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Ventricle slice detection in MRI images using Hough Transform and Object Matching techniques

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Ventricle slice detection in MRI images using Hough Transform and Object Matching techniques
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Thakkar, Chintan
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Digital image processing
Medical imaging
Medical image segmentation
Magnetic resonance imaging
Center slice detection
Dissertations, Academic -- Computer Science -- Masters -- USF   ( lcsh )
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ABSTRACT: The determination of the center slice, defined as a slice through the lateral ventricles in the axial plane in a volume of MR images is important to the segmentation of the image into its anatomical parts. The center or ventricle slice in a set of MR images is recognized by the shape of the ventricles in the axial plane as depicted by the cerebro-spinal fluids in the image. Currently, no technique exists to detect this slice and the purpose of this thesis is to find a slice through the lateral ventricles in the axial plane from a volume of MRI brain scan slices. There are several methodologies which will be discussed in the thesis, the Hough Transform and Object Matching using deformable templates being the primary ones. It is shown, in the test cases used, that these algorithms used together provided results that had almost 80 percent accuracy. However, a simple method to spatially calculate the center slice is also competitive in accuracy.
Thesis:
Thesis (M.S.C.S.)--University of South Florida, 2006.
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Includes bibliographical references.
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by Chintan Thakkar.
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Ventricle Slice Detection In MR Images Using Hough Transform and Object Matching Technique s by Chintan Thakkar A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in Computer Science Department of Computer Science and Engineering College of Engineering University of South Florida Co-Major Professor: Dmitry B.Goldgof, Ph.D. Co-Major Professor: Lawrence Hall, Ph.D. Sudeep Sarkar, Ph.D. Dewey Rundus, Ph.D. Date of Approval: November 3, 2006 Keywords: digital image processing, medical imaging medical image segmentation, magnetic resonance imaging, center slice detection Copyright 2006, Chintan Thakkar

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DEDICATION To my Mother, Sisters, and my fiance Seema

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ACKNOWLEDGEMENTS I would like to thank Dr. Goldgof and Dr.Hall for t heir patience and for giving me an opportunity to work with their MRI team. I would a lso like to thank co-team members Yuhua Gu and Prodip Hore for helping me through som e rough patches in my research and for providing me with the necessary data and to ols on a moments notice whenever I needed them. Special Thanks to Yuhua Gu for helpin g me develop the "Formula mode" and "Object Matching Mode" in my research.

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i TABLE OF CONTENTS LIST OF TABLES iii LIST OF FIGURES iv LIST OF EQUATIONS vi ABSTRACT vii CHAPTER 1: INTRODUCTION AND MOTIVATION 1 1.1 Magnetic Resonance Imaging 1 1.2 Motivation 2 1.3 Thesis Organization 3 CHAPTER 2: BACKGROUND AND RELATED LITERATURE 4 2.1 Canny Edge Detector 4 2.2 Hough Transform 5 2.3 Wilcoxon Signed – Rank Tests 6 CHAPTER 3: PROBLEM DESCRIPTION AND PROPOSED SOLUTIO N 8 3.1 Problem Description and Objective 8 3.2 Description of Data 9 3.3 Procedure 9 3.3.1 Hough Transform to Detect Eyes 9 3.3.1.1 Post Processing 11 3.3.1.2 Parameters and Tresholds Used 13 3.3.1.3 Other Heuristics and Procedures Used 15 3.3.2 Object Matching Using Deformable Templates 20 3.3.2.1 Prototype Template 21 3.3.2.2 Deformation Transformations 22 3.3.2.3 Error Function and Likelihood of a Match 23 3.4 Operation Modes 24 3.4.1 Formula Mode 2 4 3.4.2 The Hough Transform with Post Processing Mode 25 3.4.3 Object Matching Mode 27 3.4.4 Hybrid Mode 28

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ii CHAPTER 4: RESULTS 30 4.1 Mode 1: Formula 30 4.2 Mode 2: Hough Transform with Post Processing 32 4.3 Mode 3: Object Matching 36 4.4 Mode 4: Hybrid Mode Center Slice Detection 38 4.5 Time and Speedup Issues 40 CHAPTER 5: CONCLUSION AND FUTURE WORK 42 5.1 Conclusions 42 5.2 Future Work 44 REFERENCES 45

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iii LIST OF TABLES Table 1. Set MN011 and Average Vitreous Humor Intensities in First and Second Eyeball 17 Table 2. Set MN014 and Average Vitreous Humor Intensities in First and Second Eyeball 18 Table 3. Training Set to Determine Center Slic e for Formula Mode 25 Table 4. Training Set to Determine Bias value for Hough Transform 26 Table 5. Training Set for Object Matching 28 Table 6. Training Set for Hybrid Mode 29 Table 7. Results Using Formula to Predict the Center Slice 31 Table 8. Results Using Hough Transform Mode 33 Table 9. Results Using Object Matching Mode 36 Table 10. Results Using Hybrid Mode 39 Table 11. Wilcoxon Test on Hybrid and Formula Mo de 43

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iv LIST OF FIGURES Figure 1. MRI Image Planes 2 Figure 2. Center Slice Showing Butterfly Shaped CSF 3 Figure 3. Hough Space Image 11 Figure 4. Depicts the Scan Area, Average Dista nce Between Eyes and Other Features of a Typica l MRI 256 x 256 MRI 12 Figure 5. Hough Space Image After Post Process ing 13 Figure 6. Image Being Scanned 16 Figure 7. Intensities Aggregated and Averaged While in Region 16 Figure 8. Set MN011 and Average Vitreous Humor Intensities in First and Secon d Eyeball 17 Figure 9. Set MN014 and Average Vitreous Humor Intensities in First and Secon d Eyeball 18 Figure 10. An Image with Concentric Eyeballs 20 Figure 11. Template for CSF 21 Figure 12. Slice with CSF 21 Figure 13. Deformed Template with M=N=1, 1.0 ,3.0 y mn x mn 22 Figure 14. Sample Median Eyeball Slice 27 Figure 15. Formula Mode Error Plot 31 Figure 16 Hough Transform Mode Error Plot 34 Figure 17. Subset of MN023 Data Set 35 Figure 18. Object Matching Mode Error Plot 37

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v Figure 19. Hybrid Mode Error Plot 39

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vi LIST OF EQUATIONS Equation 1. Z-statistic for Wilcoxon Signed-Ra nk Test for N>25 7 Equation 2. Orthogonal Bases 21 Equation 3. Displacement Function 22 Equation 4. Displacement Function Discrete Cas e 22 Equation 5. Edge Potential 23 Equation 6. Error Function 23

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vii VENTRICLE SLICE DETECTION IN MR IMAGES USING HOUGH TRANSFORM AND OBJECT MATCHING TECHNIQUES Chintan Thakkar ABSTRACT The determination of the center slice, defined a s a slice through the lateral ventricles in the axial plane in a volume of MR images is importa nt to the segmentation of the image into its anatomical parts. The center or ventricle slice in a set of MR images is recognized by the shape of the ventricles in the ax ial plane as depicted by the cerebrospinal fluids in the image. Currently, no techniqu e exists to detect this slice and the purpose of this thesis is to find a slice through t he lateral ventricles in the axial plane from a volume of MRI brain scan slices. There are several methodologies which will be discussed in the thesis, the Hough Transform and Ob ject Matching using deformable templates being the primary ones. It is shown, in the test cases used, that these algorithms used together provided results that had almost 80 percent accuracy. However, a simple method to spatially calculate the center s lice is also competitive in accuracy.

