ALGORITHMS FOR PROCESSING CONNECTED COMPONENTS WITH GRAY VALUES - Fundamentals of Three-Dimensional Digital Image Processing - page 191

Remark 6.2. The significance of the DT of a gray-tone image is not always
clear in binary image processing. No specific applications have been reported
other than the use in preprocessing of thinning images and the concept of the
skeleton is unfamiliar.

6.2 Thinning of a gray-tone image

6.2.1 Basic idea

Information carried by a gray-tone image can be summarized as follows:

(1) The structure of line figures characterizing the spatial distribution of den-
sity values such as ridge lines and valley lines.
(2) The shape features of a figure (or of subspaces), determined by the spatial
distribution of density values (for example, the shape of contour lines (or
equidensity surfaces) of density values).
(3) Statistics concerning the distribution of density values (e.g., the histogram
of density values, etc.).

The first and second items can be condensed in a line figure. The third item
does not relate to shape information.
One way to concentrate the characteristics of a gray-tone image into a
linear figure is to extend the concept by using a method extracting a centerline
of a binary figure to a 3D gray-tone image. This process is called thinning of a
gray-tone image with the analogy of the processing of a binary image, and we
call an extracted linear figure the centerline or core line . This applies to the
first and the second case discussed above . In the second case, we first segment
a subimage (a figure containing gray values) from an input gray-tone image.
We call this segmented figure a gray-tone connected component again by the
analogy of a connected component in binary image processing. Thresholding is
the most common method of segmentation. A segmented gray-tone connected
component holds the details regarding the shape of a connected component
as well as information concerning the distribution of density values inside it.
When considering shape features of a gray-tone connected component, the
features common in the thinning process of a binary image become important,
such as the location of a centerline (center surface) of a figure and the preser-
vation of topological features. Many of the requirements (1)

∼

(7) described

below relate to these.
On the other hand, the extraction of a borderline (or a border surface)
of a gray-tone connected component (which may be substantially regarded
as an equidensity surface) is not called surface thinning or axis thinning. In
the example of a binary image, structural characteristics of density values
may become surface-like . Another example is the surface thinning of a gray-
tone image. For example, the part of a gray-tone image corresponding with a
ridgeline of the density value distribution may become a curved surface with