The task at hand is to morph / distort user submitted photos into a heart shape. All images will be cropped square and resized to the same pixel dimensions.
Desired results:


In Photoshop this would be referred to as a smudge but I can't seem to find anything similar in ImageMagick.
I tried a few executions of using combinations of explode / bulge and pinch see below diagram - but the images were distorted beyond recognition.

Any ideas or suggestions would be greatly appreciated!