MATLAB tool for evaluating the symmetry of the forehead in patients with unicoronal synostosis before and after operation.

Transcription

1 MATLAB tool for evaluating the symmetry of the forehead in patients with unicoronal synostosis before and after operation. Master of Science Thesis in Radiation Physics Author: Annelie Lindström 1/23/2011 Supervisors: Peter Bernhardt, Lars Kölby and Jacob Heydorn-Lagerlöf DEPARTMENT OF RADIATION PHYSICS UNIVERSITY OF GOTHENBURG GOTHENBURG, SWEDEN

2 Abstract Unicoronal synostosis is a condition where one of the coronal sutures, in an infant s skull, has prematurely fused. This will result in a deformed skull where the forehead is flattened on the ipsilateral side and bulges outwards on the contralateral side. The craniofacial unit at the Department of Plastic Surgery at Sahlgrenska University has continuously improved craniofacial surgery over the years. The aim of this project was to develop a MATLAB tool that evaluates the symmetry of the forehead in patients with unicoronal synostosis before and after treatment. The program will be used as a quantitative measure in a study for craniofacial surgery. The program evaluates CT images and cephalometry images of the skull. The cranium is segmented leaving only the uttermost edge of the cranium and the symmetry between the left and right side of the forehead is evaluated. By calculating the symmetry of the forehead before and after operation a quantitative measure of the outcome is achieved, and the treatment can be evaluated. The symmetry of symmetrical phantoms, both circular and elliptical, has been evaluated and the result shows that it is completely symmetrical. 15 pre-operative images and 15 postoperative images have also been evaluated and it is shown that the relative standard deviation increases for a more symmetrical cranium. The results achieved for the CT images have a lower relative standard deviation than the results achieved for the cephalometry images. The success of the operations has been evaluated with two different equations. One method calculates the absolute change and the other calculates the relative change. The relative change is demonstrated to be a better evaluation of the operation. 1

3 Table of Contents 1 Introduction Theory Digital image Digital image processing Histogram processing Spatial filtering Segmentation MATLAB Method CT images Definition of center-point, -point, and unfused side Segmentation Cephalometry images Contrast enhancement Definition of center-point, -point, and unfused side Interactive definition of the cranium Dividing the skull into two parts, one left and one right Calculation of the symmetry between the two sides Evaluation of the program Symmetry evaluation Test on symmetrical phantoms The certainty of the program Results Symmetry evaluation Test on symmetrical phantoms The certainty of the program Discussion Conclusions Acknowledgements References

4 Appix Appix I Appix II

5 1 Introduction The bones in an infant s skull are joined together by six sutures, a type of fibrous joint [1]. These sutures make it possible for the skull to compress when passing through the birth canal. They also allow the skull to expand when the brain grows. The infant s skull grows rapidly and at one year of age the brain has tripled its volume. The rapid growth requires the cranium to be able to expand. As the child gets older, and the growth of the brain is decreased, the sutures will fuse one by one. In a condition called craniofacial synostosis the sutures can fuse prematurely, days or months before birth. For these children the skull won t be able to grow at the affected suture. To compensate for the prematurely fused suture the unaffected sutures will grow in a different pattern compared to a normal skull, resulting in an abnormal shape. Deping on which suture has been fused the shape of the skull will have special features. Usually one suture is closed too early but sometimes several sutures can be closed simultaneously. The coronal suture separates the parietal and the frontal bones (Figure 1). For patients with unicoronal synostosis one of the coronals is prematurely closed [2] [3]. Unicoronal synostosis is characterized by an asymmetric forehead. On the ipsilateral side, the side where the suture has fused, the forehead is flattened and on the contralateral side the forehead bulge outwards. The face is also affected due to the abnormal shape of the forehead. The eye and the eyebrow may be pushed downward by the bulging forehead [4]. Figure 1. Image of the cranium and its sutures where the arrow points to the coronal suture [5]. 4

6 The craniofacial unit at the Department of Plastic Surgery at Sahlgrenska University has a large material of patients with synostosis. At the department many new methods in craniofacial surgery have been developed over the years. An example of a new treatment modality is stainless steel wires for implantation, which was introduced by the Gothenburg craniofacial team eleven years ago. These wires affect and guide the dynamic growth of the infant s skull. When the growth of the brain is directed and affected by the wires the skull shape is forced into normality. Today the result of an operation is evaluated by studying the patient s skull and at the x-ray images of the patient. However, this is a result that will dep on the evaluator. Therefore a quantitative measure of the result, indepent of the viewer, is preferable. A quantitative measure of the symmetry of the skull would make it possible to compare and evaluate, for example, different surgical procedures. The aim of this project was to develop a MATLAB tool that calculates the symmetry of the forehead in patients with unicoronal synostosis before and after treatment. This should be done by comparing the left and the right side of the forehead in both computed tomography (CT) and cephalometry images. The program will be used as a quantitative measure in a study where two different treatments are compared. 2 Theory 2.1 Digital image An image can be defined as a two-dimensional function f(x,y), where x and y are spatial coordinates. The intensity or gray level at the point (x,y) is the amplitude of f. It is a positive number whose value is determined by the source of the image. A digital image make up of a finite number of elements, each element has a particular location determined by the coordinates x and y, and a finite value. These elements are called picture elements also known as pixels. A digital image is stored as a two-dimensional array, a matrix, where the columns and rows corresponds to the spatial coordinates x and y respectively [6]. A digital image of size M x N can be represented as shown in equation 1. ( ) [ ( ) ( ) ] (1) ( ) ( ) 5

