MR Image Segmentation based on Local Information Entropy Geodesic Active Contour Model

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1 Vol.9, No.4 (014), pp MR Iage Segentation ased on Local Inforation Entropy Geodesic Active Contour Model Jianwei Zhang 1, Xiang Ma 1, Yunjie Chen 1, Lin Fang and Jin Wang 3 1 School of Math & Statistics, Nanjing University of Inforation Science & Technology, Nanjing 10044, China Intelligent Transportation of Anhui Province Key La., Hefei 30088, China 3 School of Coputer & Software, Nanjing University of Inforation Science & Technology, Nanjing 10044, China Astract In this paper, an iproved Geoetric Active Contour odel is presented. This odel introduced a window function to research the ean inforation of each pixel s neighor region, and constructed a novel signed pressure force function ased on the entropy to drive the contour towers the oundary. In order to iprove the efficiency and staility of the algorith, this paper adopts two valued level set ethod to realize the segentation process. The experiental results show that this ethod can otain satisfied result even when the iages have intensity inhoogeneity and weak edges. Keywords: GAC odel, signed pressure force function, Local inforation entropy, Iage segentation 1. Introduction At present, active contour odels (ACM) [1] are widely used in iage segentation. This odel was initially put forth y Kass et al. Generally speaking, the ethod ased on ACM is usually classified into two types: edges-ased odels [1, ] and region-ased ethods [3]. The edges-ased odels can well segent the target oundary with strong edges, which utilize the gradient inforation of iages, ut fail to segent the iage with weak oundaries and noise. The region-ased odels utilize the grey ean or variance can well overcoe the influence of weak oundaries or noise. However, this odels are sensitive to intensity inhoogeneous, thus it can not well segent iages with ias field. Li et al. [4] proposed the local inary fitting (LBF) odel, which utilizes the local iage inforation to segent ojects with intensity inhoogeneity and achieve the etter segentation results. Although the LBF odel utilizes local ean inforation can etter overcoe the intensity inhoogeneous of iages, ut it can not well segent the iages with strong noise and weak oundaries. Zhang et al. proposed a novel region-ased GAC odel in paper [5] can well segent the iages with noise and weak oundaries. This odel constructs a signed pressure force function ased on gloal inforation to replace the edge-stopping function of the GAC odel. This odel assued the grey inforation of age is hoogeneous, so it can not well segent the iages with ias field. Fro the research, ost edical iages local grey inforation presented gauss distriution and local statistical inforation can well descrie the grey inforation distriution of the iage. This paper can segent the edical iages with ias field or weak oundaries and noise etter y constructs a novel signed pressure force function ased on ISSN: IJMUE Copyright c 014 SERSC

2 Vol.9, No.4 (014) local entropy inforation which could utilized the local statistical to descrie grey inforation. This ethod can get etter segent result for this odel can ake full use of the grey inforation of iages.. Background Geodesic active contour (GAC) odel is put forward y V. Caselles et al. [] in 1997, and the energy functional of this odel is defined as follows: Where E GAC L C s g I C ds (1) 0 L C is the length of contour C, I is the gradient of iage I, g is the edge stopping function and s is the arc length unit of iage. The level set evolution equation corresponding to forula (1) as follows: Where g t I div g div is divergence operator, is a constant. I that decreasing with the iage gradient values I increase. () g is the edge-stopping function Generally, edical iages often exists fuzzy oundaries or weak edges and noise. Because of the GAC odel only utilize the gradient inforation ut can not utilize coprehensive features of iages to drive the evolution curves to segent the target oundary, which lead to the evolution contours over the weak oundaries or fall into the local optial. 3. Iage Inforation Entropy For the iage, I : R R, the inforation of the pixel x is: w x y log E x p I y p I y (3) Where pi y is a Gaussian distriution function in the local region, wx y is a window function which centered at the pixel point x. The inforation entropy can achieve the axiu when the grey distriution is unifor. Iage inforation entropy [6] also has a widely application in iage processing, especially in iage segentation. Such as the ACM ased on regional fitting with local entropy proposed y He Chuanjiang [7] et al. and Aitava Chatterjee et al. utilize axiu fuzzy entropy to segent rain CT iages [8]. 4. Signed Pressure Force function ased on Local Inforation Entropy Zhang et al. proposed a region-ased GAC (RGAC) [5] odel, which constructs a signed pressure force ( spf ) function replace g of the GAC odel. The definition of spf as follows: c1 c I spf c1 c ax I (4) 18 Copyright c 014 SERSC