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1 CHAPTER 1: INTRODUCTION AND MOTIVATION 1.1 Magnetic Resonance Imaging Magnetic resonance imaging is an imaging techniq ue used to produce high quality images of the insides of the human body. It is bas ed on the principles of Nuclear Magnetic Resonance (NMR), which is a spectroscopic technique used by scientists to obtain microscopic chemical and physical properties of molecules [17]. MRI was first proposed in 1975 by Richard Ernst to be used as an instrument to detect malignant tumors; it was based on previous research in the field of nuclear magnetic resonance by Edward Purcell and Felix Bloch in 1952 An MRI scanner is basically a superconducting ma gnet that produces a magnetic field. This magnetic field affects the hydrogen atoms in a human body and realigns these atoms to the field of the magnet. After when the magnet is turned off, the hydrogen atoms in the body realign releasing energy which is then pic ked up by sensors to produce an image. MRI images used in this thesis have 3 different features and can be taken 3 different ways. They can be taken along three different plan es: either sagitally, coronally, or axially (see Figure 1).

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2 Figure 1. MRI Image Planes [18] The three different features for MRI images are T1, T2, and PD (Proton density) weighted. T1 images are also called anatomical ima ges, they are fast to acquire and have excellent structural detail (white and grey matter) T2 (pathological) images are slower to acquire, and are higher resolution than T1. Proton density (PD) images are taken to show water / hydrogen concentration in a body part. For the purposes of our project we will be using the high resolution T2 images. These images originally come in DICOM format with intensity levels ranging from 0-4096, they hav e been converted to pgm formats with intensities scaled to fit the conventional range of 0-255. This was done to reduce the complexity of the image manipulation algorithms and for a speedup in processing images. 1.2 Motivation This project represents the initial step of auto matic segmentation of MR images of the human brain system. The automatic segmentation syst em will start from a “center slice” (slice that contains the lateral ventricles) in the axial plane. The choice of center slice is very important for an automatic segmentation system because it has the best uniformity

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3 of signal within an MRI volume and contains the mos t reliable anatomical information for the rules in a segmentation system. Currently w e choose the center slice by observing the shape of CSF (cerebrospinal fluid) in the slice the best center slice should contain a very good butterfly shape for CSF (Figure 2). In th is project, we have implemented two approaches: Hough transform and Object Matching usi ng Deformable Templates. Figure 2. Center Slices Showing Butterfly Shaped C SF 1.3 Thesis Organization There are four chapters following the introducti on; 2 Background and Related Literature, 3 Problem Description and Proposed So lution, 4 – Results, and 5 – Conclusion and Future work. The Background and Rel ated Literature chapter talks about some background material on the Canny Edge Detector and the basics of the Hough Transform Algorithm. The Problem Description and P roposed Solution sections describe the problem at hand and a solution using Object Mat ching techniques and variants of the Hough Transform algorithm, plus the different modes of operation. The next chapter shows the results obtained from the different opera tion modes, and lastly Chapter 5 is the conclusion along with some future work that could b e done on the thesis to make it more robust and produce better results.

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4 CHAPTER 2: BACKGROUND AND RELATED LITERATURE 2.1 Canny Edge Detector Edge Detectors have been an essential part of se veral Computer Vision Systems [6]. They generally come in several flavors but low erro r rate and good localization of the edge points are common criteria to gauge their perf ormance. John Canny wanted to design an optimal edge detecto r and created the Canny Edge Detector at MIT in 1983 [6]. The optimality of Can ny Edge Detector is related to three criterion: The Detection Criterion: Important edges should not be missed Localization Criterion: Distance between the actual and located position of the edge should be minimal The One Response Criterion: Minimize multiple respo nses to a single edge. (More specific to edges corrupted by noise) The Canny Edge Detection Algorithm Convolve an image with a Gaussian of scale Estimate Local edge normal directions n for each pi xel in image. Compute magnitude of edges. Find Location of edges using non maximal suppressio n. Threshold edges using hysterisis to remove spurious responses.

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5 Repeat previous steps for ascending values of stand ard deviation Aggregate final information about edges using a fea ture synthesis approach. Canny is used in this project because it is very robust, and is optimal [19] to detect step edges in an image corrupted by noise. It also give s a nice 1 pixel thin edge by eliminating multiple responses to the edge created by noise, this is very useful for the Hough transform as it can easily get confused by “d ouble edges”. Canny utilizes Gaussian convolution which can be separated and hen ce contributes again to its robustness. The only problem that could occur with Canny is along “Y” junctions or ridge edges because it can treat the two ridges as a single jun ction, and the third one as a line that approaches but doesn’t quite connect to that line s egment. 2.2 Hough Transform The Hough Transform [7] was developed by Paul Ho ugh at IBM labs in 1962 as a feature extraction tool in digital image processing The underlying principle of the Hough Transform in extracting features of a geometr ic shape in an image is that there are an infinite number of instances of that shape that can pass through any point, each at a different orientation: The purpose of the transform is to then find the closest match of the desired shape to the features of the image. To find the closest match, a transformation is d one of the desired shape from the image into a mathematical parameter space – usually refer red to as the Hough Space. The image is usually pre-processed using an edge detect or like Canny (section 2.1) and the edge image is given to the transform. The Hough s pace consists of “bins” each

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6 consisting of an approximate representation of the geometric shape. By simply incrementing the value stored in each bin for every feature lying on that shape, an array is built up which shows the shape that fits most close ly to the data in the image. The best fit to the feature in the image can be obtained by find ing the bins with the highest value – represented by peaks in the parameter space. The s implest way of finding these peaks is by applying some sort of a threshold so that the se arch space is limited. The Hough transform as applied in this thesis along with some post processing techniques is discussed in detail in Chapter 3. 2.3 Wilcoxon Signed Ranks Test A statistical significance test was used in comp aring the results obtained from the different algorithms utilized in this thesis. The purpose is to reject or fail to reject our null hypothesis, which states that the algorithms p erformed equally well. The most commonly used test for this purpose is the paired T -test. However the paired T-test suffers from three problems: Commensurability, wher e basically you have make sure you are comparing “apples” to “apples” and not “oranges ”, sample sizes below 30 require for the data to be normally distributed, which cannot a lways be assured, and the third problem being that just as in averaging over data s ets, the T-test is affected by outliers which can skew the test statistic. The Wilcoxon Signed-Ranks test is a non-parametr ic alternative to the paired T-test, which ranks the differences in performances of two classifiers in each data set, ignoring the signs, and compares the ranks for the positive and the negative differences [23]. It is preferred over the former method because it doesn’t suffer from the same problems of

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7 commensurability, assumption of a normal distributi on of data, and susceptibility to outliers that can skew the statistic. If i d is the difference between the performance of the t wo classifiers on the i -th out of N data sets, the differences are ranked according t o their absolute values and average ranks are assigned in case of ties. R+ is the sum of ranks where the second algorithm outperformed the first, and vice versa for R-. Ran ks of i d =0 are split evenly among the sums, and one is ignored if there is an odd number of them. The smaller of the Ranks, designated by T = min(R+,R-) is looked up in a tabl e of critical values for T, based on which the null hypothesis is either accepted or rej ected. For larger N (25 or more), a z value is calculated using the formula: 1 (1) 4 1 (1)(21) 24 TNN z NNN (1) This statistic is approximately distributed normall y and with =0.05, the null hypothesis can be rejected if z < -1.96.

