How can i find the largest inscribed rectangle within an irregular shape?

I want to find the largest rectangle (by area) inside this shape. Clearly, it should be somewhere in the bottom half, but I don't know if a longer rectangle or a more square box would be larger. Orientation does not matter. What would be the fastest way to solve this for any irregular shape? I have tried functions like imclose and imopen to no success.

Answer 1

[Image Analyst]

Try this: http://www.mathworks.com/matlabcentral/fileexchange/34767-a-suite-of-minimal-bounding-objects

[Bo]

A lot of the code here involves generating a convex hull, which would alter the shape(and the inscribed box) like so:

This would incorrectly give me the actual largest inscribed box, which i would expect to look something like this:

[Image Analyst]

Well I can't think of anything off the top of my head. If you wanted a circle, then you could simply use bwdist() but a rectangle at any orientation is tougher. Maybe John or Roger will have an idea. The only thing I can think of is to use bwboundaries and then do all possible permutations of 4 coordinates that are roughly at 90 degrees. Then you'd have to use poly2mask to make a trial rectangle mask and see if all pixels in the mask are white and none are black (which would mean it's not totally inside). I'm sure that would take a long time - 4 nested for loops - though it could be speeded up in the third for loop to break of the angle is not around 90 degrees.