Image Processing Reference
In-Depth Information
(1)
Ridgeline extraction
: Thinning based on the ridgeline extraction of a
curved surface of density values distributed on a 2D plane (= ridgeline
extraction of a surface in 3D space) is extended to the extraction of ridge-
lines of a curved surface in a 4D space [Enomoto75, Enomoto76, Yu90,
Fritsch94, Pai94, Arcelli92, Niblack92, Monga95, Thirion95, Hirano00].
One problem here is the complexity in the shape of a ridgeline. The form
of a ridgeline in a 3D gray-tone digital image may be dicult to define. It
therefore will be dicult also to derive an algorithm to extract it based
on heuristics. This type of idea can be applied to an arbitrary gray-tone
image with no background. On the other hand, the shape features of a
figure cannot be used in this type of method, and problems concerning
the preservation of topology cannot be dealt with.
(2)
Classification of the state of a voxel
: In the processing of a 2D image, the
state of each voxel is classified as
ridge-like
,
valley-like
, etc., according to
the relation of density values of voxels in its neighborhood. Results are
used for the extraction of a ridge line [Toriwaki75, Yokoi75]. This method
has been applied to the analysis of terrain elevation data [Haralick83,
O'Callaghan84, Johnston75, Peucker75]. However, a good quality ridgeline
cannot be extracted when using only the local pattern features of a 3D
image. This type of method cannot easily be extended to a 3D image. The
classification of local patterns includes relations in density values that have
not been discussed yet. Shape features cannot successfully be treated with
this type of the method. In the case of a continuous image, the problem
is treated using differential geometry [Enomoto75, Enomoto76].
(3)
Binarization of density values in a local area
: Methods of thinning a bi-
nary image may be extended to a 3D gray-tone image by binarizing local
subpatterns of a gray-tone image (with suitable thresholds and while ap-
plying methods suitable for 3D binary images). For example, a method in
[Toriwaki75, Yokoi75] can easily be extended to a 3D image. However, the
quality of an obtained result is not always good because degeneration is
likely to occur. Frequently parts of an input image remain without being
converted to a linear figure.
(4)
Use of GWDT
: Methods described in (1), (2), or (3) above may be per-
formed after GWDT has been applied to an input image. Information con-
cerning the minimal paths obtained by performing GWDT is also available
for thinning [Naruse77a, Naruse77b]. By the use of GWDT we can sup-
press random noise in an input image, and we are able to utilize some of
shape features. In combining GWDT with (1)
(3) above, shortcomings
are also inherited. The concept of a minimal path cannot be applied in
the Euclidean DT. Therefore, the use of GWDT is affected significantly
by the rotation of an input image. The topology of an input figure is not
always preserved in the use of the minimal path.
(5)
Modification of a result by methods of thinning
: After binarizing an input
image by an approximate threshold, any method of thinning a binary im-
age can be applied to obtain an approximated result of thinning. Then
∼
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