7 2.2 Digital image processing Digital image processing refers to processing digital images with a computer using mathematical algorithms. The basics of digital image processing are to enhance an image so that the result suits a specific application more than the original. Spatial processing refers to direct manipulation of the pixels in the image. There are two main categories, intensity transformation and filtering. These processes are methods whose inputs and outputs are images. There are other processes, like segmentation, where the inputs are images and the outputs are constituents extracted from those images Histogram processing The basis of a numerous spatial domain processing techniques is histogram processing. It can be used to enhance the contrast and other image processing applications, such as image compression and segmentation. A histogram of a digital image is a bar graph of the distribution of all gray levels. The x-axis shows the number of gray levels, and the y-axis shows the number of pixels with a particular gray level (figure 2). The histogram is often normalized by dividing each of its components by the total number of pixels. Figure 2. A histogram of a digital image where the x-axis shows the number of gray levels, and the y-axis shows the number of pixels with a special gray level. Histogram equalization is a histogram processing technique where a transformation function is automatically determined. The transformation function maps one pixel value to another 6

8 pixel value so that the output image produced has a uniform histogram with a predefined number of discrete gray levels (figure 3). Histogram equalization can be performed on the entire image as well as small regions in the image. For small regions, the histogram of the points in the neighborhood is computed and histogram equalization is performed for each location. This enhances details over small areas in the image which may not be enhanced in a global process where the number of pixels in these areas may have negligible influence. Figure 3. The equalized histogram after performing histogram equalization on the histogram in figure 2. The histogram has 64 discrete gray levels. Another way to process a histogram is to map intensity values in a manually defined range in the input image to intensity values in a manually defined range in the output image. The relationship between these ranges can be specified. Both processing techniques can be used to enhance the contrast in an image. Histogram equalization is simple to implement but it is not always the best approach to base the enhancement on a uniform histogram. Instead of enhancing the desirable details in the image the noise might be enhanced Spatial filtering Spatial filtering operates by working in a neighborhood of every pixel in an image and performs a predefined operation on the pixel encompassed by the neighborhood. The neighborhood is a matrix much smaller than the image. Filtering creates a new pixel on the same location as the pixel in the center of the neighborhood. The filter moves from pixel to pixel so that the center of the filter operates on each pixel in the input image. The value of 7

9 the new pixel deps on the filtering operation and the size of the filter. The operations can be linear or nonlinear. An output image that has been filtered with a linear filter is a linear function of the input image. Each pixel, in the output image, is a weighted sum of the neighborhood pixels encompassed by the filter in the input image. Examples of linear filters are smoothing and sharpening filters. A nonlinear filter ranks the pixels contained in the area encompassed by the filter. An example is a median filter. The median filter calculates the median value of the intensity in the pixels encompassed in the filter area and replaces the intensity in the center pixel with this value. The size of the filter decides how many neighborhood pixels are encompassed. Median filters are effective for noise-reduction, particularly on so called salt-and-pepper noise Segmentation Segmentation partitions the image into its constituent parts. The segmentation algorithms are based on basic properties of intensity values like discontinuity and similarity. Discontinuity algorithms partitions the image based on rapid changes in the intensity values. This is used for, among other things, identifying edges in the image. The assumption is that the intensity values of the boundaries and the background differ sufficiently from each other. In a low-contrast image it can be difficult to identify boundaries. The second category, similarity, uses a set of criteria that is predefined to partition the image into regions that are similar according to the criterions. Examples of this approach are thresholding, region growing, and region splitting and merging. 2.3 MATLAB MATrix LABoratory, MATLAB, is a high-performance technical computing tool optimized for matrix and vector calculations [7]. It is designed for developing algorithms, visualizing and analyzing data, and numeric computation. MATLAB can be used in a wide range of applications, for example signal, image and video processing, control systems, test and measurement, technical computing, mechatronics, financial modeling and analysis, and computational biology. 3 Method In this project MATLAB Version (2010b) was used to create a program for evaluating the symmetry of the forehead. The created program is designed for CT and cephalometry images in jpg-format. 8

