Medical object extraction model based on regional energy minimization and active contour model

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1 Application Research of Computers Vol. 29 No. 7 Jul * TP doi /j. issn A Medical object extraction model based on regional energy minimization and active contour model SHANG Yan-feng WANG Ning WANG Hui Shanghai Advanced Research Institute Chinese Academy of Sciences Shanghai China Abstract In order to solve the problems of traditional active contour models which move in a high speed on strong edge or leak out on weak edge this paper proposed a medical object extraction model which was based on regional energy minimization and active contour model. The model employed objects statistical intensity distribution in a level set framework and expressed energy function as an integral of probability of pixels belonging to objects. The energy function was minimized in a level set framework which led to a iterating equation. At the same time an edge based speed constrain term was able to slow down the active contours when they steped over a steep boundary of the objects which made the extraction procedure more convergent and accurately. As shown in the experiments of coronary and mitral valve extraction with comparison with several classical models and manual outline the proposed model is able to extraction medical objects in an automatic way and the results are also more robust accurate and convergent than several traditional models. Key words regional energy active contour model medical image segmentation coronary mitral valve Balloon 3 4 GAC ~ ~ 7 1 ~ 4 5 ~ 8 9 C-V 5 10 ~ DZ ZX aysyf@ 126. com

2 Hessian 9 6 F = - λ log P I α o - log P I α b δ + μ dδ 7 dφ 16 6 F + F + F = div F F F = x x y y z z x y z regional energy minimum active contour div μδ μδ μδ = x y z REMAC div μδ φ x μδ φ y μδ φ z = μdiv δ = 2 μδ div + μ δ = n μδ div dδ + μ 8 dφ E Γ α o α b = + μ ds - Γ λ log P I x α o dx + P I x α b dx 1 o blog o b o b = α o α b Γ Γ = o = - b x = x 1 x 2 x n T φ E o b Γ / t = 0 = δ λ t log P I α o - log P I α b + μdiv 10 δ φ x Γ x x φ x = 0 φ x x = 1 Heaviside δ H object o = x φ x > 0 = H x backgound b = x φ x < 0 = 1 - H x contour Γ = x φ x = 0 = δ x H = { 0 φ x 0 1 φ x > 0 δ x = H' x δ Dirac o b Γ 2 f x δ x x dx 17 Γ 1 / 1 + I I 1 Γ ds δ x x dx with = o b 3 Γ x 1 φ xx E x x α o α b = δ x x dx - log P I x α o H x dx + λ{ log P I x α b 1 - H x d x } E = + μδ - λ log P I α o H λ log P I α b 1 - H dx = F x φ dx 18 E F - F - F - F = 0 x x y y z z δ - λ log P I α o - log P I α b - μdiv = 0 9 log P I α b - log P I α o log P I α b - log P I α o t = 1 + G I μdiv + λ log P I α o - log P I α b P I α o > P I α b P I α o < P I α b 11 α o = μ o σ 2 o α b = μ b σ 2 b t = μdiv 1 + G I +

3 v - λ I - μ o 2 - I - μ b 2 + log σ o 2 2 2σ o 2σ b σ b 12 v 2λ log σ o σ b v v μ σ 13 I x H dx I x - ^μo 2 H dx ^μ o = ^σ 2 H dx o = H dx ^μ b = I x 1 - H dx I x - ^μb H dx ^σ H dx b = H dx 3 3 b REMAC REMAC a CTA MRA GAC 300 b a v 0-2 REMAC GAC C-V 300 v 0 = 1 b REMAC 3. 1 (a) 初始零水平 (b) 外部轮廓的初始 (c) 内部圆点的初始零水平的分割结果零水平的分割结果 REMAC GAC C-V 图 3 GAC 模型的冠状动脉提取 REMAC GAC C-V REMAC C-V REMAC 4 b C-V REMAC - λ I - μ o I - μ b log 2σ o 2σ b 11 log P I α o - log P I σ o REMAC - λ σ 1 I - μ o 2 + λ 2 I - μ b 2 C-V b 1 C-V GAC λ 1 = λ 2 = λc-v 25 μ o + μ b /2 GAC λ 1 λ 2 REMAC 3 a 80 Fisher REMAC C-V frequency background REMAC C 鄄 V object 12 (a) 原始 CT 图像 (b) C 鄄 V 模型的 (c) REMAC 模型的和初始零水平分割结果分割结果图 2 C 鄄 V 和 REMAC 模型的冠状动脉提取比较 GAC 3 GAC REMAC 3 a GAC 3 a α b 1 / 1 + G I (a) 从二维 MRA 提取出来的冠状动脉 area of object/pixels REMAC C 鄄 V GAC iterating times (b) REMAC C 鄄 V 和 GAC 的时间面积变化曲线图 4 REMAC C 鄄 V 和 GAC 模型的收敛性比较 0 50 滋 b 滋 o gray 3. 2 图 1 REMAC 和 C 鄄 V 模型对应的分类器 2 C-V REMAC 2 CT C-V σ o > σ b REMAC C-V 1 / 1 + G I HP Sonos

