Fast and accurate approximation of digital shape thickness distribution in arbitrary dimension

We present a fast and accurate approximation of the Euclidean thickness distribution computation of a binary shape in arbitrary dimension. Thickness functions associate a value representing the local thickness for each point of a binary shape. When considering with the Euclidean metric, a simple definition is to associate with each point x, the radius of the largest ball inscribed in the shape containing x. Such thickness distributions are widely used in many applications such as medical imaging or material sciences and direct implementations could be time consuming. In this paper, we focus on fast algorithms to extract such distribution on shapes in arbitrary dimension.