10 A flow-chart can easily illustrate the overall steps in the program (figure 4). An image is loaded by choosing the file containing the particular image. As can be seen in figure 5, CT and cephalometry images have different properties. Because of that they have to be processed differently. Figure 4. The flow-chart above illustrates the overall steps in the program. 9

11 Figure 5.. Illustration of the different properties of a CT image (left), and a cephalometry image (right). 3.1 CT images For the automatic segmentation, the CT images needs to have good contrast. Bone needs to have an intensity value over 250 in the gray-scale format. It is also important that there are no bigger open areas in the edge of the cranium (figure 6). The contrast can be enhanced by changing the window-level in any CT-image evaluation program before they are saved as jpgfiles. Changing the window level will also decrease, or increase, the size of the open areas in the edge of the cranium. Figure 6. Illustration of an open area that is too big for the segmentation to be automatic. 10

12 In the program a median filter of the size 4 x 4 is used to overcome the problem with small open areas in the edge of the cranium Definition of center-point, -point, and unfused side To be able to compare the left and the right side, of the forehead, a center-point has to be defined. This is done by hand. The point is created by clicking on the spot where the user wants to divide the two sides. The coordinates are saved and used later in the program. The user also has to define how much of the skull that is of interest for the comparison, the -point. The point is defined interactively, in the same way as the center-point, by clicking on the cranium where the comparison should. This point also defines the unfused side Segmentation The program segments the image to get the uttermost edge of the cranium. The segmentation is done by threshold the intensity values in the image. Pixel values below 105 will get the intensity value zero, pixel values above 250 will get the intensity value one, and pixel values between 105 and 250 are mapped to values between zero and one. This improves the contrast in the image. Bone gets the value one and soft tissue gets an intensity value closer to zero. The image format is converted from gray-scale to binary. A binary image has two discrete intensity values, zero and one. The output image replaces all pixels in the input image with intensities greater than graythresh with the intensity value one, and replaces all other pixels with the intensity value zero.graythresh uses Otsu s method to automatically determine a threshold that suits that gray-scale image best. The value deps on the histogram belonging to the input image [8]. When the image format has been converted, the MATLAB-command imfill is used to fill the area that is enclosed by the cranium. The output image contains the cranium and the filled area enclosed by the cranium, and sometimes parts of the table the patient lays on when the image is taken. To exclude the table a ROI is placed manually around the skull (figure 7). 11

13 Figure 7. The skull with the roi to exclude the table. To get the uttermost edge of the cranium the MATLAB-command edge, with its default settings, is used to detect the edge (figure 8). Figure 8. The uttermost edge of the cranium in a CT image. 12

14 3.2 Cephalometry images The cephalometry images are originally analogous images that have been digitalized by taking pictures of them with a digital camera. The images are resized with a scale factor from size M x N to size 400 x (N scale factor). The value of the scale factor deps on M. The image needs to be resized because the original matrix is too large for the memory on the computer Contrast enhancement In many of the cephalometry images there are very small differences in the intensity values between the cranium and the background. The MATLAB-command adapthisteq, using its default settings, enhances the contrast in the image by performing local histogram equalization Definition of center-point, -point, and unfused side Definition of center-point, -point, and unfused side are performed in the same way as in section Interactive definition of the cranium The cranium cannot be segmented automatically by the program due to poor contrast. Therefore, it has to be done by hand. By clicking along the edge of the cranium points are created, and its coordinates are saved in a vector. A MATLAB-command for creating lines is recalling the vector and creating lines between the locations where the points are. The points cannot be placed further apart than eight pixels, if they are, the program deletes the latest point and the user has to click closer to the previous point. 3.3 Dividing the skull into two parts, one left and one right The coordinates from the defined center-point are used to divide the skull into two parts, one left and one right side. The two parts are handled as two images. The unfused side is also cropped at the point that defines how much of the skull that is of interest for the comparison, the -point (figure 9). 13

15 Figure 9. The segmented skull is divided into two parts, the fused side (left) and the unfused side (right). The unfused side is cropped at the -point. The image containing the left part is mirrored in a left-right direction, about a vertical axis. To be able to perform the calculations the starting point of the two curves representing the uttermost edge of the cranium, has to start in the middle of the matrix. The matrices should also have the same size. This is done by adding matrices of zeros so that the output images have the same size and the starting point is in the center of the matrix. The output matrix contains the input image H and the matrices I and J (figure 10). I and J are zero matrices where J has the same size as H, and I is of the size d x c. c is determined by calculating a-b. The distances b and a are calculated by finding the coordinates of o in the input image H. Figure 10. Schematic image of how zero matrices are added to get the center-point, o, in the middle. H is the input matrix, and I and J are matrices of zeros. 14

