• you are required first to identify several pairs of closely matching points on both maps.
  
• the accuracy and precision of your measures will have a strong influence on the final result, so you must be very careful during this step.
• accurately choosing appropriate terrain features allowing a precise and non ambiguous identification is equally important: good candidates are e.g. bell towers, chimneys, relevant buildings (church, castle, palace, railways station), mountain pinnacles, ponds, small water bodies and alike, but it obviously widely depends on the relative scale and epoch of both maps.
• identifying at least three GCP pairs is the bare minimum required to attempt resolving a 2D problem, and at least four GCP pairs are required in the 3D case.
• defining a bigger number of GCP pairs usually helps a lot in order to achieve a better precision, because in the case of an overdetermined system several statistic methods can be usefully applied so as to smooth and correct single measure errors.
• any uneven distribution of the GCPs should always be carefully avoided, because it could easily introduce noticeable distortions; as far as possible all GCPs should be wisely placed so to regularly cover the map as a whole and possibly avoiding any directional preference.
  Placing many precisely measured points aligned along the same line is an inherently useless waste of time.
• splitting a big problem into many smaller problems usually helps: achieving a good precision is easier when separately processing small-sized samples just covering a precisely selected area of reasonable extension, because this way each single sub-zone can benefit from using its own precisely calibrated transformation.

• in this example the fully qualified map (shown in yellow on the bottom side figure) consists of two Shapefiles:
  • tuscany: administrative boundaries of Tuscan Local Councils (MultiPolygons 2D).
    SRID=4326, charset=CP1252
  • geonames_ppl: Tuscan Populated Places (Points 2D).
    SRID=4326, charset=CP1252
• the mysterious unqualified map (shown in gray on the top side figure) also consists of two Shapefiles:
  • unknown: another dataset of different origin representing the administrative boundaries of Tuscan Local Councils (MultiPolygons 2D).
    SRID=-1, charset=CP1252
  • unknown_ppl: a second dataset representing Tuscan Populated Places fully consistent with the unknown Admin Boundaries (Points 2D).
    SRID=-1, charset=CP1252

SELECT org.name, org.geometry, dst.geometry
FROM unknown_ppl AS org, geonames_ppl AS dst
WHERE Upper(org.name) = Upper(dst.name);

• all SQL functions depending on the GCP module start with a GCP_ common prefix.
• the GCP_Compute() SQL function do actually resolves a GCP problem then returning a BLOB-encoded object intended to be passed to some other GCP SQL function for further processing.
  This function will return NULL on invalid arguments or when any error is encountered (typically: too few GCP pairs were passed, or the GCP pairs are of a so poor quality that finding any valid solution was impossible).
  Note well: GCP_Compute() is an aggregate function, and consequently will take in account all GCP pairs coming from the input resultset.
  • the first argument corresponds to the origin Geometry, i.e. to the unknown component.
  • the second argument corresponds to the destination Geometry, i.e. to the fully qualified component.
  • the third (optional) argument can assume the following values:
    • 1 (default) the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 1st order.
    • 2 the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 2nd order.
    • 3 the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 3rd order.
    • 0 the GCP problem will be solved by applying the Thin Plate Spline (aka TPS) method.
• the GCP_Transform() SQL function is strictly similar to ATM_Transform(), and will directly recompute all coordinate values accordingly to the coefficients found in the BLOB-encoded object created by GCP_Compute().

CREATE TABLE tuscany_1st AS
SELECT u.name, GCP_Transform(u.geometry, g.matrix, 4326) AS geometry
FROM unknown AS u,
     (SELECT GCP_Compute(org.geometry, dst.geometry) AS matrix
      FROM unknown_ppl AS org, geonames_ppl AS dst
      WHERE Upper(org.name) = Upper(dst.name)) AS g;

SELECT RecoverGeometryColumn('tuscany_1st', 'geometry', 4326, 'MULTIPOLYGON', 'XY');

CREATE TABLE tuscany_2nd AS
SELECT u.name, GCP_Transform(u.geometry, g.matrix, 4326) AS geometry
FROM unknown AS u,
     (SELECT GCP_Compute(org.geometry, dst.geometry, 2) AS matrix
      FROM unknown_ppl AS org, geonames_ppl AS dst
      WHERE Upper(org.name) = Upper(dst.name)) AS g;

SELECT RecoverGeometryColumn('tuscany_2nd', 'geometry', 4326, 'MULTIPOLYGON', 'XY');

CREATE TABLE tuscany_3rd AS
SELECT u.name, GCP_Transform(u.geometry, g.matrix, 4326) AS geometry
FROM unknown AS u,
     (SELECT GCP_Compute(org.geometry, dst.geometry, 3) AS matrix
      FROM unknown_ppl AS org, geonames_ppl AS dst
      WHERE Upper(org.name) = Upper(dst.name)) AS g;

SELECT RecoverGeometryColumn('tuscany_3rd', 'geometry', 4326, 'MULTIPOLYGON', 'XY');

results assessment

• the yellow background corresponds to the original tuscany map (i.e. to the reference target).
• the results of the 1st order transformation are shown in red.
• the results of the 2nd order transformation are shown in blue.
• the results of the 3rd order transformation are shown in green.

