Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'16 |
93
Window Width Value Estimation Technique for CT
Brain Images Using Average of Median of Statistical
Central Moments
C. S. Ee1, K. S. Sim1, N. Koh1
1
Faculty of Engineering and Technology, Multimedia University, Jalan Ayer Keroh Lama, 75450,
Melaka, Malaysia
Abstract – For stroke detection, computed tomography (CT)
scan is always the initial choice for imaging the damages or
infraction on the brain. However, CT is commonly poor in
infarction diagnosis due possible problems of the proper
window settings. There is similar default window setting for
every CT brain images but the default setting is unable to fully
enhance the contrast of infarction of the brain images. Thus,
performance of infarction diagnosis in CT brain images is
poorer than other medical image modalities. Therefore, this
paper introduces a novel estimation method with fixed value of
window center (WC) to estimate the window width value (WW)
for selected CT brain images, by calculating average of
median of statistical central moments. This method requires
only 101 WW values to produce estimated value with
sensitivity of 0.05HU. The focus of the proposed approach is
to improve the efficiency brain infarction diagnosis for
radiologists.
Keywords: Window Width, Estimation Technique, CT Brain
Image, Statistical Central Moments, Median, Average.
1
Introduction
As stated by the World Health Organization (WHO), 15
million people suffered stroke globally every year. From this
statistic, 5 million people die while another 5 million people
suffered permanent disability. Stroke is a cerebrovascular
accident when the blood supply to an area of the brain is cut
off [1]. In order to support the stroke diagnosis, two common
image modalities have been used namely the computed
thermography (CT) scan and magnetic resonance imaging
(MRI). CT scan is preferable compared to MRI due to its
wider availability, inexpensive and ease of access [2].
Examination of brain images have been a vital task and have
received much attention in the literature. Past or present,
analysis of brain stroke lesions is difficult especially for
inexperienced radiologists or doctors. In CT images, the
stroke lesions appear with darker or hypodense region.
In CT imaging, the images are in Digital Imaging and
Communications in Medicine (DICOM) format. The DICOM
image is in a 16 bit format where 12-bits are used for storing
the image without any contrast enhancement or image preprocessing and 4-bits are used to store the textual data [3].
During the examination of the CT brain images, the first thing
that the radiologist does is to set the correct window settings
of the CT images as different window settings produce
different tissue information including the brain lesions. The
window settings consist of the window width and window
center level plays an important role for stroke lesion detection
and diagnosis accuracy. Window width is defined as the
display range while window center is defined as the mid
value of an image. Although, there are common window
setting which consists of window width of 80 HU and
window center of 40 HU proposed and used, the output brain
images may still have low contrast and the lesion area might
not appear more obviously. In image processing and
computing system, HU values for each pixels of selected CT
brain image is converted as pixel value before processed, and
respective equation is shown in equation (1) [4,5].
ܲܺ ൌ
ு௎ିோூ
ோௌ
(1)
where PX is the pixel value; HU is the Hounsfield unit, HU;
RI is the rescale intercept; and RS is rescale slope. Both RI
and RS can be found in the textual information of CT brain
image.
There were many window settings proposes in the past
namely window width of 40 HU and window center of 30
HU; window width of 3 HU and window center of 25 HU [6].
Gadda (2002), proposed with window width of 50 HU and
window center of 45 HU to 50 HU for good contrast [7]. In
2014, researchers proposed window setting with window
center of 40 HU and window width of 50 HU to 60 HU [8].
Although these parameters can show some improvement on
the contrast for diagnosis of stroke cases, it is still image
dependent and need to be manually tuned. Thus, in this paper
a new estimation on window width is proposed. This paper
aims to improve prior method in [8], and proposes a new
estimation technique to estimate window width value (WW)
automatically based on the statistical central moments.
2
Problem Statements
The default setting of window setting stored in textual
information of CT brain images for visualization is set with
WC=40 HU and WW=80 HU. However, this setting is poor in
evaluation of infarction, and not suitable for every CT brain
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images due to the dynamic differences in the terms of size
and volume of each brain.
