Amazing Dragon Illusion, Solved!

Your brain interprets everything you see and tries to make sense of it based on what you've seen before. In this case, it picks up cues that you are seeing a face, and because you don't normally encounter concave faces, it assumes the nose is closest to you. That means it has all the depths backwards, and as you move it around your brain tries to make sense of the fact that things aren't moving like it expects. You experience that as the face moving until the brain latches on to some stronger cue that causes it to properly interpret the depth.. like the loss of the "face" cues and white backside when you finally move too far.