The spherize filter does the opposite of what a fish eye lens does, so that's probably not what you're looking for. Spherize makes the center appear closer/larger and the edges farther/smaller. An extreme wide angle lens like a fish eye, on the other hand, makes the center objects look smaller and the outer rim larger. You could use the distort-->pinch filter to make the center smaller, or the "liquify" filter's pucker tool on Photoshop that pulls the image in toward the center. You might have some luck with it if you play around with brush size and selections, but it might be hard to do over an entire picture. A fish eye lens will pull in parts of the scene that won't even be in your normal picture and spread them around the rim, so it would be impossible to fish-eye a whole picture anyway, but you may have a bit of luck faking it for a center selection.
And yes, a displacement map might work well, if you could find the grid you seek. How about one like the circular graph paper they use for polar graphing...where all the lines radiate from the center through concentric circles? Don't know, just guessing. This info must be on the web somewhere...everything is, after all.
Phyllis