Another problem is that brain is scanned with CT device
into many slices, the estimated window setting for each slice
should be different. Using default window setting to these
slices may cause misinterpretation in infarction evaluation.
Besides that, it is not realistic and time consuming to suggest
that the expert radiologists to tune the value of window
settings manually, based on their experience and experiments.
Furthermore, the prior methods do not provide any
estimation method for window setting for CT brain images.
They are required to be set up manually and the values of
window setting are within a narrow range. These methods
perform well only in certain infarction cases and brain slices.
Therefore the focus of this paper is to find estimation
value for window width (WW), while value of WC is fixed as
40HU, similar with default WC. 40HU determines the central
region of brain soft tissue, which is also the region of interest
(ROI) in the paper.
3
Solutions
In this section, estimation method for window width
(WW) using average of median of statistical moments is
proposed and discussed.
3.1
Flow Chart of Proposed Method
In this subsection, a flow chart of the proposed method
is shown in Figure 1. The proposed method contains three
main steps, starting with calculating values of statistical
central moments of input image (‫ܫ‬௜௡ ) and plotting the graph of
statistical central moments versus WW. Next step is to find
the average median value of statistical central moments from
generated graphs, and then estimate value of WW. The last
step is to implement the estimated WW to input image (‫ܫ‬௜௡ ) to
generate output image (‫ܫ‬௢௨௧ ).
Figure 1: Flow chart of proposed method
3.2
Step 1: Calculate and Plot All Statistical
Central Moments for Input Image (Iin).
The first step shows the process of generating 4 graphs
of statistical central moments versus window width (WW).
The process starts to determine the setting of the range of
samples for WW. In this paper, WW is set to have p range,
from 0 HU to 100 HU, with increment rate of 1 HU.
Therefore, there are 101 samples as the x-axis for all 4 graphs
and respective formula is shown in equation (2).
ǡ‫ ݌‬ൌ Ͳ
Ͳ‫ܷܪ‬
ܹܹሺ‫݌‬ሻ ൌ ൜
ܹܹሺ‫ ݌‬െ ͳሻ ൅ ͳ‫ ܷܪ‬ǡ Ͳ ൏ ‫ ݌‬൑ ͳͲͲ
(2)
Given that selected CT brain image is the input image
(‫ܫ‬௜௡ ), and it is converted into 101 greyscale images with
vector of WW, using equation (3).
Ͳ
ǡ ‫ܫ‬௜௡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൏ ݃݉݅݊ሺ‫݌‬ሻ
ൈ ʹͷͷ ǡ ݃݉݅݊ሺ‫݌‬ሻ ൑ ‫ܫ‬௜௡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൑ ݃݉ܽ‫ݔ‬ሺ‫݌‬ሻ
ௐௐሺ௣ሻ
ǡ ‫ܫ‬௜௡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ ൐ ݃݉ܽ‫ݔ‬ሺ‫݌‬ሻ
ʹͷͷ
ூ೔೙ ሺ௫ǡ௬ሻି௚௠௜௡ሺ௣ሻ
݃ሺ‫݌‬ሻ௫ǡ௬ ൌ ቐ
(3)
where ‫ܫ‬௜௡ ሺ‫ݔ‬ǡ ‫ݕ‬ሻ is pixel value of input image (‫ܫ‬௜௡ ) at location
(x,y); ܹܹሺ‫݌‬ሻ is the pth WW value in vector WW; ݃ሺ‫݌‬ሻ is
the greyscale image after windowing with ܹܹሺ‫݌‬ሻ; ݃݉ܽ‫ݔ‬ሺ‫݌‬ሻ
is maximum window value in HU unit of ܹܹሺ‫݌‬ሻ and
illustrated in equation (4); ݃݉݅݊ሺ‫݌‬ሻ is the minimum window
value in HU unit of ܹܹሺ‫݌‬ሻ and equation (5) illustrates
respective formula.