16 3.4 Calculation of the symmetry between the two sides The symmetry can be calculated when: 1) the two sides have been segmented, 2) the left side has been mirrored, 3) the curves start at the same point in the middle of the matrix, and 4) the matrices has the same size The program finds a point, p1, on the first curve and a point, p2, on the other curve that has the same distance, l2, to the center-point, o (figure 11). The points are found by adding a circle with radius l2 to each image. The coordinates where the circle and the curve intersect are stored as p1 and p2. If the circle intersect with more than one pixel on the curve a mean of those coordinates are stored. The distance, d, between p1 and p2 is calculated and added to the variable, s. l2 starts at one and increases in steps of one until the program has reached the -point. Figure 11. Schematic image of the points p1 and p2, and the distance d. At each step the program finds p1 and p2 and calculates d. The variable s is a sum of all the calculated distances. The total sum is saved, the curve representing the fused side is rotated one degree, and the calculations are repeated. The MATLAB-command for rotating the image is imrotate which uses bilinear interpolation. For each angle the total sum are compared with the total sum achieved for the previous angle. The curve is rotated in steps of one as long as the sum decreases. Both clockwise and anti-clockwise rotation is tested. At the position where the smallest sum is found the number of pixels, n, between the two curves is calculated. 15

17 If the left and the right side of the forehead are symmetrical n will be zero. The more unsymmetrical the sides are the bigger the value is. The value does not only dep on the symmetry but also the size of the head and the size of the pixels. To be able to compare the symmetry this value has to be indepent of these two components. It is therefore divided by the number of pixels in the area denoted K which also deps on the size of the head and the size of the pixels (figure 12). The normalized value is called the symmetry ratio, N. N is multiplied with 1000 so that the numbers won t be so small (equation 2). Figure 12. The gray area represent the area K.The area K is expressed in pixels and is used to normalize the result. The point p has the same distance, l2, to the center-point, o, as the -point. (2) Two methods, relative change (equation 3) and absolute change (equation 4), was tested as an evaluation of how well the surgical operation has succeeded. (3) 16

18 is the symmetry ratio for the pre-operative image, and is the symmetry ratio for the post-operative image for the same patient. The closer C gets to one the better the operation has succeeded. C can also have a negative value which shows that the forehead is more asymmetrical after the operation. (4) The bigger B is the better the operation has succeeded. As for C, a negative value shows that the forehead is more asymmetrical after the operation. The MATLAB code is found in appix I and a user manual is found in appix II. 3.5 Evaluation of the program The program has been run several times to evaluate the program and see how reliable the results are Symmetry evaluation The main aim for the program is to calculate the symmetry of the left and the right side of the forehead. It should give a lower value for a more symmetrical forehead. The symmetry ratio, N, was calculated for two images where it can be seen that one of the foreheads is more symmetrical than the other (figure 13). The center- and -point was placed at the same structures in both images. Figure 13. Two images where it can be seen that the forehead in the left image is more asymmetrical than the forehead in the right image. 17

19 3.5.2 Test on symmetrical phantoms A few tests was performed on a CT image of a cylindrical phantom to see if the result is zero when the two sides are symmetrical, and if the result is indepent of the rotation of the head when the image is taken (figure 14). The symmetry ratio for this image was calculated ten times. At every run the center-point and the -point was placed on different places along the uttermost edge of the circle to simulate that the head is rotated. Figure 14. The cylindrical phantom. The program was also tested on an image of a symmetrical elliptical phantom (figure 15). The image was created with the command phantom(512) in MATLAB. The image of the phantom was run through the program twenty times. The aim for the first ten runs was to place the center-point and the -point at the same points on the uttermost edge of the cranium. The aim for the last ten runs was to place the center-point at the same place for each run and vary the places where the -point was placed. 18

20 Figure 15. The elliptical phantom The certainty of the program The symmetry of the forehead for 15 patients, both before and after operation, was evaluated. Seven of these patients were CT images, and eight were cephalometry images. Each image was run ten times to see how reliable the results are. For each run the aim was to put the center-point and the -point on the same structures in the image. For the cephalometry images an additional aim was to follow the edge of the cranium as thorough as possible. The relative standard deviation, and the mean for the symmetry ratio, N, was calculated for each image. C and B in equation 3 and 4, respectively was also calculated ten times for each patient, and the mean and the relative standard deviation was determined. 4 Results 4.1 Symmetry evaluation The symmetry ratio was calculated to be 68.1 for the more asymmetrical forehead in figure 13, and 4.7 for the more symmetrical forehead in the same figure. The numbers shows that the forehead in the right image is more asymmetrical. 4.2 Test on symmetrical phantoms For every run on the circular phantom the program calculated the symmetry ratio to be zero. That is, the program evaluates the two sides to be completely symmetrical, indepent of where the points are placed along the uttermost edge. 19

