Digital Distance Transforms in 3D Images Using Information from Neighbourhoods up to 5×5×5

3D distance fields: a survey of techniques and applications

“…5, where i; j; k 2 fÀ2; À1; 0; 1; 2g for a 5 Â 5 Â 5 transform, fp and bp are the sets of transform positions used in the forward and backward passes, respectively, and checks are made to ensure fp and bp only contain valid voxels at the edges of the data set. Svensson and Borgefors [102] present an analysis of chamfer distance transforms and give numerous examples of distance templates. Cuisenaire [31] also gives a good review of distance transforms (both Chamfer and Vector).…”

“…. The < a; b; c > opt method is the best 3 3 CDT as it has been optimally designed to limit the distance error [102]. .…”

On the Use of Shape Primitives for Reversible Surface Skeletonization

“…The DT can be computed in two scans of the images using local distance information only. For more information on how to use and compute DTs, we refer to [7,8,9,10]. We will use a distance function where the distance between two voxels, v and w, is dependent on the number of steps in the face (A), edge (B), and vertex (C) directions in a minimal path between v and w. The distance is given by d(v, w) = max(A, B, C), i.e., the distance equals the number of steps in a minimal 26-connected path between v and w. We refer to this distance as D 26 and to the corresponding distance transform as the D 26 DT.…”

“…We will use a distance function where the distance between two voxels, v and w, is dependent on the number of steps in the face (A), edge (B), and vertex (C) directions in a minimal path between v and w. The distance is given by d(v, w) = max(A, B, C), i.e., the distance equals the number of steps in a minimal 26-connected path between v and w. We refer to this distance as D 26 and to the corresponding distance transform as the D 26 DT. The D 26 DT has the drawback of being unstable under rotation, i.e., it is not a good approximation of the Euclidean DT, [11,12], on the other hand, the Euclidean DT has the disadvantage in being more difficult to use [13,10]. The label of a voxel v in a DT can be interpreted as the radius of a ball centred on v which is fully enclosed in the foreground (the DTball).…”

Medial Axis LUT Computation for Chamfer Norms Using $\mathcal{H}$ -Polytopes

“…Since the distance transform labels pixels with the greatest equivalent radius, criterions based on radius difference fail to recognize equivalent disks as being covered by other disks. In the case of 3 × 3 2D masks or 3 × 3 × 3 3D masks, a simple relabeling of distance map values with the smallest equivalent radius is sufficient [14,15]. However this method fails for greater masks and the most general method for medial axis extraction from the distance map involves look-up tables (LUT) that represent for each radius r and displacement…”