ALGORITHMS FOR PROCESSING CONNECTED COMPONENTS WITH GRAY VALUES - Fundamentals of Three-Dimensional Digital Image Processing - page 194

Fig. 6.2. Codes of direction for grouping border voxels in Algorithm 6.2.

we can modify results while considering the density values distribution of
an input gray-tone image [Salari84]. Density values may be available in
the process of thinning a binary image [Hilditch69, Saito95, Saito96]. The
use of shape features and preservation of topology of an input image are
realized immediately based on the discussion in Chapters 4 and 5. How-
ever, it is necessary to distinguish between the figures and the background
beforehand. The modification of intermediate results using density values
has eventually the same kind of disadvantages as in (1) and (2) above.

6.3 Examples of algorithms - (1) integration of
information concerning density values

6.3.1 Algorithm

Algorithm 6.2 presented below is based on the concept of thinning of a 2D
binary image [Hilditch69, Yokoi75], and was derived by adding to it a proce-
dure to use density values. In principle, a voxel with a smaller density value
is deleted earlier among deletable voxels. Deletable voxels of the same den-
sity value are deleted with an equal rate from six directions ( T,B,W,E,N,S )
(Fig. 6.2). The algorithm is as follows [Yasue96].

Algorithm 6.2 (Thinning of a gray-tone image).
F = : Input and output image. Input image (a positive image with the

background) at the beginning of execution and output image at the end
of execution. The size is L

{ f ijk }

× M × N .

W : Work array.

L, M, N : Numbers of rows, columns, and planes of an image.
min: Minimum of density values in an input image.
bordertype: Group number of border voxels.

= { w ijk }