21 For all twenty runs on the elliptical phantom the program calculated the symmetry ratio to be zero which means that the program evaluates the phantom to be completely symmetrical. 4.3 The certainty of the program Figure 16 shows that the relative standard deviation increases when the forehead is more symmetrical. It also shows that the cephalometry images, continuous line, have a higher relative standard deviation than the CT images, dashed line. Figure 16. The dashed line shows how the relative standard deviation changes with the symmetry of the forehead in the CT images, and the continuous line shows how the relative standard deviation changes with the symmetry of the forehead in the cephalometry images. The mean and the relative standard deviation, SD, from evaluating the operations with equation 3 and 4 are shown in table 1 and 2. Table 1 shows the results for the CT images and table 2 shows the results for the cephalometry images. A more successful operation is represented by a high value in B and a value close to one in C. 20

22 Table 1. The results, for CT images, from evaluating the operations by calculating C in equation 3 and B in equation 4, and the relative standard deviation. C SD (%) B SD (%) Table 2. The results, for cephalometry images, from evaluating the operations by calculating C in equation 3 and B in equation 4, and the relative standard deviation. C SD (%) B SD (%) The negative number in table 2 shows that the forehead is evaluated as more asymmetrical after operation than before operation. It can be seen in both table 1 and table 2 that the equations do not evaluate an operation to be equally successful. Patient six, in table 1, is evaluated to be the most successful operation of the seven patients when it is evaluated with equation 4, while it is only ranked as third best when it is evaluated using equation 3. 21

23 5 Discussion Today the result of a surgical operation on a patient with unicoronal synostosis is evaluated by studying the patient s skull and at the x-ray images of the patient. There are no clear criteria on how to evaluate the result. No clear criteria give an evaluation that is depent of the evaluator. Therefore, a program has been created as a quantitative measure to evaluate the symmetry of the forehead in CT and cephalometry images of these patients, and in the to evaluate the result of the operation. The reliability of the program has been tested on images of symmetrical phantoms and images of 15 patients before and after the operation. The poor contrast in some of the cephalometry images has caused some problems in automatically detecting the uttermost edge of the cranium. In the the solution to this problem was to do this step manually. How the points are placed deps on the user and will affect the result. If the time hadn t been limited it might have been possible to come up with a method that enhances the contrast in each image separately. This is an area which can be further developed to improve the program. Although, in some images the contrast is so poor that no enhancement technique would make it possible to segment the uttermost edge. Even if the contrast could have been enhanced so that the edge could be segmented automatically some of the pictures are in a way that the jaw is seen outside of the uttermost edge of the cranium. The edge detected in an image like that would not be the uttermost edge of the cranium but the jaw. If the program is developed to enhance the contrast in each image separately, the problem with the jaw might be overcome by a combination of automatically and manually segmentation of the edge. As can be seen in figure 16 the relative standard deviation increase when the symmetry ratio decrease. If the center-point and the -point aren t placed at exactly the same place every time, the number of pixels between the curves representing the uttermost edge of the cranium will vary. If the curves are more symmetrical the number of pixels between them will be lower and this variation will have a higher impact on the result. Figure 16 also shows that the uncertainty for the cephalometry images is considerably higher and varies more than the uncertainty for the CT images. As mentioned, the relative standard deviation increases when the symmetry ratio decreases. The curve representing the cephalometry images in figure 16 shows that this is not always the case. Although, it can be seen that despite that the values differ from what might have been expected the variation is only a few percent, and an increase of the standard deviation at lower values on the symmetry ratio can be distinguished. These variations can dep on tree things; 1) there are some distinct structures where the center-point and the -point is placed which makes it easier to place the points at exactly the same point every time, 2) the edge isn t defined as thorough for each run, and 3) if there are big changes in the curves appearances around the center-point and the -point a variation in the placement of 22

24 these points will affect the result more than if the curves is more constant around the points. Number one and number three in the previous section might also be a reason for the variations shown in the results for the CT-images in figure 16. If the skull is completely symmetrical the place where the -point is placed is less important than the place where the center-point is placed. In that case, if the center-point is placed in a way that the forehead is divided into two completely symmetrical parts the placement of the -point won t affect the result at all. This is shown by the results from the test on the elliptical phantom where it is calculated that the two sides are completely symmetrical, even if the -point is placed at different places each time. As mentioned in the result, the two evaluation methods presented in equation 3 and 4 do not evaluate an operation to be equally successful. An operation evaluated to be successful by one of the equations might be evaluated to be less successful by the other. It would have been interesting to compare the results with previous clinical evaluations but no such evaluations have been done before. If the symmetry ratio is calculated to be 70 before operation and 40 after operation, equation 4 evaluates the operation to be more successful than if the symmetry ratio is calculated to be 20 before operation and 0 after operation, even if the last operation is as successful as it can be. Equation 3 on the other hand would evaluate the last operation to be more successful than the first. By dividing the difference between the symmetry ratio before operation and after operation with the symmetry ratio before operation the result will show the relative change. The relative change allows the results for different patients to be compared even if the symmetry ratio before operation differs between the patients. If equation 4 is used an operation where the symmetry ratio before operation is high will be evaluated as a more successful operation. It seems that equation 3 is preferable for evaluation of clinical materiel, since it has an upper limit of success, i. e. C=1 means perfect operation, and C=0 means no difference, and C less than zero means that the forehead is more asymmetrical after the surgery. As discussed above equation 4 do not give this information in a clear way. In the evaluation of patient 11 in table 2, it is shown that the forehead is more asymmetrical after operation than before operation. The surgical operation has not succeeded; in fact it has worsened the symmetry of the forehead. This is shown, as discussed in the previous section, as a negative value in both evaluation methods. Both methods show a pretty low difference. Therefore, small variations between each run will affect the result more which is shown by the high relative standard deviation. As can be seen in figure 16 the relative standard deviation is relatively high for a low value of the symmetry ratio. When the absolute or the relative change is calculated the result is 23

