.net/docs/ST_Dimension.html If the dimension is unknown (empty GEOMETRYCOLLECTION) 0 is returned but that does not matter in your use case. Rereffing to the data and image in my other answer, other polygons than numbers 5, 6, 8, and 10 should be found and that happens.

1;1
2;1
3;1
4;1
5;0
6;0
7;1
8;0
9;1
10;0
11;1
12;1
13;1
14;1

I am sure it is possible to write more elegant queries based on the outer boundary and DE-9IM relations http://postgis.net/docs/using_postgis_dbmanagement.html#DE-9IM.

Assuming your polygons are topologically correct (no gaps, or overlaps), then a polygon A is enclosed by other polygons if its perimeter is equal to the sum of intersection length between its boundary and the boundary of other polygons. This method lends itself to use of a spatial index and avoids performing a relatively costly union of all other polygons.

SELECT a.id
FROM my_data a 
INNER JOIN my_data b ON (ST_Intersects(a.geom, b.geom) AND a.id != b.id) 
GROUP BY a.id
HAVING 1e-6 > 
 abs(ST_Length(ST_ExteriorRing(a.geom)) - 
 sum(ST_Length(ST_Intersection(ST_Exteriorring(a.geom), ST_ExteriorRing(b.geom)))));