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8 CHAPTER 3: PROBLEM DESCRIPTION AND PROPOSED SOLUTIO N 3.1 Problem Description and Objective The Purpose of this project is to find the “center slice” (defined as a slice through the lateral ventricles in the axial plane) from a volum e of MRI brain scan slices. The determination of the center slice in a volume of MR I images is critical to the segmentation of the image into its anatomical parts Two different methods to find the center slice automatically are implemented. Dynamically find the location of a slice which c ontains human eye balls, from which we can approximately get the location of the center slice, to detect eye balls in the slice, we used the Hough Transform algorithm. Object matching using deformable templates [1]: We will initially define some templates, which include the templates for ventricl e slices with a probabilistic deformation transformation for the template. We can easily get a contour for CSF by using some boundary extraction algorithms, for exam ple [2][3][4]. In [1], the paper addressed the problem of locating and retrieving an object from a complex image using its 2D shape/boundary information. In order to redu ce computational overhead the Hough Transform will be used first to detect the eyeballs after which the object matching will phase in. Since the “center slice” in a volume of MRI slices only comes after the eyeball slices – this is allowed. The object matching mode can also be used in a standalone way (without Hough Transform) to detect the center slic e. The different modes of operation are discussed in Section 3.4. We have some initial ly defined templates for the ventricle

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9 slice, we scan the volume from the last eyeball sli ce to the bottom of the volume and check each template to see if it can find a corresp onding object in the image. In fact, what we are concerned with is the center slice template, once we can find the center slice object in the image, our work is done. We may have more than one template for the center slice. 3.2 Description of Data The data used for the purpose of this thesis was from both the 1.5 and 3 Tesla scanners. The T2 feature image used for the Hough Transform a lgorithm shows the vitreous humor (liquid) in the eye most accurately. All three (T1 T2, and PD) features are used to threshold out the air in images. Both 1mm and 1.5m m thick slices in the axial plane were utilized. The data in DICOM format is converted to a pgm format through the use of several image conversion routines in order to reduc e overhead induced by performing operations on raw binary images. The pgm images ar e 256 x 256 in resolution, and depending on 1mm, 1.5mm, or 3mm MRI data come out t o 144, 96, or 34 slices respectively. 3.3 Procedure 3.3.1 Hough Transform to Detect the Eyes The idea behind applying the Hough Transform to det ect eyes is to detect features in the image that resemble circles. If (x,y) is an ed ge pixel in the magnitude image that belongs to a circle then all possible circles with radius r and centers (a,b) through that point are calculated, if an adjacent edge pixel (x1 ,y1) falls on the same circle with radius

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10 r and center (a,b) then that’s the continuous circl e we are looking for. The precision or probability of finding our circle is increased with more edge pixels being found on its circumference. The Hough space (Figure 3) shows all possible circl es passing through an edge pixel (x,y) in the coordinate plane, this space is used a long with the magnitude image to detect the circles in our images. 1. The image parameter space for our purposes will be a 3 dimensional space in a,b, and r where (a,b) is the center of the circle/eyeba ll and r is the radius. 2. The parameter space is quantized and a 3d accumulat or array Ac(a,b,r) is dynamically declared and initialized. A bin size i s selected for the creation of the Hough space. 3. For every edge pixel (x,y) in the Magnitude image, use all possible (a,b) values to calculate radius r = sqrt( (x –a)^2 + (y –b)^2 ) Increment the corresponding value at Ac(a,b,r) by 1 provided that r <= user defined value so that only radii of less than a def ined value by the user are displayed. 4. Find all Local Maxima’s (using the bin size) in the accumulator array by going through a 3 dimensional 3*3*3 window. These values can be thresholded to obtain only the top 40%-70% of the values calculate d. This is a step taken generally to decrease the computational load.

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11 5. Take the corresponding co-ordinates (a,b,r) of the computed maxima and use the Bresenham’s [2] circle plotting algorithm to plot a circle around the eye with radius r from the center (a,b). 6. The resulting image will be the mapping of your Hou gh space in the real (x,y) axis. Each “cone” in the Hough space or indices in the accumulator array corresponds to a circle in the (x,y) plane. 7. A superimposed image is obtained by using the infor mation provided by the gradient image and the Hough space. 100 150 200 250 300 0 5 10 15 0 10 20 30 40 50 a+b (voxels) 4D Parameter Space represented in 3D r (voxels) Number of circles detected 3.3.1.1 Post Processing Post processing of the images was done based on several observations and from knowledge obtained from the anatomy of the human br ain (Figure 4): The eyes are always located in the top half of the image and lie approximately along the same Figure 3. Hough Space Image

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12 horizontal axis and cannot be skewed by more than 4 -5 voxels, this is assuming that the images are taken in the axial plane(Figure 1) and a re aligned so that the eyes are always on top. They should come in pairs and only one pai r should exist, the two eyes are also at a certain distance apart and are approximately of t he same size in a slice that shows them fully. In case the HT algorithm detects two pairs of eyeballs that overlap or are concentric, then the eyeball with the larger radii is picked. The average size of a human eyeball is about 1214 voxels in radius when the MRI image is scaled to 256x256, and the vitreous humor solution in the eyeballs has an average intensity higher than that of the average i ntensity of tissue and other matter in the image. In order to reduce the overhead induced by the processing time of the Hough Transform algorithm, only a subset of the slices th ought to have eyeballs in them are processed. Figure 4. Depicts the Scan Area, Average Distance B etween Eyes and Other Features of a Typical MRI 256 x 256 MR Image Figure 5 shows the Hough Space after post processin g is done to detect the eyes. The two “spikes” correspond to the two eyeballs detecte d in the MRI image.

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13 140 160 180 200 220 10 10.5 11 11.5 12 0 10 20 30 40 50 a+b (voxels) 4D Parameter Space represented in 3D after post pro cessing r (voxels)Number of circles detected 3.3.1.2 Parameters and Thresholds Used There are 9 different parameters used in the pro gram, 5 of which are selected by the user. The parameters are sent to the program by th e user via a shell script / parameter file. The one’s chosen by the user are: 1. Bin size for creation and searching of Hough 3d par ameter space. Usually this is set to 1 or 2. 2. Maximum radius of circles that the user is looking for in the image. For our purpose, this will be the size of the eyeball (usua lly in the range of 12-14 voxels) 3. File prefix name. For example a file named slice1. pgm will have prefix of “slice”. This must be consistent throughout all slices. 4. Slice index begin number. This number specifies th e first slice. In the example above, this number would be 1. 5. Slice index end number. This number specifies the last slice. Figure 5. Hough Space Image After Post Processing

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14 The built-in parameters are chosen based on some observations and also in some cases after training the system with several differ ent data sets: 1. Image scan area for the eyes. Provided that the im age orientation is upright (Figure 4.) This is generally set to the top 35% of the ima ge height of a 256x256 resolution image because that’s generally where the eyes are, the other 65% of the image is mainly the skull and other parts of the brain. Mor e specifically, the top 90 (35% of 256) rows of the image are scanned for the eyes. T he eyes are also required to be along the same horizontal line in an axial image. A threshold for a skew of up to 5 voxels along the horizontal line is added for image s that are slightly tilted. 2. Distance between two successive eyeballs, this is s et to be anything greater than 10 voxels. 3. Only the top 60% of the local maxima’s are taken af ter scanning the Hough space. 4. The minimum intensity threshold for eyeball detecti on using vitreous humor is set to 75. In other words the average intensity for vi treous humor in the eye has to be greater than 75 for the algorithm to detect the fea ture as eyeballs. The average vitreous humor intensity is also averaged with the average intensity of the image and tested against the same threshold to account fo r cases where the images are darker or brighter. Anything below the set thresho ld is a false positive or other tissue of the brain. The reason for picking this t hreshold was the result of some analysis that is discussed in Section 2.3.2.3.