25 dominated by the higher symmetry ratio, resulting in a relatively low relative standard deviation. An attempt has been made to increase the size of the image, not the matrix, so that the edge can be distinguished more easily when it is defined manually. When this is done something goes wrong and some parts of the edge are lost. The reason for that has not been established. Another thing that can be further developed in the program is the processing time. At the time, one image takes approximately ten minutes, which might be a problem for longer patient series. Therefore, future studies should focus on optimizing the present MATLAB code. 24

26 6 Conclusions A MATLAB tool to evaluate the symmetry of the forehead in patients with unicoronal synostosis before and after treatment has been developed for both CT and cephalometry images which was the main aim of this project. The method is also indepent of the heads rotation at the time when the image is taken. It is shown that the results are more reliable when CT images are evaluated than when cephalometry images are evaluated. The recommation for evaluating an operation is to calculate the relative change. 25

27 Acknowledgements I would like to take the opportunity to thank everyone who has helped me to complete this project. First of all I would like to thank my supervisors Peter Bernhard at the Department of Radiation Physics, and Lars Kölby at the craniofacial unit at the Department of Plastic Surgery, for their guidance and quick answers to my less questions. Also a big thank you to my supervisor Jacob Heydorn-Lagerlöf at the Department of Radiation Physics for all his help with MATLAB, and for his guidance through everything that this computing tool has to offer. Thanks to Patrik Sund at the Department of Radiation Physics, and Giovanni Maltese at the craniofacial unit at the Department of Plastic Surgery for all their help along the way. Finally, special thanks to my classmates, fris and family who has helped me, in their own special ways, to this project as well as pass my studies. 26

28 References 1. Jane, J.A. and M.S. McKisic. Craniosynostosis. Apr 2, 2010 [cited 2010 Nov 2]; Available from: 2. Podda, S., et al. Craniosynostosis Management. sep 17, 2008 [cited 2010 oct 21]; Available from: 3. Boulet, S.L., S.A. Rasmussen, and M.A. Honein, A population-based study of craniosynostosis in metropolitan Atlanta, Am J Med Genet A, A(8): p Hayward, R., The clinical management of craniosynostosis. Clinics in developmental medicine, ; , London: Cambridge UP. 5. Wikipedia, Coronal suture. 6. Gonzalez, R.C. and R.E. Woods, Digital image processing. 2008, Upper Saddle River, N.J.: Pearson Prentice Hall. 7. MathWorks. MATLAB. [cited 2010 Nov 19]; Available from: 8. MathWorks. Functional design clunkers. [cited 2010 nov 25]; Available from: 27

29 Appix Appix I symmetry.m clear all clc %loads image nf = uigetfile('*.jpg','choose an image.'); Af = imread(nf); Af=rgb2gray(Af); o=menu('choose type of image','ct','cephalometry'); if o==1; figure(1) set(1,'name','define center-point and unfused side','numbertitle','off'); imshow(af) %Define center-point h1=impoint; wait(h1); pos1 = h1.getposition(); %Defines the unfused side and how much of the cranium to use in the %calculations h2=impoint; wait(h2); pos2=h2.getposition(); close %Filter the image and fills small open areas in the cranium A1=medfilt2(Af,[4 4]); %Adjusts the histogram Img = imadjust(a1,[105/255; 250/255],[]); %Makes the image into a binary image and fills the skull. bw = im2bw(img, graythresh(img)); bw = imfill(bw, 'holes'); figure(3) set(3,'name','make a ROI around the skull.','numbertitle','off'); imshow(bw) %Make a ROI around the skull bw2=roipoly(bw); %Multiplies the two images h=immultiply(bw,bw2); close eh=edge(h); %Segments the edge elseif o==2; Af=adapthisteq(Af); g=400/size(af,1); Ah=imresize(Af,g);%Resize image clear g 28

