How to warp and enlarge the center of an image?

Question

I am trying to smoothly enlarge the center part of an image. The Skimage code that I use need an inverse map that specifies location of input pixels that will occur at the output pixel location.

If I wanted to shrink the center, I would simply use CDF of a guassian. But I want to enlarge, so I am seeking an opposite distribution that has small gradient in the center and large gradient around the edge.

Example: I am seeking to create the following mask:

5 5 5 5 5
5 3 3 3 5
5 3 1 3 5
5 3 3 3 5
5 5 5 5 5