How to calculate the similarty of two polygons, located in different locations

calculate_hausdorff.sql

-- how to calculate the similarty of two polygons, located in different locations

-- requires PostGIS

-- the idea here is to translate both polygons to the origin, then calculate the hausdorff distance
-- between them. We can't do them at their original locations, because.. well, that's not how Hausdorff works.
-- see https://en.wikipedia.org/wiki/Hausdorff_distance#Related_concepts

-- create a sample table with
DROP TABLE IF EXISTS example_hausdorff;
CREATE TABLE example_hausdorff(
  id integer, 
  orig_geom geometry(Polygon), 
  translated_geom geometry(Polygon)
);

-- Add two polygons to it. 
-- these polygons are the same shape, but translated (i.e. they are 10x10 squares)
-- the first has one more point (100, 105) than the second.

INSERT INTO example_hausdorff(id, orig_geom) VALUES
  (1, st_geomfromtext('POLYGON((100 100,100 105,100 110,110 110,110 100,100 100))')),
  (2, st_geomfromtext('POLYGON((200 200,200 210,210 210,210 200,200 200))'));

-- same polygons, rotated 45º

INSERT INTO example_hausdorff(id, orig_geom) VALUES
  (3, st_rotate(st_geomfromtext('POLYGON((100 100,100 105,100 110,110 110,110 100,100 100))'), pi()/4)),
  (4, st_rotate(st_geomfromtext('POLYGON((200 200,200 210,210 210,210 200,200 200))'), pi()/4));

-- Now translate all those geometries so that their centroid is on the origin:

UPDATE example_hausdorff 
  SET translated_geom =
   st_translate(orig_geom,
                 st_x(st_centroid(orig_geom))*-1.0,
                 st_y(st_centroid(orig_geom))*-1.0
               );

--  have a look at what we got.
-- the translated geometries
SELECT 
  st_astext(orig_geom),
  st_astext(translated_geom)
FROM example_hausdorff;

-- the translated origins
SELECT 
  st_astext(st_centroid(orig_geom)),
  st_astext(st_centroid(translated_geom)) 
FROM example_hausdorff ;


-- these should be same (i.e. distance is 0) despite the polygons themselves not being identical
-- that is one has five points, the other has four. 
SELECT st_hausdorffdistance(
          (SELECT translated_geom FROM example_hausdorff WHERE id=1),
          (SELECT translated_geom FROM example_hausdorff WHERE id=2)
        );

-- these should be different, though the exact magnitude depends on the geometries themselves.
SELECT st_hausdorffdistance(
          (SELECT translated_geom FROM example_hausdorff WHERE id=1),
          (SELECT translated_geom FROM example_hausdorff WHERE id=3)
        );     
        
--  these will be very close, but not identical because floats
SELECT st_hausdorffdistance(
          (SELECT translated_geom FROM example_hausdorff WHERE id=3),
          (SELECT translated_geom FROM example_hausdorff WHERE id=4)
        );