An Interactive X-Ray Image Segmentation Technique for Bone Extraction

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1 An Interactive X-Ray Image Segmentation Tecnique for Bone Extraction Cristina Stolojescu-Crisan and Stefan Holban Politenica University of Timisoara V. Parvan 2, Timisoara, Romania Abstract. Image segmentation plays a fundamental role in many medical imaging applications by facilitating te contouring of te regions of interest. In tis paper, we propose an accurate interactive metod wic combines two image segmentation tecniques. In te first step, a mean sift segmentation algoritm is used for initial segmentation, followed by an adaptive region merging process based on te maximal similarity between regions, in te second step. Te proposed metod is tested on a set of real X-ray images and te goal is to separate te bones from te rest of te image. Te experimental results on real X-rays sow tat te proposed segmentation algoritm is igly effective, since it as te ability to extract te contour of te desired objects from te image. Keywords: Biomedical imaging, digital images, X-Ray Bone Segmentation, radiograpy 1 Introduction During te recent years, muc attention as been focused on medical imaging due to te appearance of less invasive and more accurate medical devices. Modern medical imaging offers te potential and promise for major advances in science and medicine, as iger fidelity images are produced. Digital images are more and more used by medical practitioners to elp tem during te disease diagnosis and decision making process, because tey display various body organs. Tere are several imaging tecnologies used in radiology to diagnose or treat diseases: X-ray radiograpy, ultrasound, computed tomograpy (CT), nuclear medicine and magnetic resonance imaging (MRI). X-ray images (radiograps) represent one of te oldest and more frequently used noninvasive medical tests tat elp pysicians during various stages of treatment, including fracture diagnosis, skeletal maturation evaluation, ip replacement surgery, or oter bone diseases. Imaging science as expanded primarily along tree distinct, but related lines of investigation: segmentation, registration and visualization [2]. One of te major callenges in medical imaging is te segmentation process, one of te most common operations in image processing. Segmentation allows te partitioning of Proceedings IWBBIO Granada 7-9 April,

2 2 Cristina Stolojescu-Crisan and Stefan Holban an image into regions wit coesive properties. Medical image segmentation is a fundamental problem in image processing and computer vision. Segmentation algoritms play a vital role in many biomedical-imaging applications, suc as diagnosis and treatment planning, localization of patology, study of anatomical structure, and computer-integrated surgery [1]. However, most of te existing articles on medical image segmentation are focused on CT and MRI and less on te segmentation of X-ray images. X-Ray image segmentation tecniques are treated in [3], [4], [5], [6]. Te goal in tese papers is te segmentation of bone structures from te X-ray images. Tis task is considered callenging because tis type of images are complex in nature since te regions delineated by bone contours are igly nonuniform in intensity and texture. Terefore, classical segmentation algoritms suc as tresolding, clustering, region growing, watersed, classifiers, etc are not applicable because tey rely on region omogeneity criteria. Deformable models (snakes, level set based models, or active sape models) can be used for X-ray image segmentation as well, but tey require a good initialization of te model contour and tus, may incorrectly segment te regions. An interesting solution is to combine two or more segmentation tecniques. In tis paper, we aim to segment X-ray images in order to separate te bones from te rest of te image. Te proposed metod automatically merges te regions tat are initially segmented using te mean sift algoritm. After te merging process ends, te object of interest (te bone structure) will be extracted from te background. Tis metod as been proposed in [7] for color image segmentation. In tis paper, we adapted tis metod for X-ray images. 2 Segmentation sceme A large amount of literature in te medical image analysis researc domain is dedicated to te segmentation topic. Some of segmentation tecniques ave acieved an extraordinary success and ave become popular in a wide range of applications. However, it is difficult to decide wic approac is te best for a particular segmentation task. Classical image segmentation algoritms including tresolding, edge detection, or region based tecniques can solve only simple medical image segmentation problems, since tey are sensitive to noise or may ave over-segmentation tendency. In tis paper, we will use a segmentation metod based on te mean-sift algoritm and region merging. Te segmentation scenario implies te following steps [8]: 1. Use an initial segmentation metod to split te entire image region, R, into smaller regions, R i, i = 1...S until tat, for any region R i, P r (R i ) = T RUE, i = 1...S, were P r is a predicate. 2. Coose a criterion for merging two adjacent regions, R j and R k, for wic P r (R j Rk ) = T RUE. 3. Merge all te adjacent regions. Stop if no furter merging is possible. Proceedings IWBBIO Granada 7-9 April,