30 figure (1) set(1,'name','define center-point, unfused side and the cranium.','numbertitle','off'); imshow(ah); h=impoint; %Defines the center-point wait(h); pos1=h.getposition(); i=impoint; %Defines the unfused side and how much of the cranium to use %in the calculations wait(i); pos2=i.getposition(); delete(h); delete(i); %Segments the cranium by hand h=impoint; t=1; while 1; i=impoint; if isempty(i);%pusch esc to the loop break posh=h.getposition(); posi=i.getposition(); %The distance between the points shouldn't be too far. while sqrt((posh(1)-posi(1))^2+(posh(2)-posi(2))^2)>8; ts=text(size(ah,2)/2-100, size(ah,1)/2,'place the point closer to the previous point.'); delete(i) i=impoint; posi=i.getposition; delete(ts) x(t)=posi(1); y(t)=posi(2); t=t+1; h=impoint(gca,posi); close %Creates a zero-matrix z=zeros(size(ah)); z=im2bw(z); figure, imshow(z); k=1; BW1=z; %Makes a line between each point. while k<t-1; f = imline(gca,[x(k) x(k+1)], [y(k) y(k+1)]); BW = createmask(f);%creates a mask so that the lines burns into a matrix. k=k+1; BW2=imadd(logical(BW1),logical(BW)); BW1=BW2; close %closes the figure clear f t z BW1 BW k h i %clears variables eh=bw2; 29

31 eh=im2bw(eh); %changes the size of the image if 2*pos1(1)>size(eh,2) if (pos1(1)*2)>size(eh,2); j1=((2*pos1(1))-size(eh,2)); j21=zeros(size(eh,1),j1); eh=[eh j21]; %changes the size of the image if pos1(1)<size(eh,2). if pos1(1)<size(eh,2)/2; j5=(size(eh,2)-2*pos1(1)); j51=zeros(size(eh,1),j5); eh=[j51 eh]; pos1(1)=pos1(1)+size(j51,2); pos2(1)=pos2(1)+size(j51,2); %crops the image into one half and one "quarter" of the skull if pos2(1)<pos1(1); ceh1=eh((pos1(2)-pos1(2)/2):pos2(2), 1:pos1(1)); ceh2=eh((pos1(2)-pos1(2)/2):size(eh,1), pos1(1): 2*pos1(1)-1); else ceh1=eh((pos1(2)-pos1(2)/2):size(eh,1), 1:pos1(1)); ceh2=eh((pos1(2)-pos1(2)/2):pos2(2), pos1(1): 2*pos1(1)-1); p4=fliplr(ceh1); %mirrors the left side %makes the matrices the same size if size(p4,1)~=size(ceh2,1); dy=sqrt((size(p4,1)-size(ceh2,1))^2); yz=zeros(dy,size(p4,2)); if size(p4,1)>size(ceh2,1); ceh2=[ceh2;yz]; else p4=[p4;yz]; %puts the center-point in the midle of a matrix a1=p4(:,1); a2=find(a1==1); a3=a2(1); a4=size(p4,1)-(2*a3); %adds matrixes of zeros to get the center-point in the midle of a matrix B1=zeros(size(p4,1), size(p4,2)); B2=zeros(a4, size(p4,2)); E=[B2 B2; B1 p4]; I=[B2 B2; B1 ceh2]; B3=zeros(size(E,1),100); E1=[B3 E B3]; I1=[B3 I B3]; %Decides what side to rotate 30

32 if pos2(1)<pos1(1); Ik=I1; E3=E1; b=1; else E3=I1; Ik=E1; b=0; s1=0; s2=0; v=0; j2=0; f=0.24; while s1<=s2; I3=imrotate(Ik,v,'bilinear','crop'); I3(find(I3>f))=1; I3=im2bw(I3); s2=s1; %Store the latest value of s1 in s2 s1=0; t=size(e1,1)/2+1; l2=1; while t<=size(e1,1); %Runs the while-loop until the line in E3 s. %Makes a cirkle with radius l2 T=zeros(size(E1)); T2=T; x0=size(t,2)/2; y0=size(t,1)/2; the for i=1:size(t,2); for j=1:size(t,1); r=sqrt((i-x0)^2+(j-y0)^2); T(j,i)=r; L=find(T<=l2); T2(L)=1; L1=edge(T2); L1=medfilt2(L1,[1 2]); %widens the edge of the circle so that the % circle won't mis the curve even if the curve hasn't ed. L2=immultiply(L1,I3); %Finds a point in I3 that has the same radii %as a point in E3. L3=immultiply(L1,E3); %Finds a point in E3 that has the same radii %as a point in I3 [row, col]=find(l2); %Finds the coordinates of every pixels with %value one [row1, col1]=find(l3); %Finds the coordinates of every pixels with %value one if isempty(row1) isempty(row);%breaks the loop when it reaches % of the curve representing the unfused side break R=L1; %finds the points where the curves and the circle intersect x1=mean(col1); x2=mean(col); 31

