Registration of X ray mammograms and 3 dimensional speed of sound images of the female breast

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1 Diploma Thesis 2008 Registration of X ray mammograms and 3 dimensional speed of sound images of the female breast by Marie Holzapfel - Student number: Course: TIT05ANS - Company: Forschungszentrum Karlsruhe Advisor: Dr. Nicole Ruiter

2 Declaration I hereby declare that the following work was autonomously created by me without the use of any unauthorized resource, or resource other than those denoted in the bibliography section. Karlsruhe, September 18, 2008

3 Abstract Breast cancer is the most common type of cancer for women in Europe and North America. The established screening method to detect breast cancer in an early stage is X ray mammography, though X ray cannot render tumors located within glandular tissue. A new approach is 3D Ultrasound Tomography rendering three dimensional speed of sound images. The aim of this work was to construct a tool to evaluate of the clinical applicability of three dimensional speed of sound images by automatically overlaying (registering) the images with the corresponding X ray mammograms. The challenge of this diploma thesis was that X ray mammograms show two dimensional projections of a deformed breast whereas speed of sound images render a three dimensional non deformed breast. This conflict requires estimating the relation between deformed and non deformed breast and applying the deformation to the three dimensional speed of sound image. This deformation is determined by a compression simulation based on a biomechanical model. After a successful estimation of the compression by a finite element method, the contours of the X ray mammogram and the projected speed of sound image overlap congruently. After implementing this registration in MATLAB and Java, the quality of the total overlap is evaluated by measuring the overlap of a tumor marked in both modalities. Using four test datasets, the evaluation of the registration resulted in an average tumor overlap of 97%. The average distance between the marked centers of the tumors was 7.3 mm. These initial evaluation results are very promising. The developed registration tool provides a basis for a systematic evaluation of the new modality of three dimensional speed of sound images. This can allow for a greater understanding of tumor depiction in these images and thus contributes to the efforts against breast cancer mortality.

4 Contents 1 Introduction Motivation State of the Art Tasks and Goals Fundamentals The Modalities X ray Mammography Ultrasound Tomography Registration Normalized Mutual Information Simulation Model Finite Element Method Realization Basic Conditions Preprocessing The Form of the Image Image Preprocessing Global Alignment Step 1: Projection of a Speed of Sound Image Step 2: Cropping the Images Step 3: Estimation of the Projection Angle Biomechanical Model i

5 3.5 Simulation Estimation of the Thickness of the Breast Registration Graphical User Interface Evaluation Results Different Image Formats Segmentation Datasets Dataset Dataset Dataset Dataset Cropping the Image New Segmentation of Speed of Sound Images Biomechanical Model and Simulation Evaluation Discussion and Conclusion Discussion of the Evaluation Results Conclusion A Appendix: Working Schedule 48 Bibliography List of Figures A C ii

6 Chapter 1 Introduction Breast cancer is the most common type of cancer for women in Europe and North America despite the efforts to decrease its mortality rates in recent years [1]. There is a 3% chance that breast cancer will be the cause of a woman s death [2]. Important factors to establish a prognosis of a woman with this disease include the size of the tumor and how far it has spread. To find breast cancer before it has spread, different screening methods are used. Screening is the process of performing medical tests to determine a disease in people who do not have any symptoms. The goal of breast cancer screening is to find a tumor which is small enough to achieve a good prognosis since the cancer has not spread yet [3]. Palpation is a screening method based on physical examination of the breast with the goal of detecting a tumor. In Germany, this screening method is performed by a gynecologist once a year beginning at the age of 30 [4]. The disadvantage of palpation is that this screening method usually detects only tumors larger than one centimeter. This means that the probability of existing metastases is already 25% [5]. From the age of 50, X ray mammography is the most common screening method [4]. It is both relatively inexpensive and accurate, and this screening method has been estimated to decrease breast cancer mortality of women over age 50 by 30% [6]. However, X ray mammography is not effective for 1

7 women with pronounced glandular tissue since X ray can not image tumors located below this high density tissue. Statistically, women with pronounced glandular tissue have a higher probability of developing breast cancer [7]. In these cases, Magnetic Resonance Imaging (MRI) is an established breast cancer screening method. Using MRI, it is possible to detect tumors in regions with glandular tissue [8]. In addition, the high sensitivity of MRI allows the detection of small tumors. However, MRI is less specific and more expensive than X ray mammography. Limited specificity means that MRI delivers false positive results by diagnosing benign structures as suspicious. In Ultrasound imaging a sound wave is emitted which is outside the range of human hearing. By measuring the reflection and attenuation of the ultrasound images can be constructed. Ultrasound is a non ionizing and low cost breast cancer screening method [9] and is most often used to clarify an suspicious tumor found by palpation or mammography, or to verify the presence of cysts [5]. 1.1 Motivation The most effective process for early detection of tumors in the breast is to combine different screening methods, thus benefiting from their respective advantages. Despite all the advantages of X ray mammography, the screening process requires the diameter of the breast to be minimized to improve the contrast of the X ray image. This deformation presents itself as a disadvantage when attempting to combine with other imaging techniques, as the results of these techniques render an image of a non deformed breast. To resolve the discrepancy between deformed and non deformed visualizations of the breast, the relationship between these two states needs to be determined. Based on the dissertation Registration of X ray Mammograms and MR Volumes [10] the present diploma thesis has the goal to combine X ray 2

