Discrete medial axis transform for discrete objects

The Medial Axis Transform MAT was defined by Blum as an alternate description of the shape of a continuous object. The MAT is the closure of the set of centers of maximal balls which can fit inside the object. A ball is maximal if it is not contained by any other such ball. This model provides dimensionality reduction, completness, it is homotopic with the object characteristics and it is continuous if the object is path-connected. In many applications of 2D digital image processing, discrete approximations of the MAT, such as skeletal representations, thinning, morphological and Distance Map based methods. The main drawback of these methods is that they do not keep up all properties of the continuous MAT simultaneously. In this report, a Discrete Medial Axis definition is proposed as a direct extension of Blum's definition in order to achieve a complete and compressed model representation of discrete objects which retains the significant features of the object and preserves the axis connectivity based on local properties of the Distance Map. This enables to construct it with a seed algorithm whose cost is linear with the size of the object