3 Vol.9, No.4 (014) Where ax indicates the asolute axiu of grey difference, grey ean c and 1 c respectively defined as follows: c 1 I H H dxdy dxdy c I 1 H 1 H Because of the RGAC odel still rely on intensity hoogeneity, and edical iage usually include the ias field, so this odel cannot to segent the oject oundary well. The grey inforation of ost edical iages in local region presents Gaussian distriution according to literature [9]. This paper introduced window function w to research the grey distriution of local iage and introduced the iage inforation entropy into spf to construct a novel drive force function which defined as follows: dxdy dxdy w x y E x Ep x dy lespf ax w x y E x E x dy Where Ep x p I y log p I y and E x p I y log p I y respectively present iage inforation of ackground region and target region, is the whole iage region, wx y is window function, p Iy and Iy p (5) (6) p respectively present Gaussian function of ackground and target regions and they respectively coputed the posterior proaility of ackground and target regions. According to literature [9], we can know: p Iy 1 exp Iy f p Iy 1 exp Iy f (7) Where f and f respectively present grey ean of ackground and target regions: f wx yi yh ydy wx yi y1 H y f wx yh y dy wx y1 H ydy dy (8) Where and respectively present variance of ackground and target regions: w x y w I y f H y x yh y dy dy wx yi yf 1 H ydy (9) wx y1 H ydy In local region, grey changes present Gaussian distriution according literature [9]. Take a point x in contour, suppose is a local region which is controlled y window function w and centered at point x. regions that the iage region x, Ep x get a saller value and y and respectively present ackground and oject divided into inside and external y the contour line. If y E x get a igger value, then lespf 0. This situation can drive evolution curves shrinkage to oject oundary. In contrast, if x, lespf 0, it can drive evolution curves expansion to oject oundary. As we can know, the Copyright c 014 SERSC 19

4 Vol.9, No.4 (014) grey inforation in local region satisfies Gaussian distriution, thus the axiu posterior proaility of inside and external regions is 1 when the contours approach to oject oundary. Moreover, we can know that p Iylog p Iy 0 and p Iylog piy 0, therefore lespf 0 and the contour line will stop evolution at the oject oundary. Fro the forula (6), the range of variation of function lespf is [-1, 1] satisfies definition of spf function ased on the aove discussion. Take lespf instead of spf in the RGAC odel; get the corresponding gradient descent flow equations as follows: lespf div lespf t Because of grey values in local region of edical iages changes slowly, the derivative of lespf approach to 0, writing as lespf 0. Siultaneously, div, and * can e used to approach in this paper. This paper through utilize Gauss filter instead of curvature regularization. Fro the aove discussion, forula (10) can e written rief as: lespf t 5. Experiental Results and Analysis Figure 1 is the segentation of left ventricle MR iage. Figure 1(a)-() is the original iage with initial curve and the true segentation result. Figure 1(c) is the segentation result of C-V odel. This odel can not well segent the iages with ias field or weak oundaries. Figure 1(d) is the result of GAC odel which iterate 600 ties. This odel can only precede single direction evolution. Figure 1(e) is the result of RGAC odel which iterate 100 ties. This odel can easy occur over-segentation. Figure 1(f)-(g) respectively presents the result of LBF and LGD odel which iterate 100 and 00 ties. The paraeter of the is , 1. 0 and kernel paraeter siga=15. Both of the can well segent iages with ias field, ut fail to segent noise iage. Figure 1(h) is segentation result of this paper ethod iterate 100 ties with paraeter siga=15 and 100. This ethod can well segent the iages with ias field and weak oundaries. In order to etter respond or copare segentation accuracy and segentation efficiency of each odel, we utilize 0 groups left ventricle MR iages for experient segentation test. The size of iage is , and utilize the Jaccard Siilarity(JS)index [10] to quantitative analysis the segentation accuracy. G (10) (11) (a) () (c) (d) 130 Copyright c 014 SERSC