8 images with a new imaging method: three dimensional speed of sound images. Three dimensional speed of sound images are generated by Ultrasound Tomography and visualize the speed at which sound travels through the recorded tissue. The breast consists of different tissues such as fatty and glandular tissue, which transmit sound at different speeds. The resulting variances in the speed of sound are used to produce an image. As sound travels faster through cancer than other tissue, this imaging method can be used to determine the presence of tumors. By combining the images produced by speed of sound imaging with those of X ray mammography, tumors may be identified without the need of surgical biopsy. In addition, the position of a tumor visible in the X ray may be localized in a three dimensional representation of a non deformed breast. 1.2 State of the Art Three dimensional speed of sound imaging is a new imaging technique to replace or support other breast cancer screening methods. Although three dimensional speed of sound imaging is not widely used, it has advantages over other screening methods. Speed of sound imaging provides a cost efficient, non ionizing and non invasive means of detecting breast cancer [9]. In addition, three dimensional speed of sound images render a non deformed breast, simplifying the localization of tumors within the breast. Due to the limited use of three dimensional speed of sound imaging, the results of this screening process have not yet been combined with the results of other breast cancer screening methods. To the author s knowledge, the registration of a three dimensional speed of sound image with an X ray mammogram has yet to be successfully accomplished. The existing approach for registering X ray mammograms and MR volumes [10] will be used to automatically combine three dimensional speed of sound images and X ray mammograms. 3

9 1.3 Tasks and Goals The task of this diploma thesis is to provide an algorithm which automatically performs a registration of two dimensional X ray images of the female breast with three dimensional speed of sound images of the female breast. Registration describes the process of accurately overlaying dissimilar displayed objects in images on each other. Successful registration therefore requires the calculation of the breast s deformation found in the X ray mammogram. This deformation then needs to be applied to the three dimensional speed of sound image. The implementation of the registration of X ray images and MR images [10] provides a basis for this assignment. The proposed implementation has to be extended to include the new modality of speed of sound images, as its functionality of the existing implementation is limited to the registration of X ray and MR images. Furthermore, this implementation can only make use of images present in RAW format. The goal of this work is to provide a dynamic interface that can accommodate different image formats and images of different modalities. After adjusting the implementation, the registration needs to be evaluated. For this purpose, datasets containing X ray and speed of sound images of the female breast have been provided by the Karmanos Cancer Institute in Detroit, USA. Using these datasets, the accuracy of the registration of tumors visible in both modalities provides the metric for the quality of this implementation. 4

10 Chapter 2 Fundamentals 2.1 The Modalities In the medical imaging field, the different types of equipment used for acquiring medical images are called modalities [11]. In this diploma thesis X ray mammography and ultrasound of the breast are considered. Images of both types are provided by the Karmanos Cancer Institute in Detroit, USA X ray Mammography To obtain an X ray mammogram, longer wavelength X ray is used in comparison to that used during radiography of bones. The X rays are absorbed differently through the various densities of human tissue and those variances can be recorded either digitally or on film. High density tissue such as glandular tissue or that of tumors is displayed brightly in the visualization. In comparison, fatty tissue appears relatively dark (examples see figure 2.1). X ray Mammograms X ray mammograms are two dimensional projections of a deformed breast (see figure 2.2). This deformation is due to the compression applied to spread the breast tissue and achieve the best possible contrast in the image. 5

11 Figure 2.1: This figure shows X ray mammograms of the right (images marked with RCC and RMLO) and the left breast (LCC and LMLO) respectively. Both breasts are recorded in cranio caudal (CC) and oblique (MLO) perspective. Glandular tissue can be seen as relatively bright whereas fatty tissue is darker. Figure 2.2: To achieve the best possible image, the breast has to be compressed between two plates during X ray mammography. This figure shows a cranio caudal projection. In the majority of cases, cranio caudal and oblique perspectives are recorded. A cranio caudal mammogram refers to the mammogram of a horizontally compressed breast, where an oblique mammogram is obtained from an angle of approximately 45. When recording a right breast the breast will appear on the right side of the 6

