Open Access Research on an Improved Medical Image Enhancement Algorithm Based on P-M Model. Luo Aijing 1 and Yin Jin 2,* u = div( c u ) u

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1 Send Orders for Reprins o reprins@benhamscience.ae The Open Biomedical Engineering Journal, 5, 9, Open Access Research on an Improved Medical Image Enhancemen Algorihm Based on P-M Model Luo Aijing and Yin Jin,* Key Laboraory of Medical Informaion Research (Cenral Souh Universiy, College of Hunan Province; The Third Xiangya Hospial of Cenral Souh Universiy; Posal code 43, Changsha, China; School of Public Healh, Cenral Souh Universiy; Xidian Universiy, Posal code 77, Xi an, China Absrac: Image enhancemen can improve he deail of he image o achieve he purpose of he idenificaion of he image. A presen, he image enhancemen is widely used in medical images, which can help docor s diagnosis. IEABPM (Image Enhancemen Algorihm Based on P-M Model is one of he mos common image enhancemen algorihms. However, i may cause he loss of he exure deails and oher feaures. To solve he problems, his paper proposes an IIEABPM (Improved Image Enhancemen Algorihm Based on P-M Model. The simulaion demonsraes ha IIEABPM can effecively solve he problems of IEABPM, and improve image clariy, image conras, and image brighness. Keywords: Bending, disorion, image enhancemen, Malab, P-M model, il.. INTRODUCTION In he field of image processing, image enhancemen is a very imporan research direcion, which has been widely used in miliary, remoe sense, public safey, biomedicine, ec []. In he field of medicine, he image is usually gahered by CT machine, ulrasonic apparaus, and so on. The colleced images may be blurry, which will affec diagnoses of he illness. To improve he qualiy of he colleced images, image enhancemen is used []. From he aspec of he realizaion, he image enhancemen algorihm can be divided ino five caegories: image enhancemen algorihm based on radiional heory, image enhancemen algorihm based on muliscale analysis [3], image enhancemen algorihm based on fuzzy heory [4], image enhancemen algorihm based on humanoid vision [5] and image enhancemen algorihm based on mahemaic morphology [6]. Among hem, he image enhancemen algorihm based on mahemaic morphology consiss of closing operaion, erosion operaion, dilaion operaion and open operaion. IEABPM (Image Enhancemen Algorihm Based on P-M Model is one of he mos widely used [7, 8]. IE- ABPM can effecively remove he noise of images, however, for he area which has rich exures, i may cause he loss of he exure deails and oher feaures. To solve he problem, IIEABPM (Improved Image Enhancemen Algorihm Based on P-M Model is proposed. And Simulaion demonsraes ha IIEABPM can improve image clariy, image conras, enropy and image brighness.. IIEABPM In IIEABPM, i firsly uses he normalizaion mehod o ranslae P-M model ino he posed problem. Secondly, a moderaor is added o conrol he process of opimizaion. *Address correspondence o his auhor a he School of Public Healh, Cenral Souh Universiy; Xidian Universiy, Posal code 77, Xi an, China; Tel: ; jyin@xidian.edu.cn Thirdly, according o differen region saus of he image, IIEABPM chooses he spread funcion. To mee he performance requiremens, he spread funcion is correced hrough four seps. The firs sep is increasing he gradien hreshold. The second sep is modifying spread funcion. The hird sep is adding gradien fideliy erm. The las sep is adding srengh coefficien. Fig. ( gives he flowchar of IIEABPM. Original image Enhanced image Consrucing P- M model Carrying ou image enhancemen Fig. (. Flow char of IIEABPM. Normalizaion Increasing gradien hreshold Modifying spread funcion Adding gradien fideliy erm Adding srengh coefficien Adding a moderaor Choosing spread funcion Correcing spread funcion According o Fig. (, when he normalizaion is used, he Gaussian ernel is adoped o smooh he images. ( u = div( c u u ( Where u(, x y, = G U(, x y,, and G is a Gaussian funcion, whose mean value and variance are respecively and. Afer normalizaion, P-M model is ranslaed ino a posed problem, and here is only one coninuous soluion, which depends on he iniial value u (, x y. And hen a moderaor is added o conrol he process of opimizaion, and 874-7/5 5 Benham Open

