ST_GeometricMedian — Returns the geometric median of a MultiPoint.


geometry ST_GeometricMedian ( geometry geom, float8 tolerance = NULL, int max_iter = 10000, boolean fail_if_not_converged = false);


Computes the approximate geometric median of a MultiPoint geometry using the Weiszfeld algorithm. The geometric median is the point minimizing the sum of distances to the input points. It provides a centrality measure that is less sensitive to outlier points than the centroid (center of mass).

The algorithm iterates until the distance change between successive iterations is less than the supplied tolerance parameter. If this condition has not been met after max_iterations iterations, the function produces an error and exits, unless fail_if_not_converged is set to false (the default).

If a tolerance argument is not provided, the tolerance value is calculated based on the extent of the input geometry.

If present, the input point M values are interpreted as their relative weights.

Availability: 2.3.0

Enhanced: 2.5.0 Added support for M as weight of points.

This function supports 3d and will not drop the z-index.

This function supports M coordinates.


Comparison of the centroid (turquoise point) and geometric median (red point) of a four-point MultiPoint (yellow points).

WITH test AS (
SELECT 'MULTIPOINT((0 0), (1 1), (2 2), (200 200))'::geometry geom)
  ST_AsText(ST_Centroid(geom)) centroid,
  ST_AsText(ST_GeometricMedian(geom)) median
FROM test;
      centroid      |                 median
 POINT(50.75 50.75) | POINT(1.9761550281255 1.9761550281255)
(1 row)

See Also