Moving Least Squares registration
This plugin implements the algorithms described in  to deform an image given a set of landmarks.
Load the original and choose the landmarks:
By clicking on the menu entry Edit › Selection › Add to Manager add this landmark set to the ROI Manager:
Duplicate the image (Image › Duplicate… ), click on the selection in the ROI manager and move the landmarks to their target location:
Now, run the plugin:
And you get the result:
Schaefer S., McPhail T., Warrent J. (2006), “Image Deformation Using Moving Least Squares”, ACM Transactions on Graphics 25: 533-540 .