I am trying to use the Selection Brush Tool to outline the profile of a head and shoulders photo (see My Gallery for the photo).

The problem is that on the left side of the face the background and foreground colors are too similar, so the selection tool spreads into the middle of the face, since it cannot see the difference.

I have used a maximum contrast effect to try and solve this problem, but the selection tool still does not recognize the full outline of the head as compared to the background.

My goal is to fully color the background with a white color, and leave the foreground image as is. At the moment, attempts to color the background white with the Paint Bucket Tool includes half of the face in the white color change.

I've also tried using the Magic Wand, Lasso and Elliptical tools with no success.
The Magic Wand has an add/subtract option, but this doesn't seem to be very precise.

Any tips on how to create a clean outline of the profile in the photo in My Gallery is greatly appreciated.