Image Processing Reference
In-Depth Information
a constant density. There are no case studies of this as far as the author is
aware. Here we will only discuss linear features such as a ridgeline and a valley
line.
6.2.2 Requirements
The requirements for thinning are almost the same as those for thinning a
binary image and we will summarize them again. Strictly speaking they are
slightly different from those in binary image processing, because properties
concerning the shape features of a connected component as well as the distri-
bution of density values relate to the actual thinning process.
[Requirements for thinning a gray-tone image]
(1)
Connectivity
: A core line keeps topological properties of an input image
without change.
(2)
Location
: A core line is located at the ridgeline of the density value dis-
tribution (in subsequent parts we simply write a
ridgeline
) of an input
image, if a ridgeline exists.
(3)
Line width
: The width of the core line is one unit width (one-voxel width).
(4)
Degeneration
: The length of a core line is close enough to the value that
a human observer recognizes as natural.
(5)
Branching part
: At the branching part and the crossing part of an input
figure, the core line also becomes a branching part and a crossing part in
the natural form.
(6)
Stability
: A core line is not affected excessively by noise irregularity in the
shape of an input figure or by random variations in the density values of
an input figure.
(7)
Rotation
: A core line is not affected by the rotation of an input figure.
It is extremely di
cult to satisfy all of these. Some of them are not com-
patible with each other in principle.
Remark 6.3.
Terms such as
centerline
and
core line
may not be suitable for
structural lines such as a ridge line or a valley line, because they are not always
located in the center of an input figure in the geometrical sense. A branching
point (5) means both the branching as a shape feature and that of a ridgeline.
6.2.3 Principles of thinning
A 3D gray-tone image is, as stated in Chapter 1, a set of voxels accompanied
by gray values (density values) in a 3D space. It seems that the thinning of
such data has not been discussed much in past papers. Although basic ideas
and methods of thinning 2D gray-tone images conceptually can be applied
to a 3D image, their implementation and algorithms are not always obvious.
We will summarize below the basic concepts of thinning 2D images and any
important problems occurring when extending them to a 3D image.
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