EE 5359 Project

Pattern Recognition Diagnostic using Phase Only
Correlation technique .
submitted by
Thejaswini Purushotham
1000616811
Pattern Recognition Diagnostic using Phase Only Correlation technique
Objective:
The objective of the thesis is to achieve diagnosis on medical imaging.
Motivation:
Diagnosis based on medical imaging means making the diagnosis after observing,
analyzing, inducing and synthesizing the medical images. Traditional diagnos
is based
on medical imaging makes diagnosis through doctor’s observation of medical images
of all types of medical imaging equipments, to get help from doctors’ professional
levels and clinical experience. As doctor’s observation will have limitations
ine
vitably, different doctors with different professional levels and clinical experience
may have a case to make different diagnostic results, resulting in misdiagnosis.
Moreover, the subjectivity omissions are inevitable and the timeliness of diagnosis
can b
e assured, these restrictions more or less impact the better development of
diagnosis based on medical imaging [6].
Details:
The schematic for the experimental set up is as shown in Fig .1
Fig. 1 Experimental setup for medical image diagnostics.
An
image database has to be maintained which includes images of the
subjects under question. These images are stored in the portable gray map(PGM) file
format. The medical images can be X

ray images of bones or electroencephalogram
images. Since the images in
the database can be modeled as two dimensional
arrays, the two dimension fast Fourier transform(2D FFTs) of the images can be
calculated. The 2D FFTs are then fed to the phase only correlation(POC) algorithm to
generate the correlation graph. Decision abo
ut the possible defect in the subject’s
medical image can be made deciding on the correlation graph.
OVERVIEW OF PHASE ONLY CORRELATION
In general both the magnitude and the phase are needed to completely
describe a function in the frequency domain. S
ometimes, only information regarding
the magnitudes is displayed, such as in the power spectrum, where phase
information is completely discarded. However when the relative roles played by the
phase and the magnitude in the Fourier domain are examined, it i
s found that the
phase information is considerably more important than the magnitude in preserving
the features of an image pattern [3].
The Fourier synthesis using full

magnitude information with a uniform phase resulted
in nothing meaningful as compared
to the original images . Inspired by the above
findings, investigations of the use of phase

only information for matched filters or
pattern recognition have been carried out. It is found that the phase only approach
produces a sharper correlation peak [3].
Consider two n
1
x n
2
images, f(n
1
, n
2
) and g(n
1
, n
2
) where we assume that
the index range are n
1
=

M
1
.…….M
1
(M
1
>0) and n
2
=

M
2
.….M
2
(M
2
>0) for mathematical
simplicity, and hence n
1
=2 x M
1
+1 and n
2
=2 x m
2
+1[4].Let
Denote the two dimension
3
discrete Fou
rier transforms(2D DFT) of the two images.
are given by
(1)
(2)
1
N
W
)
2
exp(
1
N
j
,
2
N
W
)
2
exp(
2
N
j
are the phase components.
(3)
denotes the
phase difference
.The ordinary c
orrelation function is given by
the two dimension inverse discrete Fourier transform(IDFT) of
and is
given by
(4)
is the 2 D inverse Fourier transform of
On the other hand, the cross phase spectrum
is defined as
(5)
The phase only correl
ation(POC) function
is the 2D IDFT of
and
is given by
(6)
When
and
are the same image, i.e,
, the POC
function will be given by
(7)
The equation (7) implies that the POC function between two identical images is the
kronecker’s delta function
.
The most remarkable property of POC compared to the ordinary correlation is
its accuracy in image matching. When two images are similar, their POC function
gives a distinct sharp peak. When two images are not similar, the peak
drops significantly. T
hus , the POC function exhibits much higher discrimination
capability than the ordinary correlation function. The height of the peak can be used
as a good similarity measure for image matching. The other properties of the POC
function used here are the inv
ariance to image shift and brightness change, and
highly robust against noise.
(1) Property of shift invariance
Let
be the displaced version of the original image
then ,
(8)
where
are the displacements. The POC function
between
and
will be
given by
(9)
The equation (9) shows that the correlation peak is shifted by
and the value of
the peak is invariant with respect to the positional image translation. We can
estimate image displacement from the equation (9).
(2) Property of brightness
invariance
Suppose that
is the brightness