12 mammogram whereas the left breast will be shown on the left side of the mammogram (see figure 2.1). The X ray images provided by the Karmanos Cancer Institute are analogical mammograms saved as a 8 bit graphic in TIFF [12] format. They are segmented in object and background, where the background is set to the maximum grey value (white). The resolution of the X ray mammograms is mm per pixel Ultrasound Tomography Speed of sound images are acquired by Ultrasound Tomography. Tomography is an imaging method that creates a three dimensional object by recording individual sections of an object. The speed of sound images provided by the Karmanos Cancer Institute were acquired by Ultrasound Tomography using a ring shaped ultrasound transducer (see figure 2.3). The breast is suspended in a water bath since water transports ultrasound waves better than air [9]. The transducer contains 256 ultrasound elements which can be switched between send and receive modes. The transmitted ultrasound wave is recorded by all of the 256 receivers. One position of the ring records a horizontal section of the breast by iteratively sending an ultrasound wave from various senders and measuring the time it needs to arrive at the receivers. By using different sending positions, more information can be acquired and an image can be constructed. To create a three dimensional image, the ring is translated away from the chest wall towards the nipple of the breast. This allows the construction of a cross sectional image (tomogram) for each step. The layering of these tomograms result in a three dimensional image. Speed of Sound Images For the acquisition of a speed of sound image, ultrasound is used. To calculate the speed at which sound travels through certain tissue, the distance the sound travels as well as the required time has to be measured. The breast is 7

13 Figure 2.3: During Ultrasound Tomography, the woman s breast is suspended in a water bath and a ring shaped transducer is translated downwards, recording multiple layers of the breast. The transducer contains 256 bidirectional ultrasound elements, i.e. they can send and receive ultrasound waves. positioned between ultrasound senders and receivers, where the positions of sender and receivers are exactly defined. Using this structure, the speed at which sound travelled through the tissue can be accurately determined and a speed of sound image can be constructed. To produce a three dimensional speed of sound image, this process has to be repeated in layers. The three dimensional speed of sound images of the Karmanos Cancer Institute are 32 bit multipage TIFF graphics with a resolution of 1 mm per pixel. Each slice has a size of 221x221 pixels and represents one recorded layer of the breast. The grey values correspond to the recorded speed of sound in that location measured in km/s. The faster the recorded speed, the brighter this area of the image appears. As sound travels faster through glandular tissue (approx. 1.5 km/s), it can be seen as fairly bright. In comparison, fatty tissue, which transmits sound at a lower speed (approx km/s), is seen as relatively dark. Examples are given in figure 2.4. Like the X ray mammograms, the speed of sound images are pre segmented. For each layer, the background of the image is set to the maximum observed grey value so that every slice of the image has a slightly different background 8

14 Figure 2.4: The figure shows a sequence of cross sectional speed of sound images of the breast. The speed of sound image consists of 70 slices (Z) corresponding to 7 cm of the breast s height. The recording starts at the chest wall and ends at the nipple. Glandular tissue can be observed as fairly bright, whereas fatty tissue is relatively dark. The bright areas around the darker object (prevalently seen in the images on the right) represent the water bath in which the breast is suspended during recording. color. 2.2 Registration In order to combine the two aforementioned modalities, the X ray and speed of sound images have to be registered. Registration [13] describes the process of accurately overlaying dissimilar displayed objects in images congruently on each other. Therefore, one image has to be transformed in comparison to a second image. The quality of the match is determined by a similarity metric. The process of transforming one image and comparing it to the second is performed iteratively until the optimum of the similarity metric is reached. When registering images produced by different modalities, certain tissue structures may have different grey values. Therefore, an appropriate similarity metric has to be used. For that purpose, Normalized Mutual Information [14] is implemented for the automatic registration. 9

15 2.2.1 Normalized Mutual Information In the majority of cases, two images obtained by different imaging techniques have a non linear relationship. To determine the similarity of those two images, Normalized Mutual Information (NMI) is the most commonly used method. Normalized Mutual Information is based on the measurement of the entropy H(X), which describes the information contained in an image X. For an image X, where p(x) is the probability that X has the grey value x, the entropy [15] is defined as H(X) = p(x)log 2 p(x) (2.1) x X If there are two images, X and Y, the joint entropy H(X, Y ) can be determined by H(X, Y ) = p(x, y)log 2 p(x, y) (2.2) y Y x X whereas p(x, y) is the probability that the grey values x and y occur together. According to Studholme [14], Normalized Mutual Information is defined as the sum of the entropy H(X) and the entropy H(Y ) divided by the joint entropy. NMI = 2.3 Simulation Model H(X) + H(Y ) H(X, Y ) (2.3) The abovementioned registration method does not take the deformation of the breast into account, caused during the process of X ray mammography. A simulation of the breast deformation is applied using a three dimensional biomechanical model. The construction of this model is based on a patient s three dimensional speed of sound image. The simulation of the compression between deformed and non deformed breast is created using the deformation information of the X ray mammogram. After applying a virtual compression to the breast to replicate that of the X ray mammogram, a two dimensional 10

