Ahmad Al

Determination and enhancement of X-Ray image quality using
Shannon’s information capacity metric
Ahmad Al-Nassre
University of Maastricht
September 6, 2009
Abstract
With the technological progress digital X-Ray
facilities have been established in the past few
years. These facilities have to be calibrated
and attended manually by specialists for the
most part. The challenge is to assist those
specialists among other things in calibrating
X-Ray scanners and provide them with rationalised and automated tools and methods. By
adjusting and improving of the here presented
quality metric, the Doctor’s demands can be
more efficiently taken into account.
In this thesis the focus is made on quantifying
X-Ray image quality using the Shannon’s
information capacity metric.
Keywords: Image quality assessment, XRay imaging, Shannon capacity
1
INTRODUCTION
The storage plate technique was the first in the projection radiography procedure field. There has been an
additional digital system besides the computed radiography (CR) with the flatdetector radiography for a few
years now. Whereas a cassette with a specialized storage plate is needed for the storage plate technique, the
flatdetector technique directly transmits the information
to a computer system. Digital systems offer a seperated
optimization for the individual components of the image
generation: image data acquisition, image data processing, image rendition, image archiving and image transmission.
Irrespectively of the applied digital system, the computer
system is fed with image raw data, which is now ready
for image processing. The aim of image processing is to
adjust the contrast and the luminance and to emphasize
particular details in the object. This can improve and
maintain the image quality. However an improper use
of image processing tools can decrease the image quality
and lead to a false diagnosis. There is no direct correla-
tion between the radiation dosis and the optical density.
Hence the exposure latitude is significantly larger in comparison to the film-foil-combination. Therefore over- and
underexposure can be extensively settled. Depending on
the exposure, noise increase can restrict the image quality.
The adoption of digital radiography in the medicine,
poses the question of image quality and in its resulting
diagnosis raliability compared to the conventinal filmfoil-system. Image postprocessing tools offer the facility
to adjust the luminance, contrast and sharpness. Furthermore certain structures can be emphazised in dependence of specific problems. But IP also has some
drawbacks, because it implicates the risk of suppressing
diagnostical relevant structures, which could lead to a
misinterpretation.
These developments shows the prime importance of an
objective image quality assessment for X-Ray imaging.
This thesis evaluated an information theoretic metric
that calculates the Information Capacity (IC) proposed
by Papalazarou [2]. Here the quality of an image is described in terms of its IC. Shannon has laid the foundation for this capacity in his approach about noisy channel
coding [7]. Since the noise in X-Ray images is signal dependent and non-additive the X-Ray image signal has to
be adjusted first to fit the Shannon theorem.
This approach is structured as follows : Section two will
give an introduction into the Determination criteria of
digital images. In Section three the full-reference objective image quality metric will be illuminated. The distortions used in the experiments are described in Section
four. Shannon’s entropy is explicitly presented in chapter five. The experiments performed in this research are
described in Section six, before finally the results are
specified in Section seven.
2
Determination criteria of
digital images
Both analog and digital images have the same quality
distinguishing properties, namely noise, sharpness,
Ahmad Al-Nassre
University of Maastricht
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
contrast and artifacts. However those quality varieties
have different reasons. In this approach the quality
of digital X-Ray images is of particular importance.
Therefore the focus is put on the properties of digital
images, whereby their quality is influenced and the way
it is affected.
2.1
pretentions of the beholder. Sharpness for one may be
inacceptable for the professional beholder’s pretentions.
Thus image sharpness is, at least by observing an image,
a subjective quality criterion since in particular the observed images finest observable structure and sharpness
is up to the individual beholder’s acuity as well.
Noise
Figure 2: sharpness
Figure 1: Example of quality properties in a signal
With the appearence of modern techniques, digital
imaging has been widely spread. In these acquired digital images different types of noise may occur, like photon noise, thermal noise, on-chip electronical noise, KTC
noise, amplifier noise and quantization noise. In this
approach digital X-Ray images are of importance and
photon noise mostly contributes of the noise which ammounts about 70 - 80%. The remaining 20-30% occur
due to distortions created by the X-Ray equipment and
measuring tools. Although the later mentioned proportion is humble and may have less influence on the X-Ray
image compared to the other proportion, it is of prime
importance for the patience’s weal to improve these
equipments and measuring tools. Because by enhancing image processing tools it is possible to reduce the
amount of X-Ray radiation or contrast medium, which
patients are exposed to.
2.2
Sharpness
Sharp images are characterised by a high contrast between individual objects (areas, contours) in an image.