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15 5. The Scan space for eyeball detection is set to star t at 15mm from the beginning of the data set to all the way until half the data set is reached. These limits are picked because of a-priori knowledge of the scans since th ey start from bottom of the head and go all the way until the top of the skull and n o eyes can be found in the first 15mm or the second half of the data set. 3.3.1.3 Other Heuristics and Procedures Used The general Hough Transform procedure was used t o detect eyeballs in MRI images. The post processing modifications made to it are fo r the purposes of speedup, to avoid redundancy, and false positives. Along with the st andalone Hough Transform system, several other procedures and image processing techn iques were gradually added, and parameters were relaxed while others were tightened to obtain the best results. The vitreous humor detection was later added to the sys tem because the existing heuristics and procedures used to achieve the desired results did not suffice. Vitreous Humor is the liquid in the eye that shows up as “white” in T2 we ighted MRI images due to high water content. Vitreous humor detection is done using a region scanning technique. The region of interest to us is marked clearly by the hough space circles. This image is scanned from left to right with the aid of Boolean flags which m ark the beginning and end of the region, and intensities are aggregated and averaged at the end of the scan. Since vitreous humor shows up as bright liquid in MR images, it ca n be easily segmented from the rest of the brain using this simple technique. The prob lem however arises from false positives generated by the Hough Transform in detec ting concentric or overlapping

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16 eyeballs. As a result, false positives such as con centric eyeballs / circles detected needed to be avoided, and the average intensity of the ima ges needed to be calculated from all the features (T1,T2,PD) of the MR images to compens ate for images which are lighter in intensity and may have a vitreous humor intensity t hat is less than the threshold specified. A technique to get rid of these false positives is explained later. Figure 6 and 7 in the meantime depicts the region scanning technique outl ined above. A threshold of 75 mentioned in Section 3.3.1.2 w as picked for proper detection of the eyeball after statistical analysis was done on a ra ndom test set. This threshold was also compared with the average image intensity and avera ge vitreous humor intensity to account for images that vary in intensity. Two tes t sets listed in Tables 1, 2 were used to train the system. Figures 8, 9 are plots of the respective vitreous humor intensit ies found by a variant of the region growing algorithm listed above. The red line in the plots depicts the threshold of 75 picked from these train ing data sets. Figure 6. Image Being Scanned Figure 7. Intensities Aggregated and Averaged While in Region

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17 Eyeball Slice # Average VH intensity Eyeball 1 Aver age VH intensity Eyeball 2 17 70 74 18 107 90 19 107 93 20 106 91 21 83 77 22 103 89 23 97 84 24 111 91 25 101 79 26 113 94 27 92 80 28 52 101 30 75 118 16 18 20 22 24 26 28 30 50 60 70 80 90 100 110 120 Slice NumberAverage VH IntensitySet MN011 Table 1. Set MN011 and Average Vitreous Humor Intensities in First and Second Eyeball Figure 8. Set MN011 and Average Vitreous Humor Intensities in First and Second Eyeball

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18 Eyeball Slice # Average VH intensity Eyeball 1 Aver age VH intensity Eyeball 2 15 123 104 16 117 99 17 121 104 18 112 90 19 114 91 20 116 96 21 96 104 22 131 103 23 141 110 24 143 108 25 95 110 26 113 92 27 71 100 14 16 18 20 22 24 26 28 70 80 90 100 110 120 130 140 150 Slice NumberAverage VH IntensitySet MN014 Table 2. Set MN014 and Average Vitreous Humor Intensities in First and Second Eyeball Figure 9. Set MN014 and Average Vitreous Humor Intensities in First and Second Eyeball

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19 The average image intensity is calculated using all three features (T1,T2,PD) to threshold the air represented by the region around the skull. The threshold value for air is set to < 60 by the MriSeg system i.e. if all three features contain intensities of < 60 for a particular voxel then that voxel is regarded as air and thresholded in the average image intensity calculation. The average image intensity is calculated to pick a relative threshold for the vitreous humor detection algorith m. Instead of hard-coding a vitreous humor detection threshold in the algorithm, it now more intelligently picks one using the average intensity of the image. Concentric or overlapping parametric curve detec tion is a normal occurrence in the Hough Transform. In fact the ability of the Hough transform to give you only one instance of a detected parametric curve depends on the edge detectors ability to give you good clean edges. The Canny edge detector is very good about producing single straight edges even if they are corrupted by noise but even it falters sometimes and produces multiple responses to a single edge, which in our c ase results in concentric or overlapping circles (Figure 10). These false positives general ly are of no concern (as long as the eyes are detected) but can prove to be a major hindrance to the region scanning algorithm for vitreous humor detection since flags representing t he beginning and the end of the vitreous humor region can be turned on and off at t he wrong moments. In order to rectify this situation, and ensure single truth responses, a heuristic is applied in the code which specifies that if there are two pairs of eyeballs t hat are concentric or overlap then remove the instance with the smaller radius.

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20 3.3.2 Object Matching Using Deformable Templates The Hough Method transforms points in feature space into a parameter space, and the specified feature is detected by finding the peaks in the parameter space. The HT method can be viewed as a template matching scheme: Howeve r, it is a rigid scheme in that it is not capable of detecting a shape that is different from the template by a translation, scaling or a rotation factor. A deformable templat e on the other hand, is able to “deform” itself to fit the data [1]. A deformable model is appropriate in situations whe re an inexact knowledge about the shape of the object is available and when this shap e information is not parametric or geometric (in our case the butterfly shaped CSF). In this object matching scheme, our model consists of 1. A prototype template of CSF sketched by hand. 2. A set of parametric transformations that deform the template. 3. An error function which takes in both gradient a nd magnitude information from the edge detector and compares it against the ground tr uth image to get the center slice. Figure 10. An Image with Concentric Eyeballs detected

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21 3.3.2.1 Prototype Template The prototype template describes one of the inst ances of the shape we are looking for in an image. This template is deformed, scaled, and r otated to match the desired object in the image. It is required by the deformation algor ithm that the template image is connected. A simple image processing tool can be u sed to draw up a connected edge image of the desired object on a black canvas. Fig ure 11 shows a sample template image of the cerebro-spinal fluids, along with the image it will be matched against (Figure 12) to find the ventricle slice. 3.3.2.2 Deformation Transformations The square region of the image can be thought of as a “deformable rubber sheet” that can be stretched and skewed along the 2D x, y axes. This 2D space can be represented by orthogonal bases [1]: )) sin( ) cos( 2,0( ) ( )0 ), cos( ) sin( 2( ) ( ny mx y x e ny nx y x ey mn x mn (2) Figure 11. Template for CSF Figure 12. Slice with CSF

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22 Where m,n = 1,2,3. As m and n increase, the basi s functions vary from global to smooth, to local and coarse. We perform a deformat ion on this “sheet” by using a displacement field. The displacement function is ch osen as [1]: 11. )) ( ), ( ( ) (mn mn y mn y mn x mn x mn y xe e y x D y x D y x D (3) Where .... 2,1 ), (2 2 2 n m m nmn are the normalizing constants. The parameters ,...} 2,1 ), {( n my mn x mn are projections of the displacement function on th e orthogonal basis, thereby they define the displacem ent field and the deformation. The discrete case of the displacement function above is [1]: M m N n mn y mn y mn x mn x mne e y x D11. ) ( (4) M and N are user defined parameters, and along with determine the deformation of the template. Larger values of M, N and result in larger deformations. A deformed template of the CSF in an MRI scan and the correspo nding M,N, and values are shown below in Figure 13. Figure 13. Deformed Template with M=N=1, 1.0 ,3.0 y mn x mn