16 projection of this three dimensional image can be compared to the X ray mammogram Finite Element Method To calculate and simulate the compression of the breast, the finite element method (FEM) is used [16]. FEM is a numerical technique to find a solution of a physical problem. The basic idea of the FEM is the devision of a deformable object into finite elements which are joined at discrete nodes. The desired function (strain, stress or displacement) is applied to each element influenced by internal and external conditions such as material of the node and how it is connected to others. Combined with start and boundary conditions, an equation for the simulation is formulated which is solved numerically. This solution, representing the deformation, is applied to the three dimensional speed of sound image, allowing it to be registered with the X ray mammogram. 11

17 Chapter 3 Realization This chapter provides information regarding the process of the automatic registration of three dimensional speed of sound images with X ray mammograms, as well as the implementation of this registration. 3.1 Basic Conditions The existing realization for the registration of X ray mammograms and MR volumes [10] provides Java classes for this purpose. In the field of medical imaging, the tool MATLAB is often used. MATLAB is a platform independent numerical computing environment and programming language created by The Mathworks Inc.. This tool is widely used as it allows for the easy manipulation of matrices. The easy manipulation of matrices simplifies image processing and is therefore a requirement for this thesis. To make use of the previously existing Java classes, they have to be called from MATLAB and the parameters needed for the automatic registration are provided by MATLAB. As outlined in chapter 2.1 the datasets provided by the Karmanos Cancer Institute are 8 and 32 bit pre segmented graphics. The existing Java classes make only use of certain data formats and the images used for the registration have to be present in a certain form regarding the segmentation. These con- 12

18 ditions require adjustments of the given images as described in the following chapter. 3.2 Preprocessing To provide the images in a form able to be further processed by the Java classes, they have to be adjusted first The Form of the Image The existing program for the registration of X mammograms and MR volumes can only process images present in RAW format. Data stored in RAW format is not compressed, optimized or interpreted. This means that a RAW file simply stores a byte array since no further information is needed. If image information is stored in a RAW file, the number of bits used to describe the grey value of one pixel have to be known. This is due to the fact that 8 bit graphics only need one byte per grey value, whereas 32 bit graphics need four bytes. This information is important in order to retrieve the image information from the RAW image file. Every image format stores its information in a different manner. That is due to the additional information needed to retrieve the image information, e.g. the bits used to store one pixel or the applied compression. This information has to be added to the file. Therefore, every image format would require a different method to obtain the information stored in an image. To simplify this process, the image information is held in a matrix in MATLAB. The advantage of this approach is that the images can be easily preprocessed in MATLAB and then passed to Java in an array. As described in chapter 2.1, the speed of sound images are multipage TIFF graphics. This format consisting of different layers, requires the creation of a three dimensional matrix in MATLAB. This matrix has the same dimensions as each layer of this multipage TIFF and a third dimension set to the number of layers this image contains. Each layer is iteratively saved in this 13

19 matrix. For the X ray mammogram a two dimensional matrix is created, having the dimensions of the X ray mammogram. The image information is retrieved from the X ray mammogram and stored in this two dimensional matrix. One factor to be considered during the registration, is the orientation of the breast described in chapter 2.1. If the left breast is recorded, it is shown on the left side of the image whereas the right breast is shown on the right side of the image. These differing orientations result in different search areas for performing the automatic registration. To simplify the registration, the orientation of the breast is made consistent by rotating the images. After this rotation the chest wall is always at the top of the image and the search area is similar for mammograms of left and right breasts Image Preprocessing For further processing of the speed of sound and X ray images, they have to be segmented into object and background. The Karmanos Cancer Institute provides a segmentation as described in chapter 2.1. This segmentation has disadvantages as the color of the background, white, can have different corresponding grey values. The grey value of a color is dependent upon the bits used to store this grey value. In an 8 bit graphic, a white pixel is described with the grey value 255, however, in a 16 bit graphic it is This leads to difficulties in differing properly between background and object as the grey value of the background is not consistent. To simplify this differentiation, the background of speed of sound and X ray images is set to black, which corresponds to the grey value 0 in any graphic format. This new segmentation is based on the assumption that the first pixel in the upper left corner of an image belongs to the background. For each slice of the speed of sound multipage image and for the X ray mammogram, the grey value of this pixel is determined and every other pixel with this grey value is set to 0. This process can also affect single pixels within the object. To avoid this 14