3 An Interactive X-Ray Image Segmentation Tecnique for Bone Extraction 3 Tere are various low level image segmentation metods tat can be used for initial segmentation. However, te mean-sift algoritm is more robust and produces less over segmentation. 2.1 Mean-sift algoritm Mean-sift algoritm is a powerful clustering procedure tat estimates te gradient of a probability density function using a generalized kernel approac. It as been successfully used for image segmentation in [9], [10], and [11]. Being given a set of n points, x 1...x n, in te d-dimensional Euclidean space, te kernel density estimate is defined as: ˆf(x) = 1 n d K( x x i ), (1) were is te window radius (bandwidt parameter) of te used kernel K(x). Te estimate of te density gradient is defined as te gradient of te kernel density estimate: ˆ f(x) = ˆf(x) = 1 n d K( x x i ). (2) Te kernel K(x) is a function of x 2 : K = c k,d k( x 2 ). k(x) is called te profile of K(x) and c k,d is a normalization constant, wic makes K(x) integrate to one. Tis class of kernels are called radially symmetric kernels. Te density estimator can be rewritten as: ˆ f,k (x) = c k,d n d k( x x i 2 ), (3) Two commonly used kernels are te multivariate Gaussian kernel: and te Epanecnikov kernel: K G (x) = (2π) d/2 e 1 2 x 2 (4) K E (x) = { 1 2 c 1 d (d + 2)(1 x 2 ), 0 x 1 0, x > 1 Te density gradient estimator of f,k (x) is obtained as: (5) ˆ f,k (x) = ˆ f,k (x) = 2c k,d n d+2 (x x i )k ( x x i 2 ), (6) We denote: g(x) = k (x). Using g(x) for profile, te kernel G(x) is defined as: G(x) = c k,g g x 2, (7) Proceedings IWBBIO Granada 7-9 April,

4 4 Cristina Stolojescu-Crisan and Stefan Holban were c k,g is a positive constant (te normalization coefficient). Te kernel K(x) is called te sadow of G(x). Te estimate of te density gradient becomes: ˆ f,k (x) = 2c k,d n d+2 g x x i n 2 n x xi g( )x i x xi g( ) x, (8) Te density estimator computed wit te kernel G(x) can be written as: ˆ f,g (x) = c k,g n d g( x x i ), (9) Te mean sift vector (or sample mean sift) is defined as te difference between te weigted mean using kernel G(x) and x, as te center of te kernel: m(x) = n n x xi g( )x i g( x xi ) x, (10) Te mean sift segmentation is an advanced and versatile tecnique for clustering based segmentation. Te parameters of te mean sift segmentation are: te spatial resolution parameter, (σ r ), te range resolution parameter, (σ s ) and M, te size of te smallest segment. Te use of te mean-sift algoritm for image segmentation requires te selection of (σ r ) and (σ s ). 2.2 Region merging tecnique Te initial segmentation produces a number of small regions. In te following, a region growing/merging algoritm [12] is used to merge tese small regions to larger ones. Region merging tecniques consider two regions to be merged if tey are similar and adjacent or connected to eac oter. Te main segmentation criterion in region growing is te omogeneity of regions. Te criteria for omogeneity include: gray level, color, texture, sape, model, region size, etc. Te region descriptor is compared to te descriptor of an adjacent region. If tey matc, tey are merged into a larger region, if not, te regions are marked as non-matcing. Te merging process of adjacent regions continues between all neigbors, including newly formed ones. If a region cannot be merged wit any of its neigbors, it is marked as final. Te merging process stops wen all regions are marked. Region merging tecniques usually work wit a statistical test to decide te merging of regions. Some examples of statistical test are te Euclidean distance, te Battacaryya coefficient, te Kullback Leibler divergence, or te log-likeliood ratio. Many researcers ave used te Battacaryya similarity measure and found it advantageous. Battacaryya coefficient correlates images using istograms [13] and gives a measure of similarity between te probability density functions of two populations. Being given p(i) and q(i), two multinomial populations of N classes, te Battacaryya coefficient is defined as: ρ(p, q) = N p(i)q(i), (11) Proceedings IWBBIO Granada 7-9 April,