2 The Open Biomedical Engineering Journal, 5, Volume 9 Aijing and Jin ux (, = u( x uxy (,, = u(, xy. Therefore, he mahemaical model of image enhancemen can be wrien as follows: u ( x, y = div( g ( u u uxy (,, = u( xy, Where u is he image a ime, div means divergence operaor, u is he gradien of he image, g( u is he spread funcion, whose value means he srengh of spread. İn some area of he image, he value of u decides wheher or no he image is smooh. Tha is o say, when he value of is smaller, he image in he region is smooher. u In order o eep he anisoropic diffusion of spread funcion, u mus mae spread funcion saisfy he following wo condiions: ( The spread of he noise is wihin he relaively smooh feaured area; ( The spread does no ae place beween wo adjacen areas o preserve he edge deails. When removing he noise of he image, spread funcion can be chosen from wo inds of expressions: g( u = u + ( (3 G c exp x + y 4 = Therefore, divergence operaor can be wrien as: u = div g G u u ( ( (7 (8 Where, G u gxy (,, = exp. When calculaing G u, he similariy funcional of wo signals is: β (9 Ω Eu = au ( u + u ( G u dxdy Where α and β are weigh coefficiens, ( u ( G u is he gradien fideliy erm, which ries o mae changes in he gradien which are consisen wih ( G u. g( u = e u (4.. The Firs Sep Alhough he above spread model has good effecs on he image denoise, is effec is no ideal when he noise is high. To solve he problem, Eq. (3 and Eq. (4 can be modified: g( u = g( u = e 3 u + + u 3 + (5 (6 Where,, 3 are he gradien hresholds, and! 3,, 3 >. Fig. ( shows he relaionships beween spread funcion and gradien. From Fig. (, we can see ha he gradien and spread funcion has an inverse relaionship. And compared wih Eq. (3 and Eq. (4, Eq. (5 and Eq. (6 can beer reserve he edge and exure... The Second Sep In order o more accuraely conrol he smoohness, g( u is replaced by g ( G u, where he expression of G is: Fig. (. Gradien vs. Spread Funcion..3. The Third Sep In Eq. (9, gradien fideliy erm is added o increase he smoohness of he image. However, wheher i will impede he opimal soluion has no been proved. If Eu is he convex funcion, he opimal soluion uniquely exiss. λ Theorem if,, λ >, λ+ λ =, ( λ λ λ λ E u + u E u + E u. Proof: λu+ λu u = λ u u + λ( u u = λ ( u u + λ ( u u + λ λ u u ( u u = λ ( u u + λ ( u u λλ u u ( u u λ ( u u + λ ( u u

3 Research on an Improved Medical Image Enhancemen Algorihm The Open Biomedical Engineering Journal, 5, Volume 9 Then, ( ( λu+ λu ( G * u = ( λ u λ ( G * u + λ u λ ( G * u = λ ( u ( G * u + λ u ( G * u + λλ ( u ( G * u ( u ( G * u λ ( u ( G * u + λ u ( G * u Therefore, ( λ + λ λ + λ E u u E u E u An image can be regarded as he surface in wodimensional space. The aim of using he gradien fideliy erm is o eep he consrain of he coninuiy of he image opology. In he ieraive compuaion, he gradien fideliy erm mainains consisency of he original image and enhanced image, which can eliminae he loss of he image exure deails and oher feaures. Based on he above analysis, Eq. 8 can be modified as: u = div g G u u a u G u Where α is he weigh coefficien, α >. ( ( ( (.4. The Fourh Sep. ( To increase deailed informaion, he srengh coefficien is added o he spread model. The model is: u (, x y = div( g ( G u u w + e u ( Where w is he srengh coefficien, div means divergence operaor. 3. SIMULATION RESULTS 3.. Enhancemen Effec Analysis To verify he effeciveness of IIEABPM, enhancemen effec ess were conduced, as shown in Fig. (3. In Fig. (3, he original images are (a, (b and (c, which are, respecively, hand bone image, angiocarpy image and rib image. (a, (b and (c are enhanced images, accordingly. In he es, =3, =7, 3 =3, Δ =., n=5. From Fig. (3, we can see ha enhanced images become clearer, and exure deails have also been reained. (a (b (c Fig. (3. Enhancemen effec. (a (b (c 3.. Performance Analysis To furher analyze he performance of IIEABPM, hree ess have been designed. In he firs es, Fig. 3(b was chosen as he subjec and he performance of IEABPM and IIEABPM was compared in erms of he clariy, conras, brighness and enropy. Fig. (4 gives he enhanced images, and Table gives feaures of he enhanced images. (a Enhanced Image by IEABPM Fig. (4. Enhanced images. (b Enhanced Image by IIEABPM From Fig. (4 and Table, we can see ha he performance of IIEABPM is beer han ha of IEABPM.

