GeoRef uses two main coordinate systems:

• The image coordinate system measures position in pixels (x, y) where (0, 0) is the upper-left corner of the image, x increases to the right, and y increases down.
• The Spherical Mercator coordinate system expresses position on the Earth's surface. (x, y) coordinates. Roughly speaking, x increases to the east and y increases to the north. The origin matches the origin in lat/lon coordinates. The scale of the units approximates displacement in meters. This system is also known as EPSG:3857 or EPSG:900913.

Two-way conversions between lat/lon and Spherical Mercator can be found in the latLonToMeters and metersToLatLon functions:

• JavaScript coordinate conversions
• Python coordinate conversions

Some other references:

• Google Maps Coordinates, Tile Bounds, and Projection
• PROJ.4 FAQ: Google Mercator

Exporting an overlay produces a gzip-compressed tar archive containing following files:

[imageid]-no_warp.tif

-this is a GeoTIFF version of the photo that is unmodified (unwarped) in an image sense, but contains a bunch of metadata header fields indicating the list of

control/tie/correspondence points found for alignment and some alignment fit uncertainty measures. This version gives an end user all they'd need to create their own aligned image from the embedded control points.

[imageid]-warp.tif

-this is a GeoTIFF version of the photo that is actually modified to be warped/aligned to a map, with transparency around the warped photo to fit inside a

rectangular image as usual. It does not contain a header with the list of tie points, but it contains fields with alignment fit measures.

[imageid]-no_warp_metadata.txt

-this is a text file containing a formatted dump of the header fields present in the -no_warp.tif version so that someone can get the important data without

retrieving the image.

[imageid]-warp_metadata.txt

-same as no_warp_metadata.txt but instead corresponding to the -warp.tif version.

[imageid]-uncertainty-no_warp.tif

-This is a special synthetic image (single channel floating point) where the number at each pixel represents the uncertainty (standard deviation) in meters we

estimate for our fit at that pixel. This provides data to do automated analysis of the relative accuracy of our alignment at each pixel -- it will be more accurate near tie points, and worse further away.

[imageid]-uncertainty-no_warp.tif

-analogous to the -uncertainty-no_warp.tif file, this is a warped/aligned version of the uncertainty image. It contains two floating point channels, the first

is the uncertainty as in the unwarped version, and the second is a "mask" that is 0 where there is no uncertainty data (the warped image doesn't exist there) or 255 if there is.

The transform field represents a best-fit transform that maps image coordinates to Spherical Mercator coordinates. Depending on the number of tie points specified, the transform can be expressed in two forms:

• "type": "projective". This is a 2D projective transform. Used when fewer than 7 tie point pairs are specified. The matrix field is a 3x3 transformation matrix M specified in row-major order. To apply the transform:
  • Start with image coordinates (x, y).
  • Convert to a length-3 column vector u in homogeneous coordinates: u = (x, y, 1)
  • Matrix multiply (x0, y0, w) = M * u.
  • Normalize homogeneous coordinates: x' = x0 / w, y' = y0 / w.
  • The resulting Spherical Mercator coordinates are (x', y').
• "type": "quadratic2". This transform is similar to the projective transform but adds higher-order terms to achieve a better fit when the overlay image uses a different map projection from the base layer. Used when 7 or more tie point pairs are specified. Please refer to the code for full details. Some points of interest:
  • Note that despite the name, this transform is not exactly quadratic. In order to ensure the transform has a simple analytical inverse, corrections are applied serially, which incidentally introduces some 4th-order and 6th-order terms.
  • The matrix field has essentially the same interpretation as for the 'projective' transform.
  • In order to help with numerical stability during optimization, the last step of the transform is to scale the result by 1e+7. Because of this, the matrix entries will appear much smaller than those in the projective transform.
  • The coefficients for higher-order terms are encoded in the quadraticTerms field. If all of those terms are 0, the quadratic2 transform reduces to a projective transform.

See the alignment transform reference implementations in the ProjectiveTransform and QuadraticTransform2 classes:

• JavaScript alignment transforms
• Python alignment transforms