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23 3.3.2.3 Error Function and Likelihood of a Match The likelihood of a match of an input image (Y) to a deformed template ( ) is defined by how well the edge magnitude and edge direction o f the input image matches with the deformed template. For a voxel (x,y) in the input image, its edge potential is defined as [1] [19]: } ) ( exp{ ) (2/1 2 2 y xy x (5) Where ) (y x is the displacement to the nearest edge point in th e image and is a smoothing factor which controls the degree of smoot hness of the potential field. A directional component is added to get a better matc h, and a new energy (error) function [1] is derived that predicts the likelihood of a ma tch between the deformed template and the input image. |) )) ( cos | ( 1( 1 ) (, ,y x y x n Y Es (6) Where the summation is for all the voxels in the template, n is the number of voxels in the image, ) ( y x is the angle between the tangent of the nearest ed ge and the tangent direction of the template at (x,y). The constant 1 is added so that the potentials are positive and take values between 0 and 1. This way the template matches the input image not only in edge magnitude but in edge direction – which acts as a safety net and helps to reduce errors induced by noisy edges. The best pos sible match is achieved when E = 0, or in other words, the minimum energy (error) is ca lculated.

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24 3.4 Operation Modes There are 4 modes in which the CS Detect tool op erates to give the operator flexibility. The major difference between the modes has to do wi th a tradeoff between performance vs. accuracy of the results. 3.4.1 Formula Mode The formula mode is where the center slice is de tected via a formula. This formula is based on the observation that the ventricle slice i n an MRI set of images is generally located around a predetermined slice number within that set. The training sets used to get this formula are listed in Table 3. This slice number depends on the width of the slices in mm – which also determines how many slice s there will be in a data set. For 1mm data, there are a total of 144 slices, and the formula is to take the total, divide it by 2, and add an offset of 12 slices to t hat number. This results in a center slice number of 89. For 1.5mm data, there are a total of 96 slices, and the formula is to take the total, divide it by 2, and add an offset of 8 slices to th at number. This results in a center slice number of 56. For 3mm data, there are a total of 48 slices, with the formula being the same except the offset is 4. This results is a predicte d center slice number of 28.

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25 Set Name, Slice Thickness Actual Center Slice number Predicted Formula Center Slice Error (Actual – Predicted) V007, 1mm 87 89 -2 slices, -2 mm B003, 3mm 26 28 -2 slices, -6mm MN011, 1.5mm 53 56 -3 slices, -4.5mm MN012, 1.5mm 57 56 1 slice, 1.5mm MN014, 1.5mm 53 56 -3 slices, -4.5mm Total Error = 11 slices, 18.5mm Avg = 11/5 = 2.2 slices or 18.5 / 5 = 3.7 mm Std-Dev = 0.83 slices, 1.89 mm The advantage of the formula mode is that it is easy to implement, and quick to execute. The downside to using the formula mode is that fairly uniform shape and brain structure are required for it to work; It is not ve ry accurate because it is based off observations and recurring patterns in the data set s which will certainly be violated by at least some exceptional cases. 3.4.2 The Hough Transform with Post Processing Mode This mode switches the control to use the Hough Transform only to detect the center slice. As explained in previous sections [2], the Hough transform is used to detect eyeballs in a set of slices. Then it takes the med ian eyeball slice from the entire set of eyeball slices and adds an offset to it to get the center slice. This offset of 45mm is set Table 3. Training Set to Determine Center Slice for Formula Mode

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26 using the training sets listed in Table 4. None of the train sets for calculating the bias were used in the test set shown in the results sect ion. Like the Formula mode, this offset is a rough estimation of how far the center slice c an be from the median eyeball slice (Figure 14). The median eyeball slice is picked be cause that’s the slice that resembles to the center of the eye. Set Name, Slice Thickness Eyeball Slice numbers Actual Center Slice number Predicted Center Slice (median eyeball slice + 45mm / X mm) Error (Actual – Predicted) MRI-1, 1mm 45 – 65 98 55 + 45mm / 1mm = 100 -2 slices, -2 mm MRI-2, 3mm 15 22 33 18 + 45mm / 3mm = 33 0 slice, 0mm MRI-3, 1.5mm 22 36 60 29 + 45mm / 1.5mm = 59 1 slices, 1.5mm Total Error = 3 slices, 3.5mm Avg = 3/3 = 1 slice or 3.5 / 3 = 1.16 mm Std-Dev = 1 Slices, 1.04 mm Table 4. Training Set to Determine Bias Value for Hough Transform

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27 This mode of center slice detection however, is more accurate than the formula mode because the added offset is fairly fixed due to the anatomy of the human brain. As a result you get more accurate results than the formu la mode, but more overhead in processing time and memory usage. To reduce this o verhead, only slices that are thought to have eyeballs in them are processed instead of t he entire set: These slices are generally located in the top half of an axial MR image set. 3.4.3 Object Matching Mode In contrast to the Hough Transform mode, the obj ect matching mode takes a more direct approach to finding the center slice by matc hing deformed templates of the center slice to that of the input image. There are no heu ristics applied or any offsets added to get to the correct center slice. This increases th e accuracy of the results but also increases the overhead in performance – which according to th e results (4.3,4.4) at times can also be better than the Hough Transform mode. Just like in the Hough Transform mode, the Object Matching mode reduces some overhead in scann ing the entire data set, by using apriori knowledge about approximate locations of sl ice subsets where the center slice Figure 14. Sample Median Eyeball Slice

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28 may be found. The test sets used to train the alg orithm and get the template for center slice is given below in Table 5. Set Name, Slice Thickness Actual Center Slice number Predicted Center Slice Error (Actual – Predicted) V001, 3mm 26 26 0 slice, 0mm V002, 3mm 27 28 -1 slice, -3mm V003, 3mm 26 26 0 slice, 0mm Total Error = 1 slices, 3mm Avg = 1/3 = 0.33 slice or 3 / 3 = 1 mm Std-Dev = 0.57 Slices, 1.73 mm 3.4.4 Hybrid Mode The Hybrid mode is the most CPU intensive of all 4 modes. It uses the average of the first three modes to give the user a better solutio n. Again the images scanned by the Hough Transform and Object Matching algorithms in t he data set were chosen by apriori knowledge of the set to reduce overhead. The Hough Transfor m is performed on the first half of the data set to find the eyeball slices, Ob ject Matching is used on the other half to find a direct match to the center slice, and these two results along with the formula result are combined to obtain a solution. Since Formula, Object Matching, and Hough Transform modes are used to find a result for the H ybrid Mode, the training set for the Hybrid Mode (Table 6) consists of the training sets of all 3 previous modes. Table 5. Training Set for Object Matching

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29 Set Name, Slice Thickness Actual Center Slice number Predicted Formula Center Slice Error (Actual – Predicted) V007, 1mm 87 89 -2 slices, -2 mm B003, 3mm 26 28 -2 slices, -6mm MN011, 1.5mm 53 56 -3 slices, -4.5mm MN012, 1.5mm 57 56 1 slice, 1.5mm MN014, 1.5mm 53 56 -3 slices, -4.5mm MRI-1, 1mm 98 100 -2 slices, -2 mm MRI-2, 3mm 33 33 0 slice, 0mm MRI-3, 1.5mm 60 59 1 slices, 1.5mm V001, 3mm 26 26 0 slice, 0mm V002, 3mm 27 28 -1 slice, -3mm V003, 3mm 26 26 0 slice, 0mm Total Error = 15 slices, 25mm Avg = 15/11 = 1.36 slice or 25 / 11 = 2.27 mm Std-Dev = 1.12 Slices, 2.02 mm Table 6. Training Set for Hybrid Mode

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30 CHAPTER 4: RESULTS 4.1 Mode 1: Formula The test set-up configuration consisted of a des ktop machine running the Java MriSeg system. There were a total of 9 – 1.5mm data sets that were used for the purpose of testing the formula mode. In each case, an actual (truth) center slice was obtained manually by visual inspection of the data. A secon d center slice as predicted by the formula mode was also calculated to generate the er ror from ground truth. This error was compared to the ground-truth error (always 0), and other associated statistics were calculated (Table 7). A scatter plot of the error is also shown in Figure 15.