20 problem, a closing operation is performed. Closing is a morphological operation which removes small holes in images. This complete process allows an easy differentiation between object and background. 3.3 Global Alignment With the abovementioned adjustments, the speed of sound and its corresponding X ray image are passed to the Java code in the form of method parameters. The first part of the implementation is to determine the initial alignment of speed of sound and X ray images. Initial alignment means that the amount of the breast tissue shown in the X ray mammogram and in the projected three dimensional speed of sound image are matched on each other. Furthermore, the angle of this projection has to be determined. The process of projecting the speed of sound image is described in the following section and a schematic overview is given in figure Step 1: Projection of a Speed of Sound Image The first step of aligning the speed of sound with the X ray image, is to calculate the two dimensional projection of a three dimensional speed of sound image. This image is similar to the projection used in the corresponding X ray mammogram. This requires that the image is rotated by the angle given by the type of mammogram. For a cranio caudal mammogram this angle is 0, respectively 45 for an oblique mammogram. To obtain a two dimensional projection, each slice is rotated and projected. One slice generates one line in the projection. Thus, the entire projection consists of single lines creating a two dimensional image (see figure 3.2). In order to match the contours of this two dimensional projection and the X ray mammogram on one another, an additional process is required. 15

21 Figure 3.1: The process of the global alignment of speed of sound and X ray image is carried out in different steps. First, the speed of sound image is projected and compared to the X ray mammogram which is iteratively cropped in order to achieve the same amount of breast tissue in both images. Afterwards, this cropped image is compared to the projection of the speed of sound image to estimate the projection angle used during X ray mammography. The angle for the projection of the speed of sound image is changed iteratively. The result of the global alignment is the cropped X ray mammogram and the proper projection of the speed of sound image (green). 16

22 Figure 3.2: A three dimensional speed of sound image (here presented by its finite element model) is projected and results in a two dimensional image. This image is similar to the projection shown in the corresponding X ray mammogram regarding the projection angle Step 2: Cropping the Images Different modalities may record different amounts of breast tissue. When using X ray, tissue compressed between the plates is recorded. The amount of tissue recorded in a speed of sound image is dependent upon the starting position of the ultrasound transducer in regards to the chest wall. If the ultrasound transducer has an offset to the edge of the ring described in chapter 2.1.2, parts of the breast are not recorded. This results in the necessity to crop the X ray image as it shows a larger amount of tissue than the speed of sound image. In the existing implementation, the three dimensional MRI images show a larger amount of tissue than the two dimensional images. However, in this diploma thesis the three dimensional speed of sound images show a smaller amount of tissue than the X ray mammograms. This discrepancy requires an adjustment to the existing implementation. 17

23 The differing resolutions of X ray mammograms and speed of sound images require one image to be scaled. This process is not based on the scaling of the entire image but only the shown breast. Using the difference between background and object in the segmented images the shape of the shown breast can be easily determined. Line by line, the width of the breast is compared to the corresponding width of the other modality and is then scaled by this ratio. The same process is carried out for the height of the breast. The resulting scaled image has the same contour as the corresponding image. To determine the position to crop the X ray image, it is cropped iteratively. The accurate position is found by searching the image within a range beginning at 70% of the X ray mammogram s length and ending at its full size. For each iteration, the cropped image is compared to the projection of the speed of sound image, which is scaled to the current size of the X ray mammogram. The quality of this comparison is determined by Normalized Mutual Information (see chapter 2.2.1). The X ray mammogram is then cropped at the position determined by the aforementioned process, delivering the highest NMI value Step 3: Estimation of the Projection Angle To achieve a global alignment of X ray mammograms and the projections of speed of sound images, the next step is to determine the accurate angle used while recording the X ray mammogram. Since variations of this angle can occur due to recording errors or in an effort to improve the quality of a mammogram, angles ± 10 are examined. Therefore, the projection of the speed of sound images is performed with angles ranging from -10 to 10 based on the angle given by the type of mammogram. Each projection is compared to the cropped image of the previous step and their similarity is again determined by the best NMI value. The projection angle which delivers the best result when compared to the original X ray mammogram is the angle used during recording. Applying this angle to the projected speed of sound image and cropping 18

24 the X ray image, an initial alignment is determined. This alignment is fundamental for the creation of the biomechanical model that this automatic registration is based upon. 3.4 Biomechanical Model The biomechanical model is built upon the three dimensional speed of sound image. The initial alignment (see chapter 3.3) of both images from the first part of the automatic registration is applied to the three dimensional image. The creation of the biomechanical model requires the three dimensional speed of sound image to be segmented. In the existing implementation [10] this segmentation is performed to differ between skin, glandular and fatty tissue. As the speed of sound images provided by the Karmanos Cancer Institute show many artifacts, it is difficult to set ranges of grey values corresponding to certain tissue. This is due to the high grey values of these artifacts which would result in associating these grey values with glandular tissue. Furthermore, a differentiation between various tissue does not affect the results of the simulated deformation [10]. For these reasons, the speed of sound image is segmented into background and object, whereas finite elements are created for the object only, without considering the different tissue parameters for the single finite elements within the object. The resulting biomechanical model has the shape of the breast shown in the three dimensional speed of sound images and consists of 6 3 finite elements. 3.5 Simulation To formulate the compression applied while recording the X ray mammogram, boundary conditions for the FEM simulation (see chapter 2.3.1) have to be created. The formulated equation is then computed by Ansys [17], a commercial software to solve FEM simulations. As the force to deform the breast during the X ray mammography is not 19