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Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'16 |
݃݉ܽ‫ݔ‬ሺ‫݌‬ሻ ൌ ܹ‫ ܥ‬൅
݃݉݅݊ሺ‫݌‬ሻ ൌ ܹ‫ ܥ‬െ
௪௪ሺ௣ሻ
95
(4)
ଶ
௪௪ሺ௣ሻ
(5)
ଶ
The following step is to calculate the values of statistical
central moments of all 101 generated greyscale images
(݃ሺ‫݌‬ሻ). There are 4 elements of statistical central moments.
These elements include mean, variance, skewness and
kurtosis. Table 1 shows the basic description of these
elements, and respective basic equations can be found in [8]
for more information.
(a)
Table 1: Summary of Statistical Central Moments
Statistical
Central
Moments
1st Moment
Other
Definition
Description
Mean
2nd Moment
Variance
3rd Moment
4th Moment
Skewness
Kurtosis
Measures Expected
Value
Measures Spread
Dispersion
Measures Asymmetry
Measures Peakedness
(b)
In order to implement these statistical moments with
image ݃ሺ‫݌‬ሻ, equations formulated in [8] are edited and shown
in equations (6-9).
ߤ௚ ሺ‫݌‬ሻ ൌ
ߪ݃ ʹ ሺ‫݌‬ሻ ൌ ߛ݃ ሺ‫݌‬ሻ ൌ
ͳ
ܺൈܻ
ͳ
ܺൈܻ
‫ ݃ݐݎݑܭ‬ሺ‫݌‬ሻ ൌ
ଵ
௑ൈ௒
σ଴ஸ௫ஸ௑ିଵ ݃ሺ‫݌‬ሻ௫ǡ௬
(6)
଴ஸ௬ஸ௒ିଵ
σͲ൑‫ݔ‬൑ܺെͳ ቂ݃ሺ‫݌‬ሻ‫ݔ‬ǡ‫ ݕ‬െ ߤ݃ ሺ‫݌‬ሻቃ
ʹ
(7)
Ͳ൑‫ݕ‬൑ܻെͳ
(c)
σͲ൑‫ݔ‬൑ܺെͳ ቂ݃ሺ‫݌‬ሻ‫ݔ‬ǡ‫ ݕ‬െ ߤ݃ ሺ‫݌‬ሻቃ
͵
(8)
Ͳ൑‫ݕ‬൑ܻെͳ
ͳ
ܺൈܻ
σͲ൑‫ݔ‬൑ܺെͳ ቂ݃ሺ‫݌‬ሻ‫ݔ‬ǡ‫ ݕ‬െ ߤ݃ ሺ‫݌‬ሻቃ
Ͷ
(9)
Ͳ൑‫ݕ‬൑ܻെͳ
Where ݃ሺ‫݌‬ሻ௫ǡ௬ is the pixel value of image ݃ሺ‫݌‬ሻ at position of
(x,y); ܺ is total number of rows of image ݃ሺ‫݌‬ሻ; ܻ is the total
number of columns of image ݃ሺ‫݌‬ሻ; ߤ௚ ሺ‫݌‬ሻ is the value of
mean of image ݃ሺ‫݌‬ሻ; ߪ௚ ଶ ሺ‫݌‬ሻ is the variance value of image
݃ሺ‫݌‬ሻ; ߛ௚ ሺ‫݌‬ሻ is the skewness value of image ݃ሺ‫݌‬ሻ; ‫ݐݎݑܭ‬௚ ሺ‫݌‬ሻ
is the kurtosis value of image ݃ሺ‫݌‬ሻ.
Then, equations (6-9) are implemented to image ݃ሺ‫݌‬ሻ to
calculate values of vector of mean ( ߤ௚ ), variance ( ߪ௚ ଶ ),
skewness ( ߛ௚ ), and kurtosis ( ‫ݐݎݑܭ‬௚ ). After that, graph of
these vectors versus WW are plotted, and shown in Figure 2.