scaled image of
(10)
The equation (12)implies that the POC function is not influenced by brightness
change.
Fig 3:
Simulation result for the
images in Fig 5.
F
ig 2:(a) and (b) are the X

ray images of the same chest with variation in
illumination. (c) POC graph
Fig.
4:
POC
function between two identical images along the vertical axis.
The horizontal axes represent the spatial domain of size n
1
x n
2
[4]
Fig.5:
POC
function between two dissimilar images along the vertical axis.
The
horizontal axes represent the spatial domain of size n
1
x n
2
[4]
Application of POC for pulmonary emphysema detection.
There are 80 million patents with developed pulmonary emphysema all over the world,
and 3 million patients are dying every yea
r[9] .Pulmonary emphysema is a disease that
Pulmonary alveoli destroyed on the ground of chronic smoking custom.
Stages of emphysema development [12]
The various stages of emphysema include:
At

risk
Mild emphysema
Moderate emphysema
Severe emphysema.
At

Risk
In the at

risk stage of emphysema, the breathing test is normal. Mild symptoms of
at

risk emphysema include a chronic cough and sputum production.
Mild Emphysema
In the mild stage of emphysema, the breathing test shows mild airflow limitation.
Sympto
ms may include a chronic cough and sputum production. At this stage of
emphysema, you may not be aware that airflow in your lungs is reduced.
Moderate Emphysema
In the moderate stage of emphysema, the breathing test shows a worsening airflow
limitation. Us
ually the symptoms have increased. Shortness of breath usually
d
evelops
when working hard, walking fast, or doing other brisk activity. At this stage of
emphysema, a person usually seeks medical attention.
Severe Emphysema
In the severe stage of emphysema
, the breathing test shows severe airflow
limitation. A person is short of breath after just a little activity. In very severe
emphysema, complications like respiratory failure or signs of right heart failure may
develop. At this stage of emphysema, the qu
ality of life is greatly impaired and the
worsening symptoms may be life threatening.
Studies have shown that lung tissue is about a third of the lung volume has
to be destructed before emphysema could be detected[11].This calls for a reliable
early di
agnostic method for emphysema detection.
Doctors have two methods to diagnose pulmonary emphysema.One of the
methods is spirometry, another is diagnostic imaging. Former is a quantitative method,
however, we cannot make an early detection of the disease.
Latter makes an early
detection, but this diagnosis depends on doctor’s subjectivity and it has much burden on
the doctor. Then we analyse CT(computed tomography) images to present objective
criterion for doctor, and decrease doctor’s burden [10].
The cl
assical method of CT image objective evaluation is the PI (pixel index)
method
.
Emphysema shows up on CT as areas with low attenuation coefficients, with
abnormal distribution. By determining the number of pixels with low attenuation,
emphysema can be dete
cted. PI determines the average number of pixels with lower
attenuation than the limit value(lim). The (1) represents the percentage of lung area
with lower attenuation values than a limit value. All pixels below this
limit are thought to belong to air

fil
led lung regions. Thus, this
index should describe the amount of air and, hence, detect emphysematous
lesions. A measure called HU(Hounsfield unit) is used to represent the attenuation
co

efficients.
Fig.6
:
Subject A, normal lung. These images show hom
ogeneous distribution
of air in the lung. The white dots represent areas with lower attenuation values
than
950 HU,
930 HU, and
910 HU, respectively. The calculated
percentage
s are:
3%, 5%, and 10%.[13]
Fig.7
:
Subject B, emphysematous lung. There are ob
vious abnormal
enlargements of air spaces (bullae)
—
typical for emphysematous destruction.
The bullae are marked with the grey arrows. Pixel index: 8%,13% and 21%.[13]
Fig.8
:
Subject C, severe emphysema. There is an obvious destruction of
the lung parench
yma. Pixel indexes:34%,48% and 62%.[13]
A normal subject (Fig. 5
) has with increasing thresholds from 950HU to
910HU ascending values from 3% to 10%. In the second example with emphysema,
however, values range from 8% to 21%. Although the values of no
rmal and
pathologic subjects may overlap, an expert is still in a position to distinguish
between both cases.What does an expert look at and how does he decide? If we look
at Fig. 1, there are many small areas, equally distributed over the lung. They
incre
ase in number but become only slightly bigger wi
th increasing thresholds. Fig.6
shows a completely different arrangement of the marked areas.There are bigger
bullae representing confluenced air sacs. The optical impression does not vary by the
threshold, e
xcept by increasing the area. This is very compatible with the
morphological definition of emphysema by the National Heart, Lung and
Blood Institute as:
“
an abnormal permanent enlargement of
the air spaces distal to the terminal bronchioles, accompanied by
destruction of the
alveolar walls, and without obvious fibrosis.
”
. The third subject (Fig. 7
) has severe
emphysema. This extreme case is easy to rate.[13]
Pitfall in the PI method:
The PI method is a good, well