25 recorded, the boundary conditions have to be formulated by two compression plates. These plates are added to the biomechanical model. The compression is formulated by moving the plates until a certain deformation is achieved (see figure 3.3). This deformation is defined by the estimated thickness of the breast while recording the X ray mammogram. Figure 3.3: This figure shows the biomechanical model consisting of finite elements. To formulate boundary conditions for the FEM simulation of the breast deformation, compression plates are added and moved until a certain compression is achieved Estimation of the Thickness of the Breast The thickness of the breast during the compression of the X ray mammography needs to be known in order to determine the termination condition for the FEM simulation. Since the overall compression is not known, the thickness has to be estimated using the data given by the X ray mammogram and the speed of sound image. This estimation is based on the assumption that the volume of the breast before and after compression is equal. The shape of the breast is approximated by a semi ellipsoid, hence the volume of the breast is determined by V = π x y z = 1 πxyz (3.1) 12 20

26 whereas x, y, z are the axis diameters of the breast. Equating the volume of the breast before (V n ) and after compression (V c ) leads to V n = V c and consequently to 1 12 πx ny n z n = 1 12 πx cy c z c (3.2) whereas x n, y n, z n are the axes of the non deformed breast before compression and x c, y c, z c are the axes of the breast after compression. Here y c presents the thickness of the breast after compression since y c is the dimension not visible in the X ray mammogram. Hence, the thickness of the breast can be approximated as follows: y c = x ny n z n x c z c (3.3) In the following simulation, the compression plates (see figure 3.3) are moved until the thickness of the biomechanical breast model between the plates is equal to the estimated thickness. 3.6 Registration The registration of X ray mammograms and three dimensional speed of sound images is carried out using a plate compression simulation. After simulating the deformation of the breast while recording the X ray mammogram, the resulting speed of sound image shows the applied deformation. Afterwards, the speed of sound image is projected (see description 3.3.1) and the corresponding X ray mammogram is aligned to this projection. Ideally, pixels with same coordinates show the same projected tissue particles of the breast. The registration is carried out using the nipple position to align both images in x direction (left to right) and the mean position of the chest wall to align in z direction (nipple to chest wall.) To be able to assign the location of a tumor in the three dimensional speed of sound image directly to 21

27 the X ray mammogram, the resolution of the X ray mammogram is reduced to equal that of the speed of sound image (see figure 3.4). Figure 3.4: The compression simulation makes use of a biomechanical model of the speed of sound image. The compression is calculated in Ansys and the resulting deformation is applied to the speed of sound image. Afterwards, the deformed speed of sound image is projected and registered with the X ray mammogram. 22

28 To refine these results, the simulation described in chapter 3.5 and the registration of the deformed speed of sound image with the X ray mammogram is executed twice. In the former implementation [10], the Java classes which realize this process were called two times. This approach results in avoidable double executions of parts of this implementation. For example, the segmentation of the speed of sound image into background and tissue is carried out redundantly in order to create the non deformed biomechanical model. To save computing time and make use of results which are already calculated, the Java process is stopped until the simulation with Ansys is finished. If the results of the simulation are available, the process is continued. As Ansys can not be started from Java, the user has to start the simulation with Ansys manually after the global alignment in order to continue the registration process. To reduce the workload of the user, a graphical user interface is provided. 3.7 Graphical User Interface A graphical user interface (GUI) is made available as it simplifies the registration process. The entire registration process requires the compression simulation to be executed twice in order to refine the result. To avoid redundant calculations, the process has to be stopped until the simulation delivers the compression result. With the help of a GUI, the user can manually restart this registration process after the simulation. Furthermore, the GUI allows the user to reconstruct the registration process as information regarding the status of the process is provided to the user in form of images or status messages (see screenshot in figure 3.5). A requirement for this diploma thesis was the usage of MATLAB to simplify processing of the input images (see chapter 3.1). This requires the user to start the GUI from MATLAB. After the preprocessing of the speed of sound and X ray images in MATLAB as described in 3.2.2, the user can start the registration process. This process is interrupted when the compression sim- 23

