Medial Axis Transform (MAT) of General 2D Shapes and 3D Polyhedra for Engineering Applications

Abstract

Medial Axis Transform (MAT) is a representation that encodes an object with symmetric (medial) axes in the object interior. MAT has been employed in a variety of applications such as pattern recognition of digital images, biological shape analysis and robotic motion planning. Although numerous algorithms have been proposed to determine MAT of polygonal objects, a robust model for arbitrarily shaped regions, especially suitable for engineering designs, is still an active area of research. In this paper, a 2D approach capable of efficiently constructing MAT for arbitrarily shaped 2D regions is proposed. This method can be utilized to evaluate 3D objects for a variety of applications though it does not produce a 3D MAT. Alternatively, an algorithm for calculating the MAT of 3D polyhedra is also presented.