There is no way to do what you're asking in AE. HOWEVER, you can cheat it. Just make a bunch of duplicates and offset them a pixel or two in z-space. It'll have approximately the same effect as being 3d as long as you don't view them fully on the side. It's a clever little trick. ☺
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At least Trapcode Form or Mir and Mettle Freeform Pro or Shape Shifter can do things of that nature. Each will have a slightly different look, but all of them can add 3D offset based on image luminance. None of them are a click-of-a-button fast solutions -- there's a definite learning curve involved -- but if you want to proceed that way, I would opt to go with Form. It will turn the image into particles, but that's already pretty much the look you have.