29 Figure 3.5: The graphical user interface provides information about the registration process. Furthermore, the Java process can be restarted if it is stopped in order to compute the compression simulation in Ansys. ulation has to be calculated by Ansys. After finishing this simulation, the user can continue the Java registration process until a registration of X ray mammograms and three dimensional speed of sound images is achieved. The quality of this registration then needs to be evaluated. 3.8 Evaluation The adjusted automatic registration of three dimensional speed of sound images and X ray mammograms of the female breast needs to be evaluated. The quality of the entire registration can be estimated by the accuracy of the registration of tumors visible in both modalities. For this purpose, the datasets provided by the Karmanos Cancer Institute are images containing a tumor. These tumors are marked by manually selected points within the 24

30 tumor. For speed of sound images three dimensional coordinates are used, whereas tumors visible in the X ray mammogram are marked by the according two dimensional coordinates. The points to mark the tumor are selected around the outer circumference of the tumor. In case of X ray mammograms, four points represent the vertices of a rectangle which contains the tumor and one point is in the middle of the tumor. For the speed of sound images, nine points are used. Eight of the selected points are the vertices of a cuboid surrounding the tumors, the ninth point represents again the center of the tumor. Changes in the condition of speed of sound and X ray images (for example due to the calculated deformation of the three-dimensional image) are applied to the selected points. If the entire registration is estimated correctly, the tumor visible in the X ray mammogram precisely matches the tumor visible in the projection of the deformed speed of sound image. By measuring the overlap between the selected points of the X ray mammogram and the points in the deformed speed of sound image, the quality of the registration is determined. Therefore, two circles are determined for both types of images. The center of this circle is the point representing the center of the tumor and its radius is the distance to the most distant point surrounding the tumor. Each circle represents the area in which the selected tumor is located. By determining how many pixels of the entire image are located in both circles, the overlap of the tumor in the X ray mammogram and the tumor in the speed of sound image can be calculated. A second calculation to measure the quality of the registration is the euclidean distance between the centers of both circles. The best result of the registration of X ray mammograms and three dimensional speed of sound images is hence a congruent center and an overlap of 100%. 25

31 Chapter 4 Results To evaluate the success of this diploma thesis, the single parts of the automatic registration have to be verified. 4.1 Different Image Formats To provide a dynamic interface that can accommodate different image formats, the image information is made available independent of the format of the the image data. This independence is achieved by storing the image information in a matrix in MATLAB. This approach does not require further information regarding the number of bits used to store one grey value of a single pixel. One grey value is stored in the matrix as a floating point number and thus can be easily accessed. This simple access allows for the easy adjustment of the segmentation provided by the Karmanos Cancer Institute (see chapter 2.1.2). 4.2 Segmentation For the following steps of the registration process, the speed of sound images and the X ray mammograms have to be segmented into background and ob- 26

32 Figure 4.1: This figure shows the histogram of the X ray mammogram after the segmentation into background and object. The grey value 0 representing the background occurs frequently, whereas the rest of the grey values are normally distributed. ject. This segmentation is carried out as described in chapter For the X ray mammogram the segmentation results in a histogram in which the grey value 0 representing the background occurs frequently, whereas the rest of the grey values are distributed across the entire range of grey values (see figure 4.1). However, the segmentation of speed of sound images result in a different histogram. This histogram also has a peak representing the background at its corresponding grey value 0 but the grey values representing the breast are not distributed across the entire range of the grey values. The grey values for the breast range from 1.3 to 1.6 and leave a gap between 0 and 1.3 (see figure 4.2). This gap has an impact on the projection of the speed of sound images (see chapter 3.3.1) because the variations in the grey values representing the 27

33 Figure 4.2: This figure shows the histogram of the speed of sound image after the segmentation into background and object. The grey value 0 representing the background occurs numerously, whereas the rest of the grey values are distributed in a range between 1.3 and 1.6. This leads to a gap between 0 and the grey values representing the object (blue ellipse) breast are too small in comparison to the difference between background and object. When summating the grey values of a slice of the speed of sound image in order to create a two dimensional projection, the contrast between breast and background is maintained. However, the contrast between different tissue structures is not visible in the projection (see figure 4.3). As tumors have to be visible in the speed of sound image, for example in order to evaluate the quality of the registration, this segmentation needs to be changed to visualize different tissue structures in the projection. The modification of the segmentation is based on the removal of the gap between the grey values of background and object. For each slice of the speed of sound image, the minimum grey value relating to the breast is found. For each grey value of this slice, this minimum grey value is subtracted. 28