known measure of
emphysema. But it is not ab
le to detect emphysema in cases in which emphysema
and fibrosis occur at the same time. This is because fibrosis tends to increase the
attenuation co

efficein
t of pixels whereas emphysema pixels tend
to increase the
attenuation co

efficient of pixels. Henc
e the PI
method fails to detect the pathological
condition in the case of co

existance of
fibrosis with emphysema; which i
s a common
occurance.
Fig 9: Effect of
fibrosis on emphysema detection.(a) pixel index of the CT without
fibrosis. (b) pixel index o
f the CT with fibrosis.(c) scale for image density
[10]
CT TECHNOLOGY
CHALLENGES
To reduce the health risk from exposure to radiation while making a CT scan,
it is desirable to use a radiation dose that is as low as possible. This is especially true
for s
creening studies, for which
asymptomatic people volunteer. However, the
constraint on irradiation dose leads to considerable noise in CT scans. The noise
becomes more apparent when the effective radiation dose
is lowered; the radiation
dose available in th
e lungs does not depend on the radiation dose settings of the
scanner only, but is also influenced by, e.g., the size and weight of the patient. The
presence of noise in CT scans can seriously hamper making a correct clinical
diagnosis. Indeed noise is bec
oming a fundamental bottleneck for almost any
multislice CT application. In particular, the analysis of COPD is very unreliable in low

dose CT image
s
.
[
11
]
Radiation dosages directly influence the PI index. Hence, usage of lower
radiation dosages might lead
to wrong diagnosis. This is explained wi
th the example
as shown in Fig.10
.
Fig.10
:
Coronal slice and its accompanying emphysema map calculated for a
threshold of
930 HU. (a),(b) Scan with clinical radiation dose
(PI =13.3%)
.(c),(d)
Approximately co
rresponding slice of a scan of the same patient with a ten times
lower radiation dose
(PI=15.8%)
The results in [11] showed that PI scores of low

dose CT images are biased toward
overestimation. Noise filtering prior to computation of PI of low

dose CT
images
significantly improves the agreement with the high

dose PI, although MA filtering is
likely to result in an underestimate of PI
Fig.11 :
(1a),(1b),(1c),(2a),(2b),(2c),(3a),(3b),(3c)
Simulation results for
emphysema detection
Fig.12 : Simulation results for emphysema
progression.(4a) is the image of a healthy
individual.(4b),(4c)and(4d) are images of the emphysema in different progressive
stages.(4e) shows that there 11.7% difference between (4a) and (4b). (4f) shows
that ther
e is .58% difference between (4b)and (4c). (4g) shows that there is .02%
change between (4c) and (4d)
CONCLUSION
As mentioned, a proposal to achieve diagnosis of medical imaging using the
POC algorithm is made
. POC method gives a direct mapping between
the number of
affected pixels and the percentage of visible pixels on the POC map. POC method
scores over the traditional PI method in terms of the Radiation dosage. PI method
gives better performance at higher dosages of radiation. But the POC method is n
ot
dependant on the brightness of the image. Hence it is a better method compared to
the PI method.
This technique can be extended and verified over other pathologies
like
osteoarthritis
,
Lung Nodule Detection
and
Microcalcification clusters in
mammograms.
REFERENCES
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e

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p2.html
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ACRONYMS
:
COPD
chronic obstructive pulmonary disease
CT
computed tomography
2
D
2 Dimension
DFT
Discrete Fourier Transform
IDFT
Inverse Fast Fourier Transform
FFT
Fast Fourier Transform
HU
Hounsfield unit
MA Moving average
PI P
ixel index
POC
Phase Only Correlation
PGM
Portable Gray Map
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