5 An Interactive X-Ray Image Segmentation Tecnique for Bone Extraction 5 were p(i) and q(i) are probability distributions: Np(i) = Nq(i) = 1. (12) Te Battacaryya measure can be used to compare te similarity between two istograms. If two regions ave similar contents, teir istograms will be very similar. We consider two regions Q and R. If H Qi is te normalized istogram of te first region, Q, and H Ri is te normalized istogram of te second region, R, wit i representing te it element of tem, ρ(r, Q) is defined as: ρ(r, Q) = HRi HQi, (13) i is a measure of te similarity between te two regions. Te iger te Battacaryya coefficient between two images is, te iger te similarity between tem is. Te proposed region merging metod starts wit marking te object and background. After object marking, eac region will be labeled as object marker region, background marker region, or non-marker region. Te object/background marker regions represent a small part of te object/background. Te regions tat are not marked by te user sould be identified and merged wit te corresponding regions, based on te similarity between regions. Two regions will be merged if te similarity between tem is maximal (te Battacaryya coefficient as te igest value). Briefly, considering Q a region of te image and S Q te set of all adjacent regions of Q, we compute te similarity between Q and all its adjacent regions (te Battacaryya coefficient). Q will be merged wit te region aving te igest similarity [7]. Tis means: ρ(r, Q) = max...q ρ(q, S Q i ), (14) ten R and Q will be merged. From te initial marker regions, all te non-marker regions will be gradually labeled as eiter object region or background region. In te end, eac region will be labeled as object or background. Tis is equivalent wit extracting te object contour from te background. 3 Segmentation results In te following, we will sow te segmentation results of te previously presented algoritm. We applied te algoritm on nine real X-ray images collected from a local public ospital. Te results for tree of tem are sown in Fig. 1, Fig. 2 and Fig. 3. Green markers are used to mark te object, wile blue markers are used to represent te background. Te initial segmentation using mean-sift algoritm and te positioning of markers are presented in te left image of eac figure, wile te results after region merging are sown in te rigt image. Proceedings IWBBIO Granada 7-9 April,

6 6 Cristina Stolojescu-Crisan and Stefan Holban Fig. 1. Test 1: Te initial segmentation using te mean-sift algoritm and te markers placed by te used (left) and te segmentation results after region merging procedure (rigt). Fig. 2. Test 2: Te initial segmentation using te mean-sift algoritm and te markers placed by te used (left) and te segmentation results after region merging procedure (rigt). Proceedings IWBBIO Granada 7-9 April,

7 An Interactive X-Ray Image Segmentation Tecnique for Bone Extraction 7 Fig. 3. Test 3: Te initial segmentation using te mean-sift algoritm and te markers placed by te used (left) and te segmentation results after region merging procedure (rigt). Te proposed metod is useful if te user is interested in separating a selected object from te rest of te image (background). Analyzing Fig. 1, Fig. 2 and Fig. 3, we can observe tat te bones are perfectly extracted from te background. In [14], we compared various segmentation tecniques, starting wit te most simple and fast metods and increasing te computational complexity and te processing time wit eac presented metod. By visual inspection we can conclude tat te results reported in tis paper are more accurate tan te ones presented in [14]. 4 Conclusions Te goal of tis paper was to separate te bone structures from a set of X-ray images, as X-ray bone segmentation is a vital step in te X-Ray images analysis. Te metod proposed for tis task is based on te mean-sift algoritm, followed by a region merging process, based on te maximal similarity between regions. Tis metod is very simple but it can successfully extract te objects of interest from te image. Te metod as been proposed in [7], were te autors used tis segmentation sceme to extract desired objects from a set of testing color images. In tis paper, we adapted te metod proposed in [7] for medical images. In tis paper, te algoritm (bot initial segmentation and merging process) as been implemented in MATLAB R2008a. Te proposed segmentation metod is interactive, as te user places te markers. More, te wole segmentation process is guided by te markers input by te user. Te execution time also Proceedings IWBBIO Granada 7-9 April,

