medial axis transform implementation

Question

How do I implement the Medial Axis Transform algorithm to transform the first image into the second?

_{(source: algorith at www.cs.sunysb.edu)}

_{(source: algorith at www.cs.sunysb.edu)}

What library in C++/C# have support for Medial Axis Transform?

Answer 1

There is a medial axis transform available in this C Library:http://www.pinkhq.com/ There are lot other related functionalities. Check out this Function:http://www.pinkhq.com/medialaxis_8c.html

Answer 2

There are many implementations of the medial axis transform on the Internet (personally I don't use OpenCV library but I'm sure it has a decent implementation). However, you could easily implement it yourself.

In order to perform medial axis transform, we need to define only one term: simple point. A point (P) is simple point iff removing P doesn't effect the number of connected components of either the foreground or the background. So, you have to decide the connectivity (4 or 8) for the background and for the foreground - in order to work pick different one for both (if you are interested why, look up Jordan property on google).

Medial transform axis could be implemented by sequentally deleting simple points. You get the final skeleton if there are no more simple points. You get the curved skeleton (I don't know the english name for it which is rare - please correct me) if you only have endpoints OR non-simple points. You provided examples of the latter in your question.

Finding simple points could be easily implemented with morphological operators or a look-up table. Hint: a point is simple point iff the number of connected components in the background is 1 and the number of connected components in the foreground is 1 in a 3x3 local window.