How to implement conformal transformation that wrap 2D image around a circle?

How to transform rectangular image to image that is bent at certain radius? On the plot the center line follows the radius which is 2.

Conformal transformation would be his, but there should be easier way to plot it. W = u + i*v = R*ln(Z/R) = R*ln((x+i*z)/R)

A = imread('peppers.png');
 A = A(31:330,1:500,:);

I would expect to see image that is bent like this.

Answer 1

[Image Analyst]

Looks like an image was created and then they just displayed the image with imshow() or imagesc().