Image Processing Reference
In-Depth Information
Table 3.4.
The classification of local shapes in a 3D curved surface: (
a
) Classifica-
tion by principal curvatures
k
1
and
k
2
;(
b
) classification by Gaussian curvature
K
and mean curvature
H
.
(
a
)
k
2
<
k
2
=
k
2
>
0
0
0
k
1
<
0
peak
ridge line
saddle
k
1
=
0
ridge line
planar
valley line
k
1
>
saddle
valley line
hollow
0
(
b
)
K>
0
K<
0
K
=
0
(elliptic)
(saddle like)
H<
0
peak
ridge line saddle (ridge-line like)
H
=
0
planar
minimal surface
H>
0
hollow valley line saddle (valley-line like)
(1) Stop if a given terminating rule is satisfied. Otherwise, select candidate
of a voxel or a set of voxels
r
k
(test) to be added to
R
k
according to the
procedure given beforehand. Stop if a candidate voxel set is not found.
(2) Calculate features of
r
k
(test) and test whether they satisfy the criteria
for expansion (or merging).
(3) Replace
R
k
by
R
k
∪
r
k
(test) if
r
k
(test) meets the criteria.
k
←
k
+
1
,and
go to (1). Otherwise stop.
(4) If there exist more than one candidate sets
r
k
(test) in (1), execute (1)
∼
(3) for all of them. If more than one
R
k
exists when the whole of the
procedure starts, apply (1)
∼
(3) for all of them.
The most important steps of the algorithm are the criteria for expansion
in (2) and selection of the candidate set in (1). Both of them determine the
performance of the algorithm. Examples that used (2) are many of the algo-
rithms:
(a) A set of voxels with properties similar to those in regions already ex-
tracted.
(b) A set of voxels neighboring to voxels extracted past or connected to them
in the predetermined way.
Voxels of density values within a suitable range around the average voxel
density previously extracted, that are 26-adjacent to regions extracted in the
past, are examples of the simplest criteria.
The expansion process may be executed either sequentially or in parallel.
A candidate may be tested and merged as soon as it is detected. In the other
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