A Min-Max Medial Axis Transformation

Blum's medial axis transformation (MAT) of the set S of 1's in a binary picture can be defined by an iterative shrinking and reexpanding process which detects ``corners'' on the contours of constant distance from S, and thereby yields a ``skeleton'' of S. For unsegmented (gray level) pictures, one can use an analogous definition, in which local MIN and MAX operations play the roles of shrinking and expanding, to compute a ``MMMAT value'' at each point of the picture. The set of points having high values defines a good ``skeleton'' for the set of high-gray level points in the given picture.