By pixel-by-pixel, I assume you mean the pixel-test() command?
Sadly the only way I know of is to store a copy of your map in the back buffer, where every solid tile are plain black (or has a black mask corresponding to every solid part of the tile) and the rest is white, then pixel-test from there, kinda like what I did in Super Sonic Ball. It has been 8 or 9 months since I touched Axe, though.