In total, each statistical central moment produces a vector
with the range of p, which has 101 values.
(d)
Figure 2: Graphs of Statistical Central Moments vs Window
Width, WW (HU): (a) Mean (ߤ௚ ), (b) Variance (ߪ݃ ʹ ), (c)
Skewness (ߛ݃ ), (d) Kurtosis (‫) ݃ݐݎݑܭ‬.
3.3
Step 2: Window Width Estimation Using
Average Median of Statistical Central
Moments.
Following step is to estimate window width value, by
calculating the average median of vector of statistical central
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moments (mean ( ߤ௚ ), variance (ߪ௚ ଶ ), skewness ( ߛ௚ ), and
kurtosis ( ‫ݐݎݑܭ‬௚ )), based on the graphs in Figure 2.
Measurement of median value for each vector is similar. With
mean (ߤ௚ ) vector as sample, median value for window width
can be determined by following mathematical sequences:
i. Sort all the values of mean (ߤ௚ ) vector in ascending
order to form new mean vector (ߤ௦ ).
Skewness (ߛ௚ )
Kurtosis (‫ݐݎݑܭ‬௚ )
ܵ൅ͳ
(10)
ʹ
where ܵ ൌ ͳͲͳ is the length of sorted mean vector (ߤ௦ );
‫ ݊ܽ݅݀݁݉ݏ‬is the sequence of median of sorted mean vector
(ߤ௦ ).
iii. Then, the median value of sorted mean vector (ߤ௦ ) is
determined with equation (11).
‫ ܯ݊ܽ݅݀݁ܯ‬ൌ ߤ௦ ሺ‫ݏ‬௠௘ௗ௜௔௡ ሻ
(11)
51HU
49HU
The final part in this subsection is implementing
equation (15) to determine the average value of ܹܹ݉݁݀‫ܯ‬,
ܹܹܸ݉݁݀, ܹܹ݉݁݀ܵ, and ܹܹ݉݁݀‫ܭ‬. The average value,
ܹܹ‫ ݋‬is the estimated value for window width (WW). Based
on Table 2 and equation (15), the output value of ܹܹ‫ ݋‬is
49.75HU with sensitivity of 0.05 HU.
ii. Calculate the sequence of median of sorted mean vector
(ߤ௦ ) with equation (10).
‫ ݊ܽ݅݀݁݉ݏ‬ൌ
ܹܹ݉݁݀ܵ
ܹܹ݉݁݀‫ܭ‬
ܹܹ‫ ݋‬ൌ 3.4
ሺௐௐ௠௘ௗெାௐௐ௠௘ௗ௏ାௐௐ௠௘ௗௌାௐௐ௠௘ௗ௄ሻ
ସ
(15)
Step
3:
Generate
Output
Image ( ࡵ࢕࢛࢚ ) Using Estimated Window Width
Value.
The final step for proposed method is generating the
output image ( ‫ܫ‬௢௨௧ ) by repeating step 1 and step 2 and
replacing ܹܹሺ‫݌‬ሻ with ܹܹ‫݋‬. However, for better study on
histograms, only brain structure and little background pixels
of image ‫ܫ‬௢௨௧ are manually cropped out. Figure 3 shows the
differences of visualization and histograms of image ‫ܫ‬௢௨௧ and
cropped image ‫ܫ‬௢௨௧ (‫ܫ‬௢௨௧௖ ).
iv. After that, using equations (12, 13) are used to find the
median sequence of ‫ ܯ݊ܽ݅݀݁ܯ‬value from mean (ߤ௚ )
vector (‫݌‬௠௘ௗ௜௔௡ ). Equation (12) determines the vector
of differences of ‫ ܯ݊ܽ݅݀݁ܯ‬and ߤ௚ ሺ‫݌‬ሻ , ‫ܯ‬ሺ‫݌‬ሻ , and
equation (13) calculates ‫݊݅݉ܯ‬, the minimum value of
vector ‫ܯ‬. The sequence ‫ ݌‬of vector ‫ ܯ‬that obtains the
value of ‫ ݊݅݉ܯ‬is the median sequence, ‫݌‬௠௘ௗ௜௔௡ for
window width (WW) vector.