8 8 Cristina Stolojescu-Crisan and Stefan Holban depends on te markers positioning, but also on te initial segmentation (based on te mean-sift algoritm), and te content of te image. Our work as revealed tat te proposed metod successfully and accurately separates te bones from te background. Tis researc work tus contributes to solving te difficult and callenging problem of segmenting X-ray images. As future work, we aim to reduce te computational speed of segmentation, as well as te amount of manual interaction. References 1. Pam, D. L., Xu, C., Prince, J. L.: Current metods in medical image segmentation. Rev. Biomed. Eng. 2, (2000) 2. Dougerty, G.: Medical Image Processing: Tecniques and Applications (Biological and Medical Pysics, Biomedical Engineering). In: Dougerty, G. (eds.). Springer, New York (2011) 3. Maendran, S. K., Baboo, S. S.: Enanced Automatic X-Ray Bone Image Segmentation using Wavelets and Morpological Operators. In: International Conference on Information and Electronics Engineering, vol. 6, pp Singapore (2011) 4. Feng, D.: Segmentation of Bone Structures in X-ray Images. Tesis proposal to te Scool of Computing National University of Singapore, superviser Dr. Leow Wee Keng, (2006) 5. Seise, M., McKenna, S. J., Ricketts, I. W., Wigderowitz, C. A.: Segmenting Tibia and Femur from Knee X-ray Images. Med. Image Underst. Anal., (2005) 6. Cen, Y., Ee, X., Leow, W. K., Howe, T. S.: Automatic Extraction of Femur Contours from Hip X-ray Images. In: Liu, Y., Jiang, T., Zang, C. (eds.) Computer Vision for Biomedical Image Applications. LNCS, vol.3765, pp Springer, Heidelberg (2005) 7. Ninga, J., Zanga, L., Zanga, D., Wub, C.: Interactive image segmentation by maximal similarity based region merging. J. Pattern Recognition Elsevier 43, (2009) 8. Sonka, M., Hlavac, V., Boyle, R.: Image Processing, Analysis and Macine Vision. In: Tomson-Engineering (2007) 9. Comaniciu, D., Meer, P.: Mean Sift Analysis and Applications. In: 7t IEEE International Conference on Computer Vision, pp Kerkyra, Greece (1999) 10. Comaniciu, D., Meer, P.: Mean Sift: A Robust Approac toward Feature Space Analysis. IEEE Trans. Pattern Analysis Macine Intelligence 24(5), (2002) 11. Raja, S. V. K., Kadir, A. S. A., Amed, S. S. R.: Moving toward region-based image segmentation tecniques: a study. JATIT 5(1), (2009) 12. Suri, J. S., Setaredan, S. K., Sing, S. (eds.) : Advanced Algoritmic Approaces to Medical Image Segmentation: State Of Te Art Applications in Cardiology, Neurology, Mammograpy and Patology. In: Springer, London (2002) 13. Kalid, M. S., Ilyas, M. U., Sarfaraz, M. S., Ajaz, M. A.: Battacaryya Coefficient in Correlation of Gray-Scale Objects. Journ. of Multimedia 1(1), (2006) 14. Stolojescu-Crisan, C., Holban, S: A Comparison of X-Ray Image Segmentation Tecniques. AECE 13(3),85 92 (2013) Proceedings IWBBIO Granada 7-9 April,