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31 Data Set Total # Slices Formula Center Slice Actual Center Slice Error Formula (Actual – Predicted) Error Ground Truth Difference (Error GT – Error Formula) Rank MN015 96 56 55 -1 0 1 1 MN016 96 56 52 -4 0 4 3.5 MN017 96 56 50 -6 0 6 6.0 MN018 96 56 49 -7 0 7 8.0 MN021 96 56 58 2 0 -2 2.0 MN022 96 56 61 5 0 -5 5.0 MN023 96 56 60 4 0 -4 3.5 MN025 96 56 63 7 0 -7 8.0 MN029 96 56 49 -7 0 7 8.0 TOTAL Error = 50 slices, 75mm Avg = 50 / 9 = 4.78 slices Or 75/9 = 8.3mm StdDev = 2.22 slices Or 3.33 mm R+ = 26.5 R= 18.5 T = 18.5 MN015 MN016 MN017 MN018 MN021 MN022 MN023 MN025 MN029 -8 -6 -4 -2 0 2 4 6 8 Data SetError from Truth(slices)Formula mode Error Scatter Plot Table 7. Results Using Formula to Predict the Center Slice Figure 15. Formula Mode Error Plot

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32 The Formula mode was discussed in detail in s ection 3.4.1. The Data sets used above for testing are all 1.5mm sets, which means they ha ve 96 slices. The center slice predicted by the formula for all these sets is a fi xed value of slice number 56. Although this number is very close to the truth most of the time, there are cases where the predicted result 56 was as much as 7 slices away. This is be cause the dimensions of the human skull vary from one subject to another and a determ inistic solution maybe close but not accurate at all time. A significance test using the Wilcoxon Signed-Ra nks test revealed a minimum Rank (T-value) of 18.5. A lookup in the Wilcoxon Signed -Ranks test critical Z values table for N=9, and confidence level = 0.05 reveals a critical value of 5. The minimum sum of ranks T=18.5 falls above 5 and so we fail to reject the null hypothesis which states that the algorithm produced results that were close to g round truth. 4.2 Mode 2: Hough Transform with Post Processing The test set-up configuration consisted of a des ktop machine running the Java MriSeg system. There were a total of 12 – 1.5mm data sets that were used for the purpose of testing the formula mode. In each case, an actual (truth) center slice was obtained manually by visual inspection of the data. A secon d center slice as predicted by taking the median of all Hough Transform eyeball slices wa s also calculated to generate the error from ground truth, and other associated stati stics.

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33 Data Set Total Slices HT Eyeball Slices Predicted CS = Median HT Slice + 45mm/1.5mm Actual Center Slice Error (Actual – Predicted) Error Ground Truth Diff Rank MN011 96 17,18,19 20,21,22,23 24, 25,26,27,28,29,30 25 + 30 = 55 53 -2 0 2 3.0 MN012 96 14, 28,29, 30, 31,32,33 34, 35 36, 37, 38,39,40,41,42, 43 38 + 30 = 68 57 -11 0 11 10.0 MN014 96 14 15,16,17,18,19,20 21, 22 23 24,25,26 27,28 43, 44 20 + 30 = 50 53 3 0 -3 4.5 MN015 96 13 14-16,17-20 21,22,23, 24 25, 26,27 33 ,41,43,44, 46 25 + 30 = 55 55 0 0 0 1.0 MN016 96 17 18,19,20,21, 22, 23,24, 25 26,27 28, 29,30,32,33 25 + 30 = 55 52 -3 0 3 4.5 MN017 96 7,8,9 10,11,12,13 1422,23,24 ,25 19 + 30 = 55 50 -5 0 5 7.0 MN018 96 17 18,19 20,21 ,22, 23,24 25,26 ,27,28, 29,47 24 + 30 = 54 49 -5 0 5 7.0 MN021 96 17-31 32,33,34,35,36, 39,41,42, 44 36 + 30 = 66 58 -8 0 8 9.0 MN022 96 25,26 27,28,29,30,31, 32, 33,34 35,36,37, 38, 39 41 32 + 30 = 62 61 -1 0 1 2.0 MN023 96 21-39 44,47 45 + 30 = 75 60 -15 0 15 12.0 MN025 96 25 26,27-34 35,36,37, 38,39,40,42, 47 38 + 30 = 68 63 -5 0 5 7.0 MN029 96 21 22,23,24,25,26 27,28, 29,30 31,32, 33,34,35 37,39,41,43,44 32 + 30 = 62 49 -13 0 13 11.0 *LEGEND Non-eyeball Slices detected by Algorithm Slices that should have been detected as eyeball sl ices by HT algorithm but weren’t. TOTAL = 72 slices or 108mm Avg = 72 / 12 = 6 slices or 108/12 = 9mm StdDev = 4.824 slices or 7.24mm R+ =72.5 R=4.5 T=4.5 Table 8. Results Using Hough Transform Mode

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34 MN011 MN012 MN014 MN015 MN016 MN017 MN018 MN021 MN022 MN023 MN025 MN029 -16 -14 -12 -10 -8 -6 -4 -2 0 2 4 Data SetError from Truth(slices)Hough Transform mode Error Scatter Plot Table 8 and Figure 16 show the results obtained from the Hough Transform Mode. In the representation above slice numbers in bold show non-eyeball slices that were detected by the HT algorithm, and slice numbers in underline -italics show slices that should have been detected by it. As explained in 3.4.2, in thi s mode – a set of eyeball slices are detected, out of which a median slice is picked and added to a fixed offset (in mm’s) to approximate the location of the center slice. A fi xed offset is used and like the formula mode this offset can cause an error in the final re sults because of the anatomy of the human brain. It can be seen in set MN012 and MN029 that the eyeball slices were detected correctly but the offset added caused an e rror of 11 slices in the detection of the center slice. The other set that had a large error associated with it is MN023: This was a Figure 16. Hough Transform Mode Error Plot

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35 case where the subject’s head was slightly tilted i n the scanner and the images did not conform to the assumptions made in 3.3.1.1. It can be seen by looking at a subset of the images given in Figure 17 that the images were tilt ed along the coronal and axial planes and the images were not “centered”. In several cas es, only one eyeball can be seen – an important note since the HT algorithm only detects eyeballs in pairs. A significance test using the Wilcoxon Signed-Ra nks test revealed a minimum Rank (T-value) of 4.5. A lookup in the Wilcoxon SignedRanks test critical Z values table for N=12, and confidence level = 0.05 reveals a critical value of 13. The minimu m sum of ranks T=4.5 falls below 13 and so we reject the nul l hypothesis which states that the algorithm produced results that were close to groun d truth. Figure 17. Subset of MN023 Data Set

