This is the still I started with. I removed the background in Gimp and then imported the image into Blender using the import images as planes option. Then, it was sculpting time with the "Grab" brush and the "Smooth" brush. It took a while to get it the way I wanted and it was still not 100 percent right (doesn't really have to be anyway).
This is what it looked like when I was done sculpting. When I sculpt, I always lock the X and Y directions so that any movement is along the Z axis. This guarantees that when you look at the sculpted image straight on, it will always be correct (same as what you started with).
This is a quick animation to show the result. For the animation, I just rotated the plane of the image.
Now, I called this a "2d to 3d conversion" but in Blender lingo, it is usually referred to as "camera mapping". In an animation/film setting, it's called "matte painting".