Transform 2D-image through diverging-len effect

Hi all, I am looking for a tool to transform a 2D image to some distorted version. I find the imtransform which could do some of the affine transformations but what I am looking for a way that could convert an image after passing a concave lens, just like it pass through a spherical or cylindrical lens such that the middle part of the image getting fatter and the part on the image becomes narrower.

As shown in the attachment, I am showing how before and after the image transformation looks like.

And I find an example from Matlab seems to do the trick but I the effect is more circular from the center instead of like patch on a cylinder

openExample('images/TransformColorImageUsingCustom2DTransformationExample')