Is it possible to clip a polygon from a raster layer without being georeferenced? When I try I get this error message "ERROR 1: Unable to compute a transformation between pixel/line and georeferenced coordinates" and am not really sure what it means. I'm speculating that it wants me to georeference the raster layer but I can't as it is a photo, not a map (not a photo of a map) and if I just georeference arbitrarily to try and placate it then the pictures warps.
While the raster may be left un-georeferenced, a vector layer can not. You need coordinates in a defined CRS for the vertices of the polygon.
What you can do:
Choose an arbitrary projected CRS (like Web mercator EPSG:3857), and set the extent of the raster with
gdal_translate -a_ullr (see http://www.gdal.org/gdal_translate.html) exactly to the size of the raster. This prevents the raster from getting stretched. Make sure that the layer and project CRS are EPSG:3857 if it does not look as expected.
Then you can create a polygon layer in the same CRS, and use the clip function.
Your issue seems to be a bit tricky. Gdalwarp expects to do some kind of transforming, but fails on an identical reprojection.
This way it works for me:
gdal_translate -of Gtiff -a_srs EPSG:3857 -a_ullr 0 3456 4608 0 Aarhus.jpg AarhusNew.tif gdalwarp -q -cutline clippoly.shp -tr 1.0 1.0 -of GTiff -dstnodata 0 AarhusNew.tif -overwrite clipped.tif
You have to re-create the clip layer, because all coordinates are now positive (whereas negative Y values fail in your example, beeing identical to the internal pixel/line reference).
looking like this: