PostGIS - Finding most remote point using ST_MaximumInscribedCircle?

Question

I have a database of points coordinates taken from OSM. My geometry column is called wkb_geometry. I am trying to find the most remote point (by distance to the next nearest point). I was hoping to use the new ST_MaximumInscribedCircle function and then order by radius to find the most remote point. Below is the code I have so far. It runs but returns 0 for the radius. The example on the PostGIS website is for a polygon.

SELECT
  osm_id, name,
  geom.radius,
  geom.center,   
  geom.nearest   
FROM
  australian_points AS t,
  LATERAL ST_MaximumInscribedCircle(t.wkb_geometry) AS geom
  ORDER BY geom.radius ASC
;

Answer 1

With an index structure supporting (spatial) (K)NN searches like the PostGIS GIST extension, this is trivially executed with

SELECT
  *
FROM (
  SELECT
    p1.id,
    p1.geom,
    ST_Distance(p1.geom, pn.geom) AS dist
  FROM
    australian_points AS p1
    CROSS JOIN LATERAL (
      SELECT
        p2.geom
      FROM
        australian_points AS p2
      WHERE
        p1.id <> p2.id
      ORDER BY
        p1.geom <-> p2.geom
      LIMIT
        1
    ) AS pn
) q
ORDER BY
  dist DESC
LIMIT
  1
;

Here

• we find the nearest neighbor to each point using a (K)NN query (a CROSS JOIN LATERAL "loop" in conjunction with the index-optimized <-> distance operator)
• and then filter for the highest dist value (ORDER BY dist DESC LIMIT 1)

---

If you need true geoidal surface distances, you'd want to implement a CAST to GEOGRAPHY; change the query to use

• ST_Distance(p1.geom::GEOGRAPHY, p2.geom::GEOGRAPHY) (spheroidal calculation)
• p1.geom::GEOGRAPHY <-> p2.geom::GEOGRAPHY (spherical calculation) respectively.

(Note that a CAST to GEOGRAPHY is possible only for geographic reference systems!)

But beware:

This can only ever be as performant with an appropriate index on the CAST, e.g.

CREATE INDEX
  ON australian_points
  USING ( (geom::GEOGRAPHY) )
;