σ௉ିଵ
௣ୀ଴ ൣ‫ ܯ݊ܽ݅݀݁ܯ‬െ ߤ௚ ሺ‫݌‬ሻ൧ ǡ
‫ܯ‬ሺ‫݌‬ሻ ൌ ቊ ௉ିଵ
σ௣ୀ଴ൣߤ௚ ሺ‫݌‬ሻ െ ‫ܯ݊ܽ݅݀݁ܯ‬൧ ǡ
‫ ܯ݊ܽ݅݀݁ܯ‬൒ ߤ௚ ሺ‫݌‬ሻ
(12)
ߤ௚ ሺ‫݌‬ሻ ൏ ‫ܯ݊ܽ݅݀݁ܯ‬
‫ ݊݅݉ܯ‬ൌ ‹ሼσ௉ିଵ
௣ୀ଴ ‫ܯ‬ሺ‫݌‬ሻሽ
(a)
(b)
(c)
(d)
(13)
v. Therefore, the median window width value based on
mean ( ߤ௚ ) vector ( ܹܹ݉݁݀‫) ܯ‬, is determined with
equation (14).
ܹܹ݉݁݀‫ ܯ‬ൌ ܹܹሺ‫݌‬௠௘ௗ௜௔௡ ሻ
(14)
vi. Step i to Step v are repeated for respective vectors of
variance (ߪ௚ ଶ ), skewness (ߛ௚ ), and kurtosis (‫ݐݎݑܭ‬௚ ), in
order to obtain respective median WW values of ܹܹܸ݉݁݀, ܹܹ݉݁݀ܵ, and ܹܹ݉݁݀‫ܭ‬. These values
are shown in Table 2.
Table 2: Median WW values for vector of mean (ߤ௚ ),
variance (ߪ௚ ଶ ), skewness (ߛ௚ ), and kurtosis (‫ݐݎݑܭ‬௚ ).
Vector
Mean (ߤ௚ )
Variance (ߪ௚ ଶ )
WW Values
ܹܹ݉݁݀‫ܯ‬
ܹܹܸ݉݁݀
Values (HU)
49HU
50HU
Figure 3: (a) Desired Output Image (‫ܫ‬௢௨௧ ) and (b) respective
Histogram, (c) Cropped Output Image (‫ܫ‬௢௨௧௖ ) and (d)
respective Histogram.
4
Results and Discussions
500 different CT brain images with infarctions are
chosen to evaluate the performance of proposed method.
There are 3 evaluation tests for proposed method. First test is
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to compare proposed method with 2 evaluations of expert
radiologists, E1 and E2. Figure 4 shows comparison between
image ‫ܫ‬௢௨௧௖ and expert diagnoses of E1 and E2.
(a)
(b)
(a)
(b)
(c)
(d)
(e)
(f)
(c)
Figure 4: (a) Image Enhanced with Proposed Method (‫ܫ‬௢௨௧௖ ),
(b) Evaluation of E1, (c) Evaluation of E2.
The next test is to compare image ‫ܫ‬௢௨௧௖ with grayscale
image generated with default WW (‫ܫ‬ௗ ) and prior methods.
These prior arts are mentioned in introduction section.
However, some of window parameters are set within a range;
therefore average value of the range will be selected as the
estimated value. Table 3 shows the selected windowing
parameters for prior techniques and proposed method. The
resulting image is shown in Figure 5 and respective histogram
is shown in Figure 6.
Table 3: Windowing parameters of proposed method and prior
methods.
