Image Processing Reference
In-Depth Information
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Fig. 5.3.
Voxel arrangements to be deleted in surface thinning (3D simplex).
5.4.2 Requirements of thinning
We will summarize the requirements of surface/axis thinning. An output of
these algorithms should also have these features.
(
Requirement
(
R
)
1
) Topological features of an input figure should be pre-
served in an output figure.
(
R2
) A resultant figure should be a surface figure of the unit thickness for
surface thinning or a line figure of the unit thickness for axis thinning
except for an exceptional local shape such as a cross point.
(
R3
) A resultant figure should be located on the center surface/center line of
an input figure.
(
R4
) A resultant figure does not degenerate excessively.
(
R5
) The shape of an output figure should be a reasonable one in respect to
crossing parts of an input figure.
(
R6
) The result is not affected by the rotation of an input figure. In other
words, a result of thinning of a rotated figure is not too different from the
rotation by the same angle after thinning an original input figure.
Several of these requirements are not always compatible with each other.
Theoretically strict statements cannot be given for all of them except
R1
.
Therefore, the performance of a thinning algorithm cannot help being evalu-
ated intuitively and subjectively to some extent by a human observer.
R1
and
R2
are more essential than others, and the rest are guidelines.
5.4.3 Realization - the sequential type
Let us explain here how those requirements are realized in a concrete algo-
rithm.
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