5 Vol.9, No.4 (014) (e) (f) (g) (h) Figure 1. The segentation result of left ventricle agnetic resonance (MR) iage. Figure 1(a)-() respectively present original iage with initial curve and accurate segentation result. Figure 1(d)-(h) respectively present segentation result of C-V odel, GAC odel, RGAC odel, LBF odel, LGD odel and this paper ethod As shown in the figure, the segentation accuracy of this paper ethod is ore than 90%. The C-V odel can not well segent the iages with ias field. The GAC odel can easily produces oundary leakage. The RGAC odel fails to segent the iages with ias field. Due to lots of convolution operation, the segentation efficiency of LBF and LGD odel is lower. This paper ethod can well segent the iages with ias field. Due to this ethod adopt window function to coputer, the average iteration tie no ore than 3 seconds and iteration ties less than 00 ties. This situation is still in reasonale range Figure. Segentation Accuracy Figure 3. Segentation Efficiency Figure 4 is the segentation result of left ventricle MRI with siga for [3, 9, 15, 1]. Initial iage exits of noise, ias field, weak oundaries and laeled line. Figure 4(1)-() respectively present the origin iage with initial curve and the accurate segentation result. Figure 4(3) is the result of RGAC odel iterates 100 ties with the different siga. This odel can well overcoe noise and weak oundaries, ut easy cause to segent hoogenous iages wrong. Figure 4(4)-(5) respectively present the result of LBF and LGD odel iterates 100 and 00 ties with the paraeters , The LBF odel and LGD odel can not well segent the iages included ias field with the siga increase. Figure 4(6) is the result of this paper ethod iterates 150 ties with paraeter 3. This ethod can well segent the iages with the intensity inhoogeneous. Figure 5 is the segentation result of this paper ethod iterates 150 ties with siga=15 and = [1.5, 3, 4.5, 6]. Copyright c 014 SERSC 131

6 Vol.9, No.4 (014) Figure 6 and Figure 7 respectively present the segentation accuracy and efficiency with the siga. Fro the figure, this paper ethod is oviously etter than RGAC, LBF and LGD odel. With the increase of siga, the segentation accuracy of LBF and LGD odel decrease. (1) Orign Iage with Initial Curves () Accurate Segentation Result (a.1) siga=3 (a.) siga=9 (a.3) siga=15 (a.4) siga=1 (.1) siga=3 (.) siga=9 (.3) siga=15 (.4) siga=1 (c.1) siga=3 (c.) siga=9 (c.3) siga=15 (c.4) siga=1 (d.1) siga=3 (d.) siga=9 (d.3) siga=15 (d.4) siga=1 Figure 4. The first row is the segentation result of origin iage with initial curves. The second to fifth row respectively present the segentation result of RGAC odel, LBF odel, LGD odel and this ethod ased on the size of siga is [3, 9, 15, 1] 13 Copyright c 014 SERSC