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36 4.3 Mode 3: Object Matching The test set-up configuration used was the same as for the previous mode. Again, an actually (truth) center slice is obtains by visual inspection of the data and a second center slice as predicted by the Object Matching mode is a lso calculated to generate the error (Figure 18) from the truth, and other associated st atistics. Data Set Total # Slices Object Matching Center Slice Actual Center Slice Error (Actual – Predicted) Error Ground Truth Difference Rank MN011 96 53 53 0 0 0 1.5 MN012 96 58 57 -1 0 1 3.5 MN014 96 63 53 -10 0 10 8.0 MN015 96 67 55 -12 0 12 10.0 MN016 96 51 52 1 0 -1 3.5 MN017 96 68 50 -18 0 18 11.0 MN018 96 49 49 0 0 0 1.5 MN021 96 68 58 -10 0 10 8.0 MN022 96 59 61 2 0 -2 5.5 MN023 96 50 60 10 0 -10 8.0 MN025 96 65 63 -2 0 2 5.5 MN029 96 68 49 -19 0 19 12.0 TOTAL = 83 slices or 124.5mm Avg = 83 / 12 = 6.91 or 124.5 /12 = 10.375mm StdDev = 6.9864 slices or 10.5 mm R+=59.5 R-=18.5 T=18.5 Table 9. Results Using Object Matching Mode

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37 MN011 MN012 MN014 MN015 MN016 MN017 MN018 MN021 MN022 MN023 MN025 MN029 -20 -15 -10 -5 0 5 10 Data SetError from Truth(slices)Object Matching mode Error Scatter Plot Although a comparison of the errors in Table 9 and Table 8 leads to the conclusion that Hough Transform fared better than the Object Matchi ng mode, there were cases where the Object Matching mode addressed errors associate d with tilt of the images and anatomical make up of the brain. For the MN012 dat a set in particular an error of 1 slice was found compared to 11 in Hough Transform mode. No fixed offsets are used and so this mode is independent of the anatomy of the huma n brain. Taking another look at set MN023 it can also be seen that the Object Matching mode adjusted well with the tilt of the head that caused errors in Hough Transform. Th is was due to the deformed transformations used in object matching that accoun ted for tilt and scaling of the image. The downfall of the Object Matching mode was the fa ct that it used raw edge magnitude Figure 18. Object Matching Mode Error Plot

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38 and direction of CSF to match the template to the i nput image to produce an error function that can be spoofed by other edges represe nting anatomical features of the brain. A significance test using the Wilcoxon Signed-Ra nks test revealed a minimum Rank (T-value) of 18.5. A lookup in the Wilcoxon Signed -Ranks test critical Z values table for N=12, and confidence level = 0.05 reveals a critical value of 13. The minimu m sum of ranks T=18.5 falls above 13 and so we fail to rejec t the null hypothesis which states that the algorithm produced results that were close to g round truth. 4.4 Mode 4: Hybrid Mode Center Slice Detection The test set-up configuration is the same as pre vious modes except that a total of 9 data sets were used: Sets MN011, MN012, MN014 were disca rded because they were used as training sets for the Formula Mode (Table 3). An a ctual (truth) center slice is obtained manually by visual inspection of the data. A secon d center slice as predicted by the Hybrid mode was also calculated to generate the err or from the truth, and other associated statistics. Figure 19 is a scatter plot of the error from ground truth for the Hybrid Mode.

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39 Data Set Total # Slices Hybrid Mode Center Slice Actual Center Slice Error (Actual – Predicted) Error Ground Truth Difference Rank MN015 96 58 55 -3 0 3 6.0 MN016 96 54 52 -2 0 2 4.0 MN017 96 57 50 -7 0 7 8.0 MN018 96 53 49 -4 0 4 7.0 MN021 96 60 58 -2 0 2 4.0 MN022 96 59 61 2 0 -2 4.0 MN023 96 60 60 0 0 0 1.0 MN025 96 63 63 0 0 0 1.0 MN029 96 62 49 -13 0 13 9.0 TOTAL = 33 slices or 49.5mm Avg = 33 / 9 = 3.67 slices or 49.5/9 = 5.5mm StdDev = 4.09 slices or 5.53mm R+ = 39.5 R= 5.5 T = 5.5 MN015 MN016 MN017 MN018 MN021 MN022 MN023 MN025 MN029 -10 -5 0 5 10 15 Data SetError from Truth(slices)Hybrid mode Error Scatter Plot Table 10. Results Using Hybrid Mode Figure 19. Hybrid Mode Error Plot

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40 The Hybrid mode used the results (Table 10) f rom all three modes and averaged them to get a final result. Since Object Matching compl iments the Hough Transform mode so well, the results were “smoothed” out and the avera ge error caused in this mode was a lot less than the other three. There were sets like MN 029, and MN017 where the errors caused were still significantly large because both the Hough Transform and Object Matching failed to obtain a more accurate solution. As mentioned in 3.4.4, 5.1.1, and 5.1.2 this mode is the most computationally expensive of all three but the average error caused (in slices) was 3.67 – a lot less than 6 and 6.91 caused by the Hough Transform and Object Matching respectively. Although the For mula mode had a higher mean, it had a lower standard deviation than the hybrid mode. A significance test using the Wilcoxon Signed-Ra nks test revealed a minimum Rank (T-value) of 5.5. A lookup in the Wilcoxon SignedRanks test critical Z values table for N=9, and confidence level = 0.05 reveals a critical value of 5. The minimum sum of ranks T=5.5 falls above 5 and so we fail to reject the null hypothesis which states that the algorithm produced results that were close to groun d truth. 4.5 Time and Speedup Issues All the tests related to processing time were ru n on a machine with a 2Ghz, 64-bit AMD Athlon processor, and 512MB RAM. Results may v ary as future tests are run on different machines with a different configuration. It was found that on an average the Hough Transform mode took about 45 seconds worth of processing time per slice, this means that it took roughly 27 minutes of processing time to go through a 1.5mm Data set according to the heuristics listed above. By contr ast, the Object Matching Mode only

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41 took 5 seconds per slice and about 5 minutes to run through the same data set. This is a significant speed up and is due to less processing required in going through 4 dimensional arrays / parameter spaces in the Hough Transform Mo de. The Formula Mode responds the fastest with a result because the center slice is produced based on a simple arithmetic computation, with the Hybrid Mode coming in last fo r processing time required because it utilizes both Hough Transform and Object Matchin g to produce a final result. On an average, the Hybrid Mode used up about 25-35 minute s of processing time to get an answer but was also the most accurate of all the 4 modes.

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42 CHAPTER 5: CONCLUSIONS AND FUTURE WORK 5.1 Conclusions This Thesis discusses an attempt to use known im age processing techniques along with some post processing to detect the center slice (a slice through lateral ventricles in the axial plane) in a set of MRI images. It uses a var iant of the Hough Transform procedure, along with some Object Matching techniques, and som e known heuristics about the human brain and MRI images to accomplish the task, from which other segmentation algorithms take over and segment the center slice t o separate the different anatomical features of the brain. The system operates in sev eral different modes to give the operator flexibility in choosing between processing speed an d accuracy of results. All the modes complement each other well in accuracy and speedup and can work independently or in a hybrid mode to obtain the solution. The results above show that of all four modes, t he hybrid and formula mode produced results that seemed to most closely match to ground truth. The Hough Transform and Object Matching standalone modes worked well in cer tain cases and failed to work in certain others, but managed to work well together i n the hybrid mode because of one mode’s ability to generate accurate results when th e other failed. However looking at the mean error from the Object Matching and Hough Trans form standalone modes, one can tell that they did not perform as well as the other two modes, which is why they were ruled out of from the next step in our analysis. T he Wilcoxon Signed-Ranks test was

