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 dimension3 discrete Fourier transforms 2D DFT of the two images are given by 1 2 W N1 WN2 exp exp j 2 N2 j 2 N1 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 given by When and function will be given by is the 2D IDFT of 6 are the same image i e and is the POC 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 and are the displacements The POC function will be given by between 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 2 a and b are the X ray images of the same chest with variation in illumination c POC graph 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 atrisk 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
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