7 Vol.9, No.4 (014) (a) alpha=1.5 () alpha=3 (c) alpha=4.5 (d) alpha=6 Figure 5. The segentation result with the influence of the paraeter in this paper RGAC LBF LGD This Method RGAC LBF LGD This Method Figure 6. The influence of segentation accutare with siga Figure 7. The influence of segentation efficiency with siga 6. Conclusions This paper proposed an iproved GAC odel for the iages with noise, ias field and weak oundaries. This paper odel utilizes the window function to investigate the grey inforation of local region, while introduce the local inforation entropy to descrie the distriution of the grey inforation. Copared with GAC odel, this ethod can achieve the high segentation accuracy. Copared with C-V and RGAC odel, this ethod can well segent the iages with ias field. And copared with LBF and LGD odel, this ethod has ore choice of kernel paraeters. Acknowledgeents This research work was supported y the National Nature Science Foundation of China ( , ), and the Natural Science Foundation of Jiangsu Province (BK01184, BK01461). References [1] M. Kass, A. Witkin and D. Terzopulos, Snake active contours odels, International Journal of Coputer Vision, vol. 1, no. 3, (1988). [] V. Caselles, R. Kiel and G. Sapiro, Geodesic active contours, International Journal of Coputer Vision, vol., no. 1, (1997). [3] T. Chan and L. Vese, Active contours without edges, IEEE Transactions on Iage processing, vol. 10, no., (001). Copyright c 014 SERSC 133

8 Vol.9, No.4 (014) [4] C. Li, C.-Y. Kao, et al., Iplicit Active Contours Driven y Local Binary Fitting Energy, Coputer Vision and Pattern Recognition, (007) June 17-, Minneapolis, MN, USA. [5] K. Zhang, L. Zhang, et al., Active contours with selective local or gloal segentation: A new forulation and level set ethod, Iage and Vision coputing, vol. 8, (010), pp [6] C. E. Shannon, A Matheatical Theory of Counication, The Bell Syste Technical Journal, vol. 7, (1948). [7] C. He, Y. Wang and Q. Chen, Active contours driven y weighted region-scalale fitting energy ased on local entropy, Signal Processing, vol. 9, no., (01). [8] A. Chatterjee, P. Siarry, A. Naki and R. Blanc, An iproved iogeography ased optiization approach for segentation of huan head CT-scan iages eploying fuzzy entropy, Engineering Applications of Artificial Intelligence, vol. 5, no. 8, (01). [9] L. Wang, L. He, A. Mishra and C. Li, Active contours driven y local Gaussian distriution fitting energy, Signal Processing, vol. 89, no. 1, (009). [10] U. Vork, F. Pernnus and B. Likar, A review of ethods for correction of intensity inhoogeneity in MRI, IEEE Transactions on Medical Iaging, vol. 6, no. 3, (007). Jianwei Zhang Authors He is Professor at the College of Matheatics and Physics, Nanjing University of Inforation Science and Technology. His research interest covers pattern recognition, artificial intelligence, and reote sensing inforation processing. Xiang Ma Graduate students, Nanjing University of Inforation Science and Technology. His research interest covers iage processing, pattern recognition. YunJie Chen He received the B.S. and M.S. degree in the Applied Matheatics fro Nanjing University of Inforation Science and Technology, China in 00 and 005, respectively. He received Ph.D. degree in Pattern Recognition and Intelligent Systes fro NUST. Now, he is an associate professor in NUIST. His research interests include iage processing, pattern recognition and nuerical analysis. 134 Copyright c 014 SERSC

9 Vol.9, No.4 (014) Lin Fang He received M.S. degree in Applied Matheatics fro Nanjing University of Inforation Science and Technology. Now, he works in Intelligent Transportation of Anhui Province Key La. His research interests include iage processing, pattern recognition and nuerical analysis. Jin Wang He received the B.S. and M.S. degree in the Electronical Engineering fro Nanjing University of Posts and Telecounications, China in 00 and 005, respectively. He received Ph.D. degree in the Uiquitous Coputing laoratory fro the Coputer Engineering Departent of Kyung Hee University Korea in 010. Now, he is a professor in the Coputer and Software Institute, Nanjing University of Inforation Science and technology. His research interests ainly include routing ethod and algorith design, perforance evaluation and optiization for wireless ad hoc and sensor networks. He is a eer of the IEEE and ACM. Copyright c 014 SERSC 135

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