Exploring shortest paths@ Steve

Regarding Steve's topic finding the shortest path, I'm now asked to find the shortest path for all the pixels of any two object. What do I mean by this: In the image below I want a path such that the whole T letter gets to S. Yes, that might be a challenging, involving some rotations, etc... but in my problem I only have circular objects.

Here it is its topic: http://blogs.mathworks.com/steve/2011/12/13/exploring-shortest-paths-part-5/

So the question is: Can I have some restrictions such that the whole object gets to its destination? Thank you!

[Alexandru Miculescu]

Same with this path: