remap into polar projection
for the northpole and southpole
add a cap
here are the real mars Northpole and Southpole ice caps
North
South
gimp has a nice Distort filter
that remaps a Simple Cylindrical 2 x 1 proportion (ie. 8192x4096) to polar stereographic
used that on the above 23,040 x 11,520 map and cropped
( 2048x1024 resize of the Simple Cylindrical map)
-- this is close to the real color of mars --