EE 5359 Project-Pattern Recognition Diagnostic Using Phase Only Correlation Technique

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 diagnosis 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 inevitably, 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 be 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 about 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. Sometimes, 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 is 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 n1 x n2 images, f(n1 , n2 ) and g(n1 , n2 ) where we assume that the index range are n1 =-M1.…….M1(M1>0) and n2=-M2.….M2(M2>0) for mathematical simplicity, and hence n1=2 x M1+1 and n2=2 x m2+1[4].Let Denote the two dimension1 discrete Fourier transforms(2D DFT) of the two images. are given by

(1)

(2)

,

are the phase components.

(3)

denotes the phase difference .The ordinary correlation 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 correlation(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. Thus , 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 invariance 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.

Fig.4:POC function between two identical images along the vertical axis. The horizontal axes represent the spatial domain of size n1 x n2 [4]

Fig.5:POC function between two dissimilar images along the vertical axis. The horizontal axes represent the spatial domain of size n1 x n2 [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 year[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. Symptoms 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. Usually the symptoms have increased. Shortness of breath usually develops 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 quality 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 diagnostic 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 classical 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 detected. 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-filled 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 homogeneous distribution

of air in the lung. The white dots represent areas with lower attenuation values

than950 HU,930 HU, and910 HU, respectively. The calculated percentages are:

3%, 5%, and 10%.[13]

Fig.7: Subject B, emphysematous lung. There are obvious 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 parenchyma. 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 normal 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 increase in number but become only slightly bigger with 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, except 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 able 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-efficeint of pixels whereas emphysema pixels tend to increase the attenuation co-efficient of pixels. Hence the PImethod fails to detect the pathological condition in the case of co-existance of fibrosis with emphysema; which is a common occurance.

Fig 9: Effect of fibrosis on emphysema detection.(a) pixel index of the CT without fibrosis. (b) pixel index of 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 screening studies, for whichasymptomatic 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 the 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 becoming a fundamental bottleneck for almost any multislice CT application. In particular, the analysis of COPD is very unreliable in low-dose CT images.[11]

Radiation dosages directly influence the PI index. Hence, usage of lower radiation dosages might lead to wrong diagnosis. This is explained with 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 corresponding 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 there 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 not 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.

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[23] ,YaleSchool of medicine.

ACRONYMS:

COPD chronic obstructive pulmonary disease

CT computed tomography

2D2 Dimension

DFTDiscrete Fourier Transform

IDFTInverse Fast Fourier Transform

FFTFast Fourier Transform

HUHounsfield unit

MA Moving average

PI Pixel index

POCPhase Only Correlation

PGMPortable Gray Map