I have a raster image of the world map in Mercator projection, square 1:1 format. I want transform the image into an Equirectangular projection accurately.
I assumed from my research that GDAL would be the way to go, specifically gdalwarp. I used gdaltranslate to add gcp points to the image on the four corners, and then used gdalwarp to make the transformation.
It produced an image with the correct size – 2:1 ratio – but the projection has not been accurately transformed. It looks exactly the same as if I had taken it into Photoshop and simply stretched it to that shape. The proportional relationship between Mercator and Equirectangular is obviously more complicated than a simple, global stretch like this.
So my question is: is there a way to accurately transform between projections for raster images?
Edit / Additional Information
Here is the starting image: https://i.stack.imgur.com/akU9Z.jpg
I then applied to GCP points using the following gdal_translate command:
gdal_translate -gcp 0.0 0.0 -180.0 90.0 -gcp 1000.0 0.0 180.0 90.0 -gcp 1000.0 1000.0 180.0 -90.0 -gcp 0.0 1000.0 -180.0 -90.0 Mercator.tif MercatorGCP.tif
Then I used the following gdalwarp command to make the intended reprojection from Mercator (ESPG:3857) to Equirectangular (ESPG:32662):
gdalwarp -s_srs EPSG:3857 -t_srs EPSG:32662 MercatorGCP.tif Equirectangular.tif
Here is the resulting image: https://i.stack.imgur.com/HWg8W.jpg
Compare it to a map with proper Equirectangular projection, like this: https://i.stack.imgur.com/RDPlk.jpg
You can see that the proportions have not been properly adjusted, the map not actually reprojected at all, simply squashed uniformly.
Am I doing something wrong, or is this simply not possible with gdal? If not, is there another way to do this?