• We've got decently accurate and fairly self-consistent transformations near to the center of the map.
• Anyway there is an obvious degrading accuracy and a strong dispersion in the most peripheral areas of the map.
• Short conclusion: our candidate GCP pairs are of very poor quality, and fail to produce hi-quality results.
  Honestly we were expecting something like this, once considered that we've lazily used GCP pairs of unchecked quality simply based on matching Populated Places coming from two unrelated sources.
  It wasn't too much difficult imagining that a so simplistic approach was rather inadequate.

SELECT org.name, org.geometry, dst.geometry
FROM unknown_ppl AS org, geonames_ppl AS dst
WHERE dst.selected = 1 AND Upper(org.name) = Upper(dst.name);

CREATE TABLE tuscany_bis_3rd AS
SELECT u.name, GCP_Transform(u.geometry, g.matrix, 4326) AS geometry
FROM unknown AS u,
     (SELECT GCP_Compute(org.geometry, dst.geometry, 3) AS matrix
      FROM unknown_ppl AS org, geonames_ppl AS dst
      WHERE dst.selected = 1 AND Upper(org.name) = Upper(dst.name)) AS g;

SELECT RecoverGeometryColumn('tuscany_bis_3rd', 'geometry', 4326, 'MULTIPOLYGON', 'XY');

results assessment

• the yellow background corresponds to the original tuscany map (i.e. to the reference target).
• the results of the 1st order transformation are shown in red.
• the results of the 2nd order transformation are shown in blue.
• the results of the 3rd order transformation are shown in green.
• the results of the TPS transformation are shown in cyan.

Quality assessment

• the tuscany dataset (represented as a yellowish surface with brown edges) is an excerpt of Admin Boundaries produced by ISTAT in the context of the 2011 national census.
• the unknown dataset (represented as a blue line) is an excerpt of Admin Boundaries produced by Tuscany Region.
• it's rather obvious that the Tuscany Region dataset is more rich of fine grained details, and is more accurate. The ISTAT dataset is more like a summarized sketchy representation and intentionally ignores many small details.
• Anyway a fairly good spatial correspondence clearly exists between the two datasets.

• only well marked and easily identifiable small-sized map features have been used so to reduce any error margin.
  Considering the specific geographic area all GCPs identify a cliff, a cape or a pier.
• all GCPs have been located in such a way so to regularly cover the whole map extension as far as possible.
• an exceeding number of GCPs has been determined so to compensate for eventual inaccurate Point placements.

results assessment

• the yellow background corresponds to the original tuscany map (i.e. to the reference target).
• the results of the 1st order transformation are shown in red.
• the results of the 2nd order transformation are shown in blue.
• the results of the 3rd order transformation are shown in green.
• the results of the TPS transformation are shown in cyan.

Quality assessment

• 1st order polynomial transformation: represented as a red line.
  Not really perfect, but reasonably good; some evident shift.
• 2nd order polynomial transformation: represented as a blue line.
  Almost perfect alignment, very small and practically negligible shift.
• 3rd order polynomial transformation: represented as a dotted line.
  Still decent, but obviously affected by a noticeable shift.
• TPS transformation: represented as a green line.
  Very similar to the 2nd order transformation; almost perfect alignment.

• results of the 1st order transformation are shown as a pink line.
• the 2st order is shown as a blue line.
• the TPS transformation is shown as a red line.

• the first two arguments are always expected to be Geometries of the POINT type.
• a strong dimensional consistency is always required: all input Points are required to be exclusively of the 2D type or exclusively of the 3D type.
  Mixing together 2D and 3D Points will be considered an illegal operation.
• the first argument corresponds to the origin Geometry, i.e. to the unknown component.
• the second argument corresponds to the destination Geometry, i.e. to the fully qualified component.
• the third (optional) argument can assume one of the following values:
  • 1 (default) the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 1st order.
    Note: all polynomial solutions can be either of the 2D or of the 3D type; the selection of the dimensional mode is implicitly determined by the nature of the input Points.
  • 2 the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 2nd order.
  • 3 the GCP problem will be solved by applying the RMSE regression method and will return a set of polynomial coefficients of the 3rd order.
  • 0 the GCP problem will be solved by applying the Thin Plate Spline (aka TPS) method.
    Note: all TPS solutions are always of the 2D type, even when 3D Points are supplied.