Gaussian Higher Order Derivative Based Structural Enhancement of Digital Bone X-ray Images

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1 ISSN : 9-09 Gaussian Higher Order erivative Based Structural Enhancement of igital Bone X-ra Images a Raka Kundu b Ratnesh Kumar a Biswajit Biswas a4 Amlan Chakrabarti a A. K. Choudhur School of Information Technolog Universit of Calcutta Kolkata India. kundu.raka@gmail.com biswajit.cu.08@gmail.com 4 acakcs@caluniv.ac.in b National Institute for The Orthopaedicall Handicapped B. T. Road Bon-Hoogl Kolkata India. director@nioh.in Abstract A novel method for enhancement of digital X-ra images of bones is presented in this paper. It has come to observation that the proposed method based on the Gaussian higher order derivative shows an appreciable enhancement of edges in digital X-ra images of bones that can be used for detection of various bone deformities as well as for the better understanding of the bone structure. We have achieved a level of improvement in distinguishing the bone information from the other parts of the digital X-ra images. Kewords: Gaussian function higher order derivative operator digital X-ra image image enhancement.. Introduction igital X-ra images are the common form of electromagnetic radiation image. X-ra images [] pla a significant role in medical images for the diagnosis of diseases and deformities of bone in human bod. Edges are the basic features of a given image and the are the regions of rapid intensit change i.e. high frequenc regions in the spatial domain. Edges characterize the boundaries thus preserving the important structural properties of an image. Therefore enhancing high-frequenc components of the image can sharpen edges effectivel. ue to lack of sharpness digital X-ra images sometimes do not hold enough information for medical diagnosis. Here we have undergone a process of image enhancement of bone structures in digital X- ra images. The basic common method of sharpening [] [] is addition or subtraction of Laplacian image [] to the original input image. Therefore a stud was carried out on the third order Gaussian operator for increasing the sharpness of the digital bone X-ra image. The higher order Gaussian operators are eas to realize but are ver sensitive to noise. So prior to application of the higher order Gaussian operator there is need of smoothing the image b noise removal filter. Here in this paper we mainl focus our research on the derivation of Gaussian higher order derivative operator and its use in highlighting the regions of bones of digital X-ra image b detection of meaningful edges of the image. The organization of this paper is as follows. Section II contains the proposed method of our paper work. Here we have discussed the algorithms. Section III compares and illustrates the results. Concluding remarks are in Section IV.. Methodolog.. Proposed Gaussian Operator Algorithm The formulation of the proposed higher order derivative is from Gaussian function []. The one-

2 dimensional Gaussian function is given b: * ep μ = mean with μ = 0 σ = variance. *ep The two dimensional Gaussian function is the product of two such Gaussians function one in each dimension. The two dimensional Gaussian function is: ep * For simplicit we drop. ep 4 Now *ep 5 4 *ep *ep 7 Similarl *ep 8 So *ep 9 the Gaussian third order operator is convolved with input image to obtain the third order Gaussian image. Figure and Figure show the input image and Gaussian third order image respectivel. Figure : Original Image Figure : Results of Gaussian operator applied on Figure Figure is the plot of Gaussian derivative function for order of it shows the variation of the function w.r.t.. It is a zero crossing operator whose polnomial is σ - σ. This polnomial is also known as Hermit polnomial [4]. Figure : plot of the rd order Gaussian operator The convolution mask of equation 9 with the adjustment of variance σ from 0.5 to 0. gives the

3 desirable result for the enhancement of bone structure of digital X-ra image... Image enhancement original image. This gives a clear view of the structure of the bone. The window obtained from third order Gaussian derivative is net used for digital X-ra image sharpening. Considering the centre piel of the obtained window as positive we add the third order Gaussian image with the original digital X-ra image. Resultant image obtained after addition is the edge sharpened image. Let S I [ I ] 0 Where I and S are the input image and structural enhanced image respectivel. I is the third order Gaussian image. Figure4 describes the proposed method. Figure 5: Mesh plot of the test image Figure 9 I I S Figure4: Procedure for the generation of the enhanced image The resultant image is significantl sharper than the original input image and is able to confer the structure of the bone of the digital image.. Results and iscussions Let us demonstrate the structural enhancement of the digital X-ra image from our eperimental results. Figure 5 and Figure illustrate the mesh plot of the input digital X-ra image Figure 9 and the enhanced digital X-ra image Figure 0. If we compare the values of Figure with Figure 5 we see that the Figure have much higher peaks for the edges whereas the non-edges remains almost same as compared to the random distribution in Figure 5. Thus it can be visualized from the results that the edge regions of the bone of the processed image is much sharper than the Figure : Mesh plot of the enhanced image Figure 0 The contour plot of the original image and enhanced image gives more clear idea of the edge enhancement. The result in Figure 8 shows that the contour of the bones has been well detected in the enhanced image compared to the initial input as in Figure 7. This proves that our algorithm is efficient and serves the purpose of edge enhancement.

4 Figure 7: Contour plot of test image Figure 9 Figure 9: Original image Figure 8: Contour plot of enhanced image Figure 0 A visual assessment of the prior and post processed digital X-ra images are carried out for comparison. Where Figure 9 Figure are the input digital images and Figure 0 Figure are the higher order Gaussian applied enhanced images. Figure 0 and Figure clearl shows the bone region and its structural formation which cannot be so clearl seen in the original digital X-ra image of Figure 9 and Figure. The bones from the soft tissues are easil distinguishable. The new image formed b addition of the higher order Gaussian image provides us more information than the normal digital X-ra image. The results displaed here are encouraging evidence that the new process will be helpful in ielding better informative X-ra images. Figure 0: Enhanced image Figure : Original image

5 []Gonzalez R.C R.E. Woods igital Image Processing Using Matlab Publisher Pearson Education 008. []Spock Gaussian derivatives Shape and algebraic structure pp [4]W.T. Freeman E.H. Adelson The esign and Use of Steerable Filters TRANSACTIONS ON PATTERN ANALYSIS AN MACHINE INTELLIGENCE Vol. No.9 September 99 pp Conclusion Figure : Enhanced image This work proposes an efficient technique of generating enhanced images from the given digital bone X-ra images. The results show that this is also a useful technique for identifing contours in bone images which has a numerous applications in understanding and diagnosing bone deformities. Our future work in this line will be segmentation of bone information from the bone X-ra images and characterizing the amount of deformities through quantitative means. References [] Gonzalez R.C. R.E. Woods igital Image Processing Publisher Pearson Education. [5]M. Juneja P.S. Sandhu Performance Evaluation of Edge etection Techniques for Image in Spatial omain International Journal of Computer Theor and Engineering 009 pp. 4-. []S. Lakshmi V. Sankaranaraan A Novel Approach for Edge etection International Journal of Computer Science and Network Securit Vol.0 No.4 April 00 pp [7]R. Maini H. Aggarwal Stud and Comparison of Various Image Edge etection Techniques International Journal of Image Processing IJIP Volume : Issue pp. -. [8]S. Sarkar K. Ghosh K. Bhaumik A Bio-inspired Interpolation Kernel for Medical Image Processing Implemented on SP Processor 5 th International Conference on Advanced Computing and Communications 007 pp [9]M.S. Khalid M.U. Ilas M.S. Sarfaraz M.A. Ajaz Bhattachara Coefficient in Correlation of Gra-Scale Objects JOURNAL OF MULTIMEIA Vol. No. April 00 pp. 5-.