||Given a binary image consisting of object and background grid points, the distance transform assigns to each object grid point its distance value to the closest background grid point. The distance transfform provides valuable information for shape analysis and is widely used in several applications such as, for example, skeleton extraction, shape based interpolation or image registration.
Weighed distance transform is an efficient way to compute distance transforms on discrete images. It can be computed using a two-scan algorithm, a chamfer algorithm in the usual square grid.
In this presentation, we recall weighted distance properties found in the literature for 2D and 3D cubic grid. To allow the use of different kinds of grids as for example fcc and bcc grids, we generalized these properties and prove them to be true in a wider framework: modules of dimension n.