Biomedical Engineering Reference
In-Depth Information
SSD, NCC, MI, and NGF discussed in Section 7.4.1.2 are suitable for general
intensity-based validation (see Denitions 5{8). In Section 7.4.2 some addi-
tional validation criteria are introduced with E
MAG
, E
O
, and E
deg
to measure
deviations in magnitude and orientation of vector fields.
To supplement the intensity-based criteria the relative error is defined. It
measures the distance of two images I and R relative to the norm of the
reference image R.
Definition 12 (RE) For an image I and a reference image R the relative
error is defined as
Z
(I(x) R(x))
2
R(x)
2
RE(I;R) :=
dx :
(7.36)
The relative error (RE) is closely related to the SSD measure. The differ-
ence of RE compared to SSD is that it is normalized by the intensity of R.
Hence, dierently scaled images have the same relative error: RE(I;R) =
RE(
R), 2R
+
. The relative error is minimal for RE = 0.
In some cases it is interesting to compare the relative similarity of two im-
ages before and after processing. This is expressed by the following alternative
definition of the relative error:
·
I;
·
Definition 13 (RE
alt
) For an image I, a reference image R and the original
version I
o
of I before processing the alternative relative error is defined as (if
I
o
and R are not equal)
Z
(I(x) R(x))
2
(I
o
(x) R(x))
2
dx :
RE
alt
(I;I
o
;R) :=
(7.37)
If the similarity of I and R is comparable to the similarity of I
o
and R (before
processing), RE
alt
is about 1. The higher the improvement of the similarity
the closer RE
alt
gets to 0.
In Section 7.2 it is stated that noise is omnipresent in medical imaging. In
some cases it is necessary to quantify the noise level of an image. A noise level
comparison before and after processing (e.g., filtering) is also often useful.
For quantifying the noise level the signal to noise ratio (SNR) is a possible
choice. As the noiseless image is generally unknown the SNR can be estimated
according to the following definition:
Definition 14 (SNR) For a non-constant image I the signal to noise ratio
(SNR) can be dened as
R
I(x)dx
1
jj
SNR(I) :=
(I)
(I)
q
1
jj
=
;
(7.38)
R
(I(x) (I))
2
dx
where is the expected value and the standard deviation.
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