Digital Signal Processing Reference
In-Depth Information
TABLE 3.3
Color Image Denoising Results for Balloon Image Corrupted
by Component Independent and Correlated Gaussian Noise
Method
CMSE
NMSE
CMAE
Independent
Noisy
1760
0.1083
24
MED
51
0.0032
5.3
MED
v
(
L
2
)
94
0.0058
7.5
MED
v
(
L
1
)
91
0.0056
7.4
VDF
91
0.0056
7.1
DDF
131
0.0081
8.7
FMED
41
0.0026
4.7
FMED
v
46
0.0029
5.1
Correlated
Noisy
1765
0.1086
24
MED
51
0.0031
5.3
MED
v
(
L
2
)
52
0.0032
5.4
MED
v
(
L
1
)
53
0.0033
5.4
VDF
73
0.0045
6.4
DDF
67
0.0041
6.1
FMED
41
0.0026
4.7
FMED
v
40 0.0025 4.7
Note:
The MED and FMED filters are applied marginally to each com-
ponent and all other methods operate directly on the multivariate data.
Bold indicates best performance.
3.3.3
Surface Smoothing
Multivariate processing is also integral to surface smoothing. The impor-
tance of this problem is growing with advances in computing power and 3D
acquisition technology as there has been increasing deployment of 3D models
in engineering, medical, and entertainment applications. These 3D models are
usually stored and rendered as surfaces represented by polygonal, primarily
triangular, meshes. It is important to note that in all stages of the 3D model
construction process noise is inevitably introduced, due, for example, to mea-
surement errors, sampling resolution limitations, algorithmic errors, etc. This
is also true for 3D medical images reconstructed from computed tomography
(CT) or magnetic resonance imaging (MRI) volumetric data. Surface smooth-
ing, or denoising, adjusts vertex positions so that the overall surface becomes
smoother while keeping mesh connectivity, or topology, unchanged. Surface
smoothing is an active area of research.
To consider the surface smoothing problem, the triangular surface rep-
resentation must first be defined. A triangular mesh is characterized by its
topology and geometry. The topology is specified by a set of vertices
V
,aset
of edges
E
, and a set of faces or triangles
F
. The symbols
V
,
E
, and
F
are also
used to denote the cardinality of corresponding sets. An individual vertex is
denoted as
v
={
i
}
, while
e
={
i, j
}
and
f
={
i, j, k
}
are used to denote an
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