But when is it possible to say that a certain image is
sharp or unsharp? On the face of it, this question seems
to be redundant, because an image can immediately be
judged as sharp or not by the first view.
In this regard, first problems occur by enlarging the image. An image could prove to be keenly unsharp by
enlarging it a certain factor. The question if the image as such is sharp or not is up to the preferences and
2.3
Contrast
The contrast characterises the difference between the
pale and the dark areas in a visual representation. It is a
distinction criteria of an images pale process or between
two pixels. Furthermore the contrast range describes
luminosity discrepancy between the palest and darkest
pixel of an image.
2.4
Artifacts
In the domain of computer graphics artifacts are described as a visible negative representation of a rendered
image which is not caused by the original input data.
There are several reasons for such inaccurate representations. Visual artificats may occur in image compression
(JPEG) or in video compression (MPEG) due to missing
information. These for the human eye hardly recognisable artifacts are unavoidable in compression, but the
improved image processing algorithms try to minimize
them. Grafical artifacts are also caused by screening an
object into the two-dimensional display resolution. This
disturbance is minimized by Antialiasing.
In X-Ray images artificats may also occur caused among
other things by X-Ray scattering. The figure 3 exemplifies those artifacts marked by the white arrow.
3
SHANNON’S
INFORMATION CAPACITY
METRIC
There are several Objective Image Quality metrics
(OIQ) which can be mainly classified into three cate-
(v. September 6, 2009, p.2)
Ahmad Al-Nassre
University of Maastricht
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
Figure 3: Artifact in the interpetrous region (white arrow)
gories: no-reference, reduced-reference and full-reference
metrics. Shannon’s information capacty metric belongs
to neither of the three categories. It only exhibits some
similitudes to the full-reference model.The full-reference
model requires a perfect reference image to accurately
obtain the quality of images. In former researches
the full-reference IQ metric was applied to determine
the qualitiys decline of compressed images. Therefore
the compressed image was compared to the original
image and a quality score was evaluated. It is nearly
impossible to get a perfect reference X-Ray image
hands-on. The full-reference model has been improved
and adjusted in further researches to get an approximated perfect reference image. To obtain this image,
a certain amount of X-Ray images of the same object
in the same situation has to be made. Subsequently,
the average of the X-Ray image set which serves as a
reference image is taken in this metric. On the other
hand, in Shannon’s information capacity metric this
averaged image is regarded as a noiseless version of the
objective instead of a reference image. In figure 4 the
process is simplifiedly illustrated.
The noiseless version mentioned above is subtracted
from the input image to seperate the noise from the
input signal. Accordingly a fourrier transformation of
the signal and the noise of the image is done in order
to subsequently figure out the Information Capacity.
Figure 5 shows this approach apparitional.
Figure 4: Information Capacity Model
Image Set
(1...M) (m >> 1)
Average
Input Image
"I"
Noiseless Image
"S"
Make Noise Independent
mapping function
A(x) = ∫(1/σ(x) ) dx
Noise Image
A(I) - A(S) = "N"
Noise
Power Spectrum
math In the context of research into communication
through telephone wires, Shannon (1948) defined the
first historical metric of information - the Shannon entropy:
H(X) = −
n
X
i=1
p(xi ) ∗ log(p(xi ).
(1)
Signal
Power Spectrum
Calculate
Information Capacity
Figure 5: Scheme Information Capacity
(v. September 6, 2009, p.3)
Ahmad Al-Nassre
University of Maastricht
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
The random variable X can be expressed in terms of the
underlying distribution p(xi ), while n is the number of
states that the (discrete) signal can assume. The information term of Shannon does not evaluate the semantical content or the meaning of a message, but its unpredictability (contingency, disarrangement). The more information a message has, the more insecure one is about
the syntactical content. The Shannon entropy is the classical measure for information.The name ’Entropy’ goes
back to the analogue meaning of the formula in the thermodynamics.
Mutual information (MI), sometimes also called transinformation, is a quantity of the information theory, which
indicates the statistical correlation of two random variables. Here it indicates the correlation between the distribution X and an output Y .
M I(X; Y ) = H(X) + H(Y ) − H(X; Y ) =
X
p(x, y)
H(Y ) − H(Y | X) =
p(x, y) log2
p(x) ∗ p(y)
4
Distortions
Since it was impossible to inverse the image processing
tools integrated in the X-Ray image facility, for instance
noise reduction or deblurring techniques, artificial distortions were added. Therefore the Information Capacity
Model was extended with a distortion module, shown in
figure 6. This distortion module consists of noise addi-
(2)
X,Y
For this approach another aspect of the Shannon theory
is of quite importance and will be considered in respect
of coding. The channel capacity is equal to the already
introduced mutual information, maximized over all input distributions. For the case of a one-dimensional,
zero-mean signal of bandwidth B, which is corrupted by
independent additive white Gaussian noise, the maximum information capacity of the channel CShannon can
be written in the simple form [1] :
CShannon = max(H(Y )−H(Y | X) = B ∗log2 (1+(
S 2
) )
N
(3)
The Shannon-theorem deals with the relation between
the available bandwidth, the Signal to Noise ratio and
the outcome of this is the maximum data transmission
rate.
