Figure 5.

Two choices for the definition of neighborhood on the 2D image raster. The central pixel of interest is black and the neighbors are dark gray. (A) 4-neighborhood (4-NB), where all pixels sharing an edge are neighbors and (B) 8-neighborhood (8-NB), where all pixels with common corners and sides are considered as neighbors. (C, D) Topology is sensitive to the neighborhood definition. (C) Contains two 4-connected objects or only one 8-connected object. (D) The object is an 8-connected loop but a 4-connected open arc. (E–H) Topological skeletons (denoted by black dots) of four raster objects. The topological skeleton is not unique, for (E) and (F) any point in the object will equally well present a topological skeleton. (G) The skeleton contains a loop, e.g., due to lumen effect. (H) Skeletonization is inherently sensitive to small boundary perturbations; single pixels will lead to stubs in the skeleton. (I, J) Two raster midline representations of a line (I) and a curve (J) on an 8-NB topology. The piecewise linear approximate (solid line) is longer or equal to the actual distance (dashed line).