Image Processing Reference
In-Depth Information
Scan an output image with the raster scan (Fig. 2.13), and perform row by
row the following restoration process.
(1) Substitute
0
to a work variable
N
.
(2) If the value of a voxel changes to
1
from
1
, then set the value of
N
as
1
, and substitute the value
1
to subsequent voxels on the same row in turn.
If the voxel of the value
−
1
is met again on the same row, reset the value of
N
as
0
, and stop substitution of the value
1
after that.
(3) Search the same row to detect change of the value from
−
−
1
to
1
,and
repeat the same procedure.
(4) If the end of the row is reached, go to the next row and go to (1). If the
whole of an output image has been scanned, go to (5).
(5) Scan the output image again and erase all of
−
1
by replacing with
0
.
Remark 5.20.
Border surface following for a 3D image began to be studied
actively in earlier days (1980s) in the history of 3D image processing chiefly
by G. Hermam and his colleagues, and many papers have been published
[Artzy85, Herman98]. Details are known from topics and papers referred to in
[Herman98, Kong85, Kong89, Toriwaki04]. That research is characterized, in
particular, by the ideas that applications to simulate surgical operations were
clearly intended, as well as authors' research [Artzy85, Herman78]. It should
be noted that memory limitation was severe in computers in those days.
One example of applications in those days was fast processing of a 3D CT
image of the skull. The border surface following algorithm was different from
the one presented above and was studied in detail both theoretically and ex-
perimentally. For example, the basic idea is to trace the surface of a 3D figure
consisting of cubes corresponding to voxels, that is, tracing the surface of a
continuous figure defined in Def. 4.5, while in the above algorithm, border vox-
els themselves are followed. According to the former idea, the border surface
becomes a continuous figure and is treated in a clear-cut way theoretically,
although the number of voxels becomes much larger than the trace of voxel
themselves.
Nowadays, memory has become much cheaper and a device with a much
larger memory capacity is available even in portable computers, and the size
of a 3D image data to be processed has also become much larger. A 3D CT
image is becoming more precise and is required to be processed as a gray-tone
image in many of applications. Thus the significance of border following is
now changing.
5.7 Knot and link
5.7.1 Outline
One of the most important features specific to a 3D image is
knot
and
link
in a line figure (Fig. 5.19). In mathematics, a large amount of research work
has been performed concerning the knot and the link. Almost all of the work
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