34 Figure 4.3: The projection of the speed of sound image after the segmentation shows no different tissue structures since the variations in the grey values are too small. As described in chapter 2.1.2, each slice of the speed of sound images as provided by the Karmanos Cancer Institute has a slightly differing background color. This affects the mean grey value of each slice resulting in a differentiation across all of the slices. Hence, every single line can clearly be seen in the projection of the speed of sound image. To create a homogeneous projection (see figure 4.4), the grey values of each slice are divided by the mean grey value of the current slice. These adjustments of the segmentation result in a Figure 4.4: In the projection of the speed of sound image after the improved segmentation different tissue structures are rendered and the single lines of the projection are marginally visible. histogram in which the grey values are distributed over the full range of grey values (see figure 4.5). The gap between the grey values of background and object (see figure 4.2) is removed which improves the overall contrast of the 29

35 image. Different tissue structures are rendered in the projection of the speed of sound image (see figure 4.4). Figure 4.5: This figure shows the histogram after the adjustments of the segmentation. The grey values are distributed over the entire range. The segmentation as described in chapter was modified in order to enhance the contrast of the projection of the speed of sound image. In addition, the quality of the projection is improved since the entire projection is imaged more homogeneously. The quality of the projection is crucial for the analysis of the datasets and for the comparison with the X ray mammogram. 4.3 Datasets To provide a better comprehension of the following steps, the given datasets are described in this chapter. The three dimensional speed of sound images are represented by their segmented projections. Every image shows the breast from right to left in x direction and from chest wall to nipple in y direction. 30

36 Aside from dataset 1, every X ray mammogram has a resolution of mm per pixel. The speed of sound images have a resolution of 1 mm per pixel Dataset 1 According to the Karmanos Cancer Institute, the breast of dataset 1 is dense. This leads to difficulties in recognizing tumors located below the high density tissue. For a non expert it is not possible to recognize a tumor in both,the speed of sound and X ray image (see figure 4.6). The X ray mammogram has been reviewed by a radiologist and the woman related to dataset 1 has a tumor of the size 46x20x40 mm 3 on the left side of the right breast. The resolution of the X ray mammograms differ from the other dataset and is mm per pixel. Figure 4.6: This figure shows the X ray mammogram and the projection of the speed of sound image of dataset 1. A tumor is not clearly visible in either image. 31

37 4.3.2 Dataset 2 Dataset 2 shows the left breast of a breast cancer patient. In the X ray mammogram, a tumor is clearly visible on the left side of the breast (right side of the image). In the projection of the corresponding speed of sound image, this tumor can be noticed as well (see figure 4.7). The tumor size is 35x17x35 mm 3. Figure 4.7: This figure shows the X ray mammogram and the projection of the speed of sound image of dataset 2. In the X ray mammogram, a tumor of the size 35x17x35 mm 3 is clearly visible on the left side of the breast. In the projection of speed of sound this tumor can be noticed as a slightly brighter area Dataset 3 In the X ray mammogram of dataset 3, two tumors are visible. In the projection of the speed of sound image, the bigger tumor with a size of 20x21x24 mm 3 is clearly noticeable whereas the tumor which is located closer to the chest wall can barely be seen (see figure 4.8). The speed of sound image of dataset 3 differs from the other datasets as the 32

38 distance between the single slices is 1.2 mm instead of 1 mm as in the case for dataset 1, 2 and 4. This is due to the size of the breast and the attempt to have the same number of slices for every three dimensional speed of sound image. Figure 4.8: The X ray mammogram of dataset 3 clearly renders two tumors. However, in the projection of the speed of sound image only the tumor located closer to the nipple is clearly visible; the second tumor is harder to detect Dataset 4 The right breast of dataset 4 has a large volume of glandular tissue which complicates the detection of a tumor (see figure 4.9). According to the radiologist, there is a tumor on the left side of the breast with a size of 19x15x22 mm Cropping the Image With the preceding datasets and the visual comparison between X ray mammogram and projection of the speed of sound image, the cropping of the 33

39 Figure 4.9: This figure shows the X ray mammogram and the projection of the speed of sound image of dataset 4. Both images render large amounts of glandular tissue. On the left side of the breast is a tumor of the size 19x15x22. X ray mammogram can be examined. As described in chapter 3.3.2, the position to crop the X ray mammogram is determined by scaling the projection of the speed of sound image to match the contours of the X ray mammogram and assessing the similarity between X ray mammogram and scaled projection. This similarity is measured by NMI (see chapter 2.2.1). To achieve the best NMI, the projection of the speed of sound image needs to render tissue structures similar to the structures rendered in the corresponding X ray mammogram. The adjustments of the segmentation described in chapter 4.2 supports a proper rendering of these tissue structures. The first test is carried out with dataset 3 as the tumors are visible in both, X ray mammogram and projection of speed of sound image. The X ray mammogram of dataset 3 has a length of 668 pixels (235 mm). According to chapter 3.3.2, the first position to crop the X ray mammogram is at 70% of its length. 70% of the length equates to 467 pixels (164 mm). After comparison with the scaled projection of the speed of sound image, the length of 467 pixels delivers the best NMI. This length is the estimated 34

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