33 y1=mean(row1); y2=mean(row); if v==0; r1=max(row); r2=max(row1); d=sqrt((x1-x2)^2+(y1-y2)^2); %Calculates the distance between the % points, that has the same radii, at the curves I3 and E3 t=t+1; s1=s1+d; l2=l2+1; if s2==0; %Extra to come around the first loop s2=s1; v=v+1; j2=j2+1; if j2==2; %Does the previous loop break at j2=2, the other direction is tested. v=-2; %Starts at v=-2 not to miss v=0 due to the extra command added. s1=0; s2=0; j3=0; while s1<=s2; I3=imrotate(Ik,-v,'bilinear','crop'); I3(find(I3>f))=1; I3=im2bw(I3); s2=s1; s1=0; t=size(e1,1)/2+1; l2=1; while t<=size(e1,1) %Makes a circle of radii l2 T=zeros(size(E1)); T2=T; x0=size(t,2)/2; y0=size(t,1)/2; the radii radii for i=1:size(t,2); for j=1:size(t,1); r=sqrt((i-x0)^2+(j-y0)^2); T(j,i)=r; L=find(T<=l2); T2(L)=1; L1=edge(T2); L1=medfilt2(L1,[1 2]); %widens the edge of the circle so that % circle won't mis the curve even if the curve hasn't ed. L2=immultiply(L1,I3); %Finds a point in I3 that has the same %as a point in E3. L3=immultiply(L1,E3); %Finds a point in E3 that has the same %as a point in I3 32

34 with with reaches the the [row, col]=find(l2); %Finds the coordinates of every pixels %value one [row1, col1]=find(l3); %Finds the coordinates of every pixels %value one if isempty(row1) isempty(row); %Breaks the loop when it % of the curve representing the unfused side break R=L1; %finds the points where the curves and the circle intersect x1=mean(col1); x2=mean(col); y1=mean(row1); y2=mean(row); if v==0; r1=max(row); r2=max(row1); d=sqrt((x1-x2)^2+(y1-y2)^2); %Calculates the distance between % points, that has the same radii, at the curves I3 and E3 t=t+1; s1=s1+d; l2=l2+1; if s2==0; %extra to get around the first lap s2=s1; v=v+1; j3=j3+1; %calculates the number of pixels between the two curves if j2>2; I3=imrotate(Ik,(v-2),'bilinear','crop'); I3(find(I3>f))=1; else I3=imrotate(Ik,-(v-2),'bilinear','crop'); I3(find(I3>f))=1; I3=im2bw(I3); p5=imadd(i3,logical(e3)); p5=im2bw(p5); R1=immultiply(I3,R); [row10 col10]=find(r1==1); y21=mean(row10); x21=mean(col10); figure, imshow(p5); li=imline(gca,[x1 x21], [y1 y21]); cm=createmask(li); close cm1=imadd(cm,logical(p5)); cm1=im2bw(cm1); p8=imfill(cm1,'holes'); 33

35 p9=imsubtract(p8,p5); n1=find(p9==1); n3=length(n1);%the number of pixels between the two curves %calculates the number of pixels in the area denoted K N=fliplr(E1); if b==1; f3=n(r2,:); col4=find(f3==1); z3=col4(1); f4=i1(r1,:); col5=find(f4==1); z4=col5(1); else f3=i1(r2,:); col4=find(f3==1); z3=col4(1); f4=n(r1,:); col5=find(f4==1); z4=col5(1); N4=imadd(N,I1); g=imline(gca,[z3 z4], [r2 r1]); bw1 = createmask(g); close k=imadd(bw1,logical(n4)); k1=imfill(k,'holes'); k2=imsubtract(k1,k); figure, imshow(k2); n=find(k2==1); n2=length(n); %number of pixels in the area K sum2=round(n3/n2*1000);%the symmetry ratio is calculated and multiplied %with 1000 so that the numbers won't be so small. sum=num2str(sum2); resultatruta(sum) 34

36 Appix II User manual. Install program 1. Run Symmetry_pkg. 2. Run the program Symmetry. Run program 1. Choose an image (it is important that the image is in the same folder as the program). Verify what type of image it is CT Define the center-point and how much of the cranium the program should use when doing the calculations, this point is placed on the unfused side. Using the mouse, you select the points by left-clicking. The point can be moved until you verify the location by double-clicking on the point Place a ROI around the skull. Using the mouse, you specify the region by selecting vertices around the skull by left-clicking. To close the ROI move the pointer over the initial vertex of the polygon that you selected. The pointer changes to a circle. Click either mouse button. You can move or resize the ROI using the mouse. When you are finished positioning and sizing the ROI, doubleclicking or right-clicking inside the region will start the calculations Cephalometry Define the center-point and how much of the cranium the program should use when doing the calculations, this point is placed on the unfused side. Using the mouse, you select the points by left-clicking. The point can be moved until you verify the location by double-clicking on the point. Also define the cranium by interactive placement of points along the whole edge of the cranium. Once the point is placed it cannot be moved. When the cranium is defined push esc to proceed. 35