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43 used to break the close tie in performance of the f ormula and hybrid modes. The results from the test are shown in Table 11. Data Set Total # Slices Error Hybrid Mode Error Formula Mode Difference Rank MN015 96 3 1 -2 3.5 MN016 96 2 4 2 3.5 MN017 96 7 6 -1 2.0 MN018 96 4 7 3 5.5 MN021 96 2 2 0 1.0 MN022 96 2 5 3 5.5 MN023 96 0 4 4 7.0 MN025 96 0 7 7 9.0 MN029 96 13 7 -6 8.0 R+= 30.5 R= 13.5 T = 13.5 The test revealed a minimum Rank (T-value) of 26. 5. A lookup in the Wilcoxon Signed-Ranks test critical Z values table for N=9, and confidence level = 0.05 reveals a critical value of 5. The minimum sum of Ranks T=13 .5 falls above 5 and so we fail to reject the null hypothesis which states that both a lgorithms performed equally well. However, given then speedup in processing time that the formula mode has over the hybrid mode – it can be safely inferred that the fo rmula mode worked better than the other 3 modes and also produced results that were e quivalent to the ground truth. Table 11. Wilcoxon Test on Hybrid and Formula Mode

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44 5.2 Future Work In the test cases used to generate results in Ch apter 4 the CS detect tool generated an average error of 5 slices (7.5mm) from truth amongs t all 4 modes. All these results were based on a standard set of parameters used for the operation of HT and Object Matching modes. Switching the input parameters in some cas es resulted in a better or worse solution. For future work, use of statistical tool s can be implemented to calculate a “goodness of the parameters” based on the results o btained; this would cause more computational overhead but can produce even more ac curate results than any of the other modes listed above. More deformations can also be implemented in the Object Matching using Deformable Templates mode by switching parame ters to guarantee a better result in test cases such as MN023 (Figure 20) where scaling and tilt of the image can cause a problem. The code is as optimized as it can be in terms o f speedup and memory usage: Dynamic memory allocation is used to allocate and free memo ry; excessive loops are avoided but in some cases it was necessary to loop through 3 an d 4 dimensional data structures and parameter spaces created by the Hough Transform. H owever measures can be taken in those areas as more advanced image processing algor ithms are developed to reduce the overhead and increase the accuracy of solutions [13 ][14][15].

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45 REFERENCES [1] A.K. Jain, Y. Zhong, and S. Lakshamanan, “Objec t Matching Using Deformable Templates,” IEEE Trans. Pattern Anal. Machine Intel l., vol. 18, no.3, pp. 267-278, Mar. 1996. [2] M. Kass, A. Witkin, and D. Terzopoulos, “Snakes: Ac tive Contour Models,” Int. J. Comput. Vis. vol. 1, pp. 321–331, 1988. [3] H. Staib and J. S. Duncan, “Boundary Finding Wi th Parametrically Deformable Models,” IEEE Trans. Pattern Anal. Machine Intell. vol. 14, pp. 1061–1075, Nov. 1992. [4] K. F. Lai and R. T. Chin, “Deformable Contour: Modeling and Extraction,” IEEE Trans. Pattern Anal. Machine Intell. vol. 17, pp.1084–1090, Nov. 1995. [5] Dinggang Shen*, Edward H. Herskovits, and Chris tos Davatzikos, “An AdaptiveFocus Statistical Shape Model for Segmentation and Shape Modeling of 3-D Brain Structures”, IEEE TRANSACTIONS ON MEDICAL IMAGING VOL. 20, NO. 4, APRIL 2001. [6] “A computational approach to edge detection.” J ohn Canny. "IEEE Trans. Pattern Anal. Machine Intell., vol. PAMI-8, pp. 679-697, 19 86. [7] P.V.C Hough, “Method and Means for Recognizing Complex Patterns,” U.S. Patent 3069654, 1962. [8] D.H. Ballard, “Generalizing the Hough Transform to Detect Arbitrary Shapes”, Pattern Recognition, vol.13, no.2, pp. 111-122, 198 1. [9] Lawrence Hall, Lynn M. Fletcher – Heath, Dmitry Goldgof, F. Reed Murtagh, “Automatic Segmentation of Non Enhancing Brain Tumo rs in Magnetic Resonance Images”, Artificial Intelligence in Medicine, V. 21, pp. 4363, 2001. [10] Lawrence Hall, Matthew C. Clark, Dmitry Goldgo f, F. Reed Murtagh, Robert Velthuizen, Martin S. Silbiger, “Unsupervised Brain Tumor Segmentation Using Knowledge Based and Fuzzy Techniques”. Fuzzy and N euro-Fuzzy Systems in Medicine, Ed. H-N Teodorescu, A. Kandel, L.C. Jain, pp. 137-169, 1998.

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46 [11] Lawrence Hall, Matthew C. Clark, Dmitry Goldgo f, F. Reed Murtagh, Robert Velthuizen, Martin S. Silbiger, “MRI Segmentation U sing Fuzzy Clustering Techniques”, Engineering in Medicine and Biology Magazine, IEEE. Volume 13, Issue 5, Nov.-Dec. 1994 Page(s):730 – 742. [12] Matthew C. Clark, “Knowledge Guided Processing of Magnetic Resonance Images of The Brain”, Doctoral Thesis, Dept. of Computer S cience and Engineering, University of South Florida, May, 1998. [13] Raymond K.K. Yip, Dennis N.K. Leung, Stephen O Harold, “Line Segment Pattern Hough Transform For Circles Detection Using A 2-Dim ensional Array”, Department of Electrical Engineering, City Polytechnic of Hong Ko ng. Industrial Electronics, Control, and Instrumentation, 1993. Proceedings of the IECON '93., International Conference on 15-19 Nov. 1993 Page(s):1361 1365 vol.3. [14] Luciano Da Fontoura Costa, Doron Ben-Tzvit, Ma rk Sandlert, “Performance Improvements to the Hough Transform”, Kings College University of London, UK. University of Sao Paolo, Brazil. UK IT 1990 Confere nce 19-22 Mar 1990 Page(s):98 – 103. [15] Olivier Strauss, “Reducing the Precision / Unc ertainty Duality in the Hough Transform”, LIRMM. Image Processing, 1996. Procee dings., International Conference on Volume 1, 16-19 Sept. 1996 Page(s):967 970 vo l.2. [16] Zhone Xue, Stan Z. Li, Eam Khwang Teoh, “Effic ient Object Matching Using Affine – Invariant Deformable Contour”, Pattern Rec ognition Conference 2000, Proceedings. 15th International Conference on Volume 1, 3-7 Sept. 20 00 Page(s):672 – 675. [18] Milan Sonka et al, “Image Processing, Analysis and Machine Vision”, PWS/ITP 1999. [19] Leow, A.; Ming-Chang Chiang; Protas, H.; Thomp son, P; Vese,L.; Huang, H.S.C., “Linear and non-linear geometric object matching wi th implicit representation” Pattern Recognition, 2004. ICPR 2004. Proceedings of the 17th International Conference on Volume 3, 23-2 6 Aug. 2004 Page(s): 710-713 Vol.3. [20] Dong-Gyu Sim; Oh-Kyu Kwon; Rae-Hong Park, “Obj ect matching algorithms using robust Hausdroff distance measures”, Image Processi ng, IEEE Transactions on Volume 8, Issue 3, March 1999 Page(s): 425-429. [21] Koshimizu, H.; Murakami, K.; Numada, M., “Glob al feature extraction using efficient Hough transform”, Industrial Applications of Machine Intelligence and Vision, 1989., International Workshop on 10-12 April 1989 P age(s): 298-303.

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47 [22] Demsar, J., “Statistical Comparisons of Classi fiers over Multiple Data Sets”, Journal of Machine Learning Research 7 (2006) 1-30.


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