Graphics Reference
In-Depth Information
Note that the underlying structure is completely recovered and therefore near-
optimalestimates oftheprobabilities andintensities areobtained forbothourbinary
and our Poisson image.
Example: Denoising of Digital Color Images
8.4.3
In digital color images, the information in each pixel consists of a vector of three
values. Each value is an intensity in one channel of a three-dimensional color space,
usually the RGB space. Additionally, each pixel may carry some transparency in-
formation. Ideally the image is recorded in RAW format (minimally processed data
from the image sensor of a digital camera, see Wikipedia RAW (
)). and then
transformed to TIFF to avoid artifacts caused by lossy image compression and dis-
cretization to a low number of color values.
Iftheimagewasrecordedunderbadlightconditions, usingahighsensorsensitiv-
ity, such images can carry substantial noise. his noise is usually spatially correlated
(i.e., colored). We also observe a correlation between the noise components in the
three RGB channels. RGB is an additive color model in which red, green and blue
light are combined in various ways to reproduce other colors; see Wikipedia RGB
(
) or Gonzales and Woods (
).
An appropriate model for describing such a situation is given by
Y
i
h
,i
v
θ
X
i
ε
i
h
,i
v
,
(
.
)
=
(
)+
where the components of X
i
=(
i
h
, i
v
)
are the horizontal and vertical image coordi-
and ε
i
h
,i
v
take values in R
. he errors follow a distribution with
nates. Y
i
h
,i
v
, θ
(
X
i
)
Σand
E
ε
i
h
,i
v
ε
i
h
+
,i
v
E
ε
i
h
,i
v
ε
i
h
,i
v
+
E
ε
i
h
,i
v
=
,Var ε
i
h
,i
v
=
=
=
ρ for each color channel
c. he covariance matrix Σmay vary with the value of θ
i
h
,i
v
.
he algorithm from Sect.
.
.
can be applied in this situation with a statistical
penalty
(
k
−)
i
λ
N
(
k
)
ij
θ
(
k
−)
i
θ
(
k
−)
j
θ
(
k
−)
i
θ
(
k
−)
j
−
s
=
−
Σ
−
(
.
)
he model can oten be simplified by transforming the image to a suitable color
space. We observe that a transformation to the YUV space decorrelates the noise be-
tween channels, so that a diagonal form of Σseems appropriate under such a trans-
formation. he YUV model defines a color space in terms of one luminance and
two chrominance components, see Wikipedia YUV (
) or Gonzales and Woods
(
).Inthiscase,errorvariancecanbeestimatedseparatelyinthethreecolorchan-
nels, accounting for the spatial correlation.
Figures
.
and
.
provide an example. he upper let image was obtained by
deteriorating a digital image showing the Concert Hall at the Gendarmenmarkt in
Berlin. he image resolution is
pixels.
he original image was transformed from RGB into YUV space. In YUV space,
the values in the three channels are scaled to fall into the range
(
,
)
,
(−
.
,
.
)
and
(−
.
,
.
)
, respectively. In each YUV channel colored noise with ρ
=
.
and
