Converting a pixel coordinate in GeoTIFF to a latitude and longitude?

Question

I have a GeoTIFF with the following meta information:

PROJCS["WGS 84 / Pseudo-Mercator",
    GEOGCS["WGS 84",
        DATUM["WGS_1984",
            SPHEROID["WGS 84",6378137,298.257223563,
                AUTHORITY["EPSG","7030"]],
            AUTHORITY["EPSG","6326"]],
        PRIMEM["Greenwich",0,
            AUTHORITY["EPSG","8901"]],
        UNIT["degree",0.0174532925199433,
            AUTHORITY["EPSG","9122"]],
        AUTHORITY["EPSG","4326"]],
    PROJECTION["Mercator_1SP"],
    PARAMETER["central_meridian",0],
    PARAMETER["scale_factor",1],
    PARAMETER["false_easting",0],
    PARAMETER["false_northing",0],
    UNIT["metre",1,
        AUTHORITY["EPSG","9001"]],
    AXIS["X",EAST],
    AXIS["Y",NORTH],
    EXTENSION["PROJ4","+proj=merc +a=6378137 +b=6378137 +lat_ts=0.0 +lon_0=0.0 +x_0=0.0 +y_0=0 +k=1.0 +units=m +nadgrids=@null +wktext +no_defs"],
    AUTHORITY["EPSG","3857"]]

How to I find the geographic coordinate (lat, lon) in Web Mercator of a pixel in the image (e.g. x=500, y=600)

Answer 1

Assuming that you use python gdal. The Geotransform object contains the coordinates of the pixel at the bottom left corner and x and y pixel size. The units are specified in the projection object that you posted. Since you have a projected reference system, you have meter units See description of your coordinate system here Once you have the Geotransform information it is easy to get to the desired pixel coordinates.

import gdal
tif = gdal.Open(my_tiff)
gt = tif.GetGeoTransform()

For example:

gt
>>>(1100000.0, 25.0, 0.0, -4200000.0, 0.0, -25.0)

We can extract the values we need:

x_min = gt[0]
x_size = gt[1]
y_min = gt[3]
y_size = gt[5]

And use them to calculate the coordinates of a given pixel:

mx, my = 500, 600  #coord in map units, as in question
px = mx * x_size + x_min #x pixel
py = my * y_size + y_min #y pixel