Approaches
Windowing Parameters
WC (HU)
WW (HU)
Default
40 HU
80 HU
Przelaskowski
30 HU
40 HU
(2005) [6]
25 HU
3 HU
Gadda, (2002) [7]
47.5 HU
50 HU
Sim (2014) [8]
40 HU
55 HU
Proposed method
40 HU
ܹܹ‫݋‬
(a)
(b)
(c)
(d)
(e)
(f)
Figure 5: Image Produced by Window Settings of (a)
Default, (b) and (c) Przelaskowski (2005) [6], (d) Gadda,
(2002) [7], (e) Sim (2014) [8], and (f) Proposed Method.
Figure 6: Histogram Produced by Window Settings of (a)
Default, (b) and (c) Przelaskowski et al.(2005) [6], (d) Gadda,
(2002) [7], (e) Sim et al.(2014) [8], and (f) Proposed Method.
Figure 5 and Figure 6 show the output images and
respective histograms produced by all the approaches in
Table 3. Przelaskowski’s window setting [6] with WC = 25
HU and WW = 3HU, produces output image with over
enhancement problem. The healthy brain tissue and parts of
the infarctions is washed out. Thus, this method is
unadvisable to be implemented for infarction diagnoses.
While for Gadda’s window setting [7], it produces
output image with under enhancement problem and
introduces unwanted artifacts. So, this method will cause
misinterpretation by assuming some healthy tissue as brain
infarction. Next, the output image produced by Przelaskowski
window setting [6] with WC = 30 HU and WW = 40HU, is
slightly washed out. This may causes misinterpretation by
assuming some brain infarction as healthy brain tissue.
Therefore, this window setting is also not recommended for
infarction diagnoses.
Sim’s window setting [8] and proposed method window
setting produce better output image when compared with
default window setting. This method is highly enhance
infarction region and slightly brighter the normal brain tissue.
Thus, the visibility of infarction is better than other methods.
However, proposed method has two advantages over Sim’s
window setting [8]. The first advantage is that it improves the
visibility of infarctions better than Sim’s method [8]. Another
advantage is the value of ܹܹ‫ ݋‬that is image dependent the
range of ܹܹ‫ ݋‬is not fixed.
The last measurement of visualization is to determine
the changes of ܹܹ‫ ݋‬value in different slices of CT brain
images. Table 4 shows five CT brain images at different parts
of brain soft tissue area. This table proves the robustness of
our proposed method which is able to estimate window width
value (ܹܹ‫)݋‬, based on any CT brain images.
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Table 4: ܹܹ‫ ݋‬value in HU unit for five different CT
brain images with infarctions.
No.
CT Brain Image
ܹܹ‫݋‬
A
43 HU
B
49.75 HU
has proven that it provides better window setting for
infarction evaluation than other existing methods. Existing
methods are required to be identified manually, but our
proposed method is able to estimate the value for window
width (ܹܹ‫ )݋‬by itself. Furthermore, the sensitivity of ܹܹ‫݋‬
of proposed method is 0.05 HU and only requires a vector of
101 values from 0HU to 100 HU to estimate ܹܹ‫݋‬. ܹܹ‫݋‬
produced by proposed method is able to provide a good
reference for those fresh radiologists who have low
experience in infarction diagnosis. Finally, our technique
helps to speeds up the duration of infarction diagnosis by
expert radiologists.
6
References
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C
50.75 HU
D
50 HU
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[4] B. Liu, M. Zhu, Z. Zhang, C. Yin, Z. Liu, and J. Gu.
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E
50.5 HU
[5] National Electrical Manufacturers Association
(NEMA). “Digital imaging and communications in
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[6] A. Przelaskowski, J. Walecki, K. Szerewicz and P.
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5
Conclusions
Based on the results of experiments and
observations on 500 CT brain images, our proposed method
[7] D. Gadda, L. Vannucchi, F. Niccolai, A. T. Neri, L.
Carmigani, and P. Pacini. “CT in Acute Stroke:
Improved Detection of Dense Intracranial Arteries by
Varying Window Parameters and Performing a Thin-
ISBN: 1-60132-442-1, CSREA Press ©
Int'l Conf. IP, Comp. Vision, and Pattern Recognition | IPCV'16 |
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