In this approach a generalization of the equation above
for two-dimensional signals, where the additive noise is
not white and both the signal and noise are zero-mean
and bandwidth-limited, is given in equation 4:
fN y
fN x Z
Z
C0 =
log2 (1 +
P (fx , fy )
)dfx dfy
N (fx , fy )
(4)
−fN x −fN y
Where C0 is the Channel capacity in bits per second,
P (fx , fy ) and N (fx , fy ) are the signal and noise power
spectra, f is the frequency in Hz and the integration is
taken up the Nyquist frequency.
Figure 6: Extended Information Capacity Model
tion and blur filters which were seperately added to the
input images.
Gaussian noise is supposed to simulate the photon noise
in X-Ray images and is increasingly added to the input
images. Details of obtaining the experimental X-Ray image set will be explained in Chapter 5. Figure 7 shows
an X-Ray image before and after adding gaussian noise.
An odd gaussian blurring filter, illustrated in figure 8,
is apllied on the input image by increasing the window
size to intensify the blurring. An extension is shown in
figure 9.
5
EXPERIMENTS
The experiments were all performed on an iMac 24” with
a 2.93 GHz Intel Core 2 Duo processor and 4 GB DDR3
RAM under Mac OS X using Matlab 7.4 (R2007a).
In Chapter 3 it was already mentioned that the Information Capacity metric only exhibits some similitudes
to the full-reference model. Its experimental design differs in various aspects, which will be illuminated in the
following part. Since there were some technical difficulties to accomplish a similar design of experiment performed by C. Papalazarou in her research [1], an alternative experimental setup obtaining the required X-Ray
set was performed. Different X-Ray images were made
using a Provatec X-Ray facility. For this approach it was
assumed that these images are noiseless and they were
(v. September 6, 2009, p.4)
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
Ahmad Al-Nassre
University of Maastricht
•
•
Figure 9: X-Ray of knee before and after gaussian blur
addition
•
•
•
Figure
7: X-Ray of shoulder before and after gaussian
noise addition
Figure 8: Odd blurring filter with a window size of 10
and a sigma of 5
seen as the signal in the original image.
The objective of these experiments is to figure out how
Shannon’s IC responds to miscellaneous types of distortions. In this research the distortions gaussian noise and
blurring are of particular interest.
The gaussian noise was added increasingly in one hundred steps to obtain a representative X-Ray set with the
power of hundred images. In each step the noise was
seperated by subtracting the noiseless image from the
noisy image. Accordingly a fourrier transformation of
the signal and noise image is done in order to subsequently figure out the signal to noise ratio. In the context of imaging it can be enunciated that the greater
the signal to noise ratio, the more information the image contains and hence it indicates an image of a high
quality. It can be definetly expected to lose quality by
adding noise.
In the second part of the experiments several blurring
filters with different parameter settings were applied to
the X-Ray images. Only two of them will be presented
in this approach. The Gaussian and Laplace-filter. For
the Gaussian-filter the parameters, σ i.e. the standard
deviation and the window size are important, whereas
for the Laplace filter the value of the diffusion coefficient
and the number of steps influence the blur of the image.
The Gaussian-filter was applied by increasing the window size in fifty steps, whereas the parameter sigma took
the value of half of the respective window size.
Furthermore the Laplace-filter was used with the diffusion coefficient α in a similar as aforementioned experimental setup.
For both blurring filters, in each step the noise was sper-
(v. September 6, 2009, p.5)
Ahmad Al-Nassre
University of Maastricht
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
ated by subtracting the noiseless image from the blurred
image. Accordingly a fourrier transformation of the signal and blurred image is done in order to subsequently
figure out the signal to noise ratio. In the IP, blurring
is also used as a denoising technique. Consequently it is
expected of a small quality increase.
RESULTS
By contemplating this metric the results of the experiments were in some respects surprising and unexpected.
The noise addition test yield as expected in a decrease of
the image quality score. Figure 11 shows this result numerical and figure 10 visual. The IC of the noisy image
already indicated the quality loss compared to the noiseless image, and figure 12 shows explicitly that no medical
relevant information can be determined anymore.
