Image Processing Reference
In-Depth Information
(
a
)
(
b
)
Fig. 6.4.
Experimental results of Algorithm 6.2 (applied to real CT images): (
a
)
Input image (blood vessels in a chest X-ray CT image); (
b
) the result of thinning.
were relatively better in the thinning of vessel region images used in this
experiment. In fact, it is known from Fig. 6.4 that the core line obtained by
Algorithm 6.2 preserves most of the important structure of vessel regions.
More details are reported in [Yasue96].
6.4 Examples of algorithms - (2) ridgeline following
6.4.1 Meanings of a ridgeline
In order to extend the basic idea of ridgeline extraction of a 2D image (in (1)
of Section 6.2.1) to a 3D image, we need to develop a procedure to extract a
ridgeline of a hypersurface
u
=
f
(
x, y, z
) representing a hypercurved surface
of the density distribution in 3D space, that is, a hyper-curved surface in
4D space
u
f
(
x, y, z
)=
0
. To achieve this, we first have to decide what
conditions should be satisfied by points (voxels) on a
ridgeline
.
Let us consider a 2D image to find keys to a solution (Fig. 6.5). Our idea
is to follow a point sequence to the direction of the minimum curvature from
a local maximum (top) of density values. This means that we consider the
direction of the minimum curvature coincides with the direction of a ridgeline.
The minimum curvature means the minimum of principal curvature described
in Section 3.4. However, it may not be correct to extract points with zero
curvature because all parts that are locally flat may be extracted. If we exclude
points of zero curvature, another inconvenience may be caused because any
smooth top of a mountain that is differentiable is excluded.
So two different types of requirements are contained in the concept of
ridgeline
as follows.
−
(1) The state of the spatial distribution of density values in the neighborhood
of each voxel is ridge-like. We call such a point a
ridge voxel
.
(2) Ridge voxels are arranged linearly.
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