How to create a morph of this organic form

[svpribyl]

I'm a morph newbie. Could someone give me an idea of a method to use to create a morph of the top half of this case? I have a 2d plan view. I want the roundness to engulf the whole form, not just the edge, so fillet wouldn't produce the right effect, even if I could get it to work. Any suggestions?

Thanks.