However, the blur addition test results are surprising and
raise some questions. In respect to the IC the blurring
tests yield an increase of the quality score of the blurred
image??. The initial improvement can be explained by
the fact that every image contains some certain type of
noise, which has been removed by blurring the image .
Actual the quality score of the blurred image should have
been drop down by increasing the intense of the blur factor. But according to the IC the opposite effect occurs.
The quality score increases continuously even at a gaussian blur windows size of 50 units. The reason for this
is that the IC determines the information content e.g.
entropy of an image. Blurring an image has the effect
of increasing the information content of it . Despite the
high quality score of the blurred image, it is impossible
to achieve any medical relevant and reliable information
out of it.
A mathematical technical motivation could be that in
Shannon’s signal to noise ratio, the noise and signal
strength are weighted differently. A possible explanation for this is, that the signal and noise strength are
averaged over the frequency bins that the fourier transform calculates. The noise reduction is felt in the entire
spectrum and the decrease will be in every frequency bin
[2].
7
Conclusion
Figure 10: Hip X-Ray before and after 3 steps of noise
addition
4
12
Shannons IC of noisy hip x−rays
x 10
11
10
9
Quality score of x−ray
6
8
7
6
5
4
In this approach an image quality metric was proposed,
the Shannon’s information capacity metric. It emerges
with some insignificant flaws as a reliable and applicable
image quality metric. In the noise experiments its performance was sufficient. On the other hand the adjustments
of the parameters of the blur filter experiments were difficult. This issue keeps a challenge in future researches.
Summing up, once the optimal parameters found it, it
obtains a substantial indicator for comparison to other
specific metrics.
3
2
0
10
20
30
40
50
60
noisy hip x−rays
70
80
90
100
Figure 11: Basic noise addition test results of Shannon’s
IC of hip X-Ray
(v. September 6, 2009, p.6)
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
Ahmad Al-Nassre
University of Maastricht
Figure 12: Knee X-Ray before and after 3 steps of noise
addition
Figure 14: Spine X-Ray before and after gaussian blurring with windows size 25
4
10
Shannons IC of noisy knee 2 x−rays
x 10
6
16
8
14
7
12
6
Quality score
Quality score of x−ray
9
5
Shannons IC of blurred Spine x−ray
x 10
10
8
4
6
3
4
2
0
10
20
30
40
50
60
noisy knee 2 x−rays
70
80
90
100
2
Figure 13: Basic noise addition test results of Shannon’s
IC of knee2 X-Ray
0
5
10
15
20
25
30
Blur filter window size
35
40
45
Figure 15: Basic blur addition test results of Shannon’s
IC of spine X-Ray
(v. September 6, 2009, p.7)
50
Ahmad Al-Nassre
University of Maastricht
Determination and enhancement of X-Ray image quality using Shannon’s information capacity metric
References
[1] Chrysi Papalazarou, Rudolph M.Snoeren,Frans M.J.
Willems, Peter H.N. de With,Han Kroon and Peter Rongen Towards a full-reference, informationtheoretic quality assessment method for X-Ray images 2008
[2] Jop Daalmans Objective Image Quality Assessment
for X-Ray imaging May 2008
[3] Blanchet, Grard, Maurice Charbit Digital signal and
image processing using Matlab
[4] Robert M. Gray and Lee D. Davisson An Introduction to Statistical Signal Processing 2003
[5] Ting-Chung Poon Partha P. Banerjee Contemporary
Optical Image Processing with MATLAB 2001
[6] Martin Werner Digitale Signalverarbeitung mit
MATLAB-Praktikum
[7] C. E. Shannon, A mathematical theory of communication, Bel l Syst. Tech. J. 27, pp. 379423, 1948.
[8] The Mathematical Theory Of Communication,
Shannon & Weaver September 1949
Figure 16: Shoulder X-Ray before and after gaussian
blurring with windows size 25
[9] Multidimensional Signal, Image, and Video Processing and Coding, John W.Woods 2006
[10] Discrete Fourier Analysis And Wavelets , S.Allen
Broughton, Kurt Bryan 2009
[11] Digital Filters Design for Signal and Image Processing, Mohamed Najim 2006
6
4.5
Shannons IC of blurred Shoulder x−ray
x 10
4
Quality score
3.5
3
2.5
2
1.5
1
0
5
10
15
20
25
30
Blur filter window size
35
40
45
50
Figure 17: Basic blur addition test results of Shannon’s
IC of shoulder X-Ray
(v. September 6, 2009, p.8)