Image Processing Reference
In-Depth Information
The normal curvature
k
(
A
) varies as a function of the direction A when
we rotate the tangential line A around the normal of the surface
S
2
at a point
P
. Then the maximum
k
1
and the minimum
k
2
of
k
(
A
) and other values
calculated from them are called as follows. They are regarded as features of
local shape of the surface.
k
1
,k
2
; principal curvature
(3.50)
H
=(
k
1
+
k
2
)
/
2
; mean curvature
(3.51)
k
2
; total curvature or Gauss curvature (3.52)
Directions of tangents corresponding to
k
1
and
k
2
; principal directions (3.53)
K
=
k
1
ยท
The outline of local shapes on a surface of a 2D image (or a 3D surface) is
illustrated in Fig. 3.8 and Table 3.4.
3.5 Region growing (region merging)
3.5.1 Outline
A procedure called
region growing
(
region merging
) or more generally most
region-based segmentation procedures can be applied to a 3D image directly.
We will only explain them briefly.
Region growing
is a procedure starting from suitably selected set of voxels
(initial regions, initial voxels) and expands them sequentially by adding adja-
cent voxels or regions while incorporating predetermined conditions. The core
of the region-growing algorithm consists of the following three parts:
(i) Selection of starting voxels (or regions).
(ii) Expansion (growing, merging) of regions .
(iii) Testing of terminating condition.
There are two typical procedures for the third step: a fixed rule (a
procedure-
independent rule
)anda
procedure-dependent rule
. For example, a maximum
voxel number for a region may be given beforehand (procedure-independent
rule). Alternatively, the procedure may be terminated unless a new voxel
involved in a merging condition is found (a procedure-dependent rule).
3.5.2 Region expansion
The kernel of the algorithm is the iterative execution of the second and the
third step of the above procedure summarized as follows:
Algorithm 3.1 (Region growing).
Iterate the following for
k
=
1
,
2
,...
.
Denote by
R
k
the region that has been detected when the
k
-th iteration of
processing starts. For
k
=
1
,R
1
has been assumed to be given by the other
procedure.
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