Computing 3D Medial Axis for Chamfer Distances

Abstract

Abstract. Medial Axis, also known as Centres of Maximal Disks, is a representation of a shape, which is useful for image description and analysis. Chamfer or Weighted Distances, are discrete distances which allow to approximate the Euclidean Distance with integers. Computing medial axis with chamfer distances has been discussed in the literature for some simple cases, mainly in 2D. In this paper we give a method to compute the medial axis for any chamfer distance in 2D and 3D, by local tests using a lookup table. Our algorithm computes very efficiently the lookup tables and, very important, the neighbourhood to be tested.

Weighted distance transforms for volume images digitized in elongated voxel grids

“…The Look-up tables store, for each voxel value of the WDT, the smallest values of its different neighbours that prohibit the voxel to be part of the MA. The Look-up tables were calculated by the method presented in (Remy and Thiel, 2000). To produce the Look-up tables, they first calculate the WDT from each point in the first 1/48th of the volume to the origin.…”

Weighted Distance Transforms for Images Using Elongated Voxel Grids

“…The Look-up tables store, for each voxel value of the WDT, the smallest values of the neighbours that prohibit the voxel to be part of the MA. The Look-up tables were calculated by the method presented by Remy and Thiel in [6]. To produce the Look-up tables, they first calculate the WDT from each point in the first 1/48th of the volume to the origin.…”

Morphological Analysis of Slip‐Cast Emulsion‐Templated Alumina Foams by Microfocus Computer Tomography

“…This method starts with a “skeletonization” identifying the medial axes of all structures. Then, the “sphere‐fitting” local thickness measurement is made for all the voxels lying along this axis 15 …”