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.