4 The Open Biomedical Engineering Journal, 5, Volume 9 Aijing and Jin Table. Feaures of images. Brighness Conras Enropy Clariy Original image IEABPM IIEABPM In he second es, Fig. (4a wih noise was chosen as he subjec. The performance of image enhancemen by he median filer, image enhancemen by Gaussian filer, image enhancemen by wavele filer, IIEABPM and IEABPM were compared in erms of he enhancemen effec, as shown in Fig. (5. In Fig. (5, we can see ha he performances of IEABPM and IIEABPM are beer han he performances of he oher. In Fig. (5e, many deails have been removed. However, in Fig. (5f, no only he image noise is resrained, bu deails were also reserved. In he hird es, Fig. (3a was chosen as he subjec. The performance of image enhancemen by he median filer, image enhancemen by Gaussian filer, image enhancemen by wavele filer, IIEABPM and IEABPM were compared in erms of he enhancemen effec, as shown in Fig. (6. Fig. (5. Compared resuls for Lena. Fig. (6. Compared resuls for rib image.

5 Research on an Improved Medical Image Enhancemen Algorihm The Open Biomedical Engineering Journal, 5, Volume 9 3 From Fig. (6, we can see ha he performance of IIEABPM is he bes. CONCLUSION To solve he problems of IEABPM, he paper proposes IIEABPM, and simulaion demonsraes ha IIEABPM can effecively improve image clariy, image conras, and image brighness. CONFLICT OF INTEREST The auhors confirm ha his aricle conen has no conflic of ineres. ACKNOWLEDGEMENTS This wor was suppored by he Youh Foundaion of he Educaion Deparmen of Hebei Province (QN48, Science and Technology Deparmen of Hebei Province (359, Youh Foundaion of Naural Science of Hebei Norh Universiy (Q48, Youh Foundaion of Naural Science of Hebei Norh Universiy (Q4. REFERENCES [] M. P. Esrom, Digial Image Processing Techniques, Academic Press,. [] H. Wang, Y. Pan, and K. Chen, Enhancemen of low-dose lung CT image based on sochasic resonance of FHN neurons, Hangian Yixue yu Yixue Gongcheng, vol. 5, pp. -5, 4. [3] S. S. Bedi, and R. Khandelwal, Various image enhancemen echniques-a criical review, Inernaional Journal of Advanced Research in Compuer and Communicaion Engineering, vol., pp. 5-57, 3. [4] D. K. Pael, and S. A. More, An enhanced approach for edge image enhancemen using fuzzy se heory and cellular learning auomaa (CLA, World Journal of Science and Technology, vol., pp. 58-6,. [5] I. Busheri, and A. Herman, Digial image enhancemen improves diagnosis of non displaced proximal femur fracures, Clinical Orhopedics and Relaed Research, vol. 3, pp , 8. [6] Y. Kimori, Mahemaical morphology-based approach o he enhancemen of morphological feaures in medical images, Journal of Clinical Bioinformaics, vol., pp. -,. [7] Y. Cai, and Y. Huang, Image smoohing process model and improving based on P&M model, Compuer Simulaion, vol. 8, pp ,. [8] Y. Mu, and Y. Yu, Reasearch on image filering algorihm, Compuer Engineering, vol., pp.3-37, 4. Received: April, 5 Revised: May, 5 Acceped: June 5, 5 Aijing and Jin; Licensee Benham Open. This is an open access aricle licensed under he erms of he (hps://creaivecommons.org/licenses/by/4./legalcode, which permis unresriced, noncommercial use, disribuion and reproducion in any medium, provided he wor is properly cied.