Image processing Lens distortion in circular

I have a image of circular lens with grid points on it. Space between grid points is all different because of distortion. I googled for some codes to easily rectify the image for case like right, but the problem is that my image consists of specific region that has distortion and the others does not, so fixing whole image induce even more error. What I want to do is that select the grid point on the image(intersection) and make a matrix that is evenly spaced as square grid, to convert the circular image to rectangle. Any idea would be appreciated.