4 TTO Philips Sonos Visual Studio C GHz 4 REMAC 1 mm = pixels (b) REMAC 分割的二尖瓣 (a) 原始超声图像 (c) 二尖瓣的面重建图 5 REMAC 模型分割的二尖瓣 ( 图像来自 HP Sonos 5500 超声设备 ) (b) REMAC 模型分割的二尖瓣 CTA /MRA C-V REMAC (a) 原始图像图 6 (c) 原始图像的体重建 (d) 二尖瓣的面重建实时三维超声图像的 REMAC 模型分割 3 front propagation a level set approach J. IEEE Trans on Pattern 24 fps 60 Analysis and Machine Intelligence COHEN L D. On active contour models and balloons J. Computer Vision Graphics and Image Processing REMAC GHz 4 10 s 1 CASELLES V KIMMEL R SAPIRO G. Geodesic active contours J. International Journal of Computer Vision MALLADI R SETHIAN J A VEMURI B C. Shape modeling with 4 COHEN L D COHEN I. Finite-element methods for active contour models and balloons for 2-D and 3-D images J. IEEE Trans on Pattern Analysis and Machine Intelligence CHAN T F VESE L A. Active contours without edges J. IEEE Trans on Image Processing ZHU Song-chun YUILLE A L. Region competition unifying snakes region growing and Bayes /MDL for multiband image segmentation 9 ~ 18 J. IEEE Trans on Pattern Analysis and Machine Intelligence % PRECIOSO F BARLAUD M BLU T et al. Robust real-time segmentation of images and videos using a smooth-spline snake-based algo- 2 REMAC rithm J. IEEE Trans on Image Processing MUKHERJEE D P RAY N ACTON S T. Level set analysis for leukocyte detection and tracking J. IEEE Trans on Image Proces GHz 4 8 s REMAC sing LORIGO L M FAUGERAS O D GRIMSON W E L et al. CURVES curve evolution for vessel segmentation J. Medical Image Analysis CREMERS D TISCHHAUSER F WEICKERT J et al. Diffusion snakes introducing statistical shape knowledge into the Mumford-Shah REMAC functional J. International Journal of Computer Vision REMAC 1 mm = pixels 11 CHEN Yun-mei TAGARE H D THIRUVENKADAM S et al. Using prior shapes in geometric active contours in a variational framework J. International Journal of Computer Vision

5 b ASR 5 2 OCR YANG Jun HAUPTMANN A G. Naming every individual in news c video monologues C / /Proc of the 12th ACM International Conference on Multimedia ASR 2. D E J F 4. D C / / FENG Hua-min FANG Wei LIU Sen et al. A new general framework for shot boundary detection and key-frame extraction C / /Proc of the 7th ACM SIGMM International Workshop on Multimedia Information 3 ASR Retrieval. New York ACM Press ASR C / / A FENG Hua-min JIANG Chao YANG Xin-hua. An audio classification B C D E F % % and speech recognition system for video content analysis C / / Proc of the 2nd International Conference on Multimedia Technology J HUA Xian-sheng LIU Wen-yin ZHANG Hong-jiang. An automatic performance evaluation protocol for video text detection algorithms J. Circuits and Systems for Video Technology LTP v1. 4 EB /OL. http / /ir. hit. edu. cn /ltp /#ner. 12 Welcome to apache nutch EB /OL. http / /nutch. apache. org / SHANG Yan-feng YANG Xin ZHU Ming et al. Prior based cardiac valve segmentation in echocardiographic sequences geodesic active contour guided by region and shape prior C / /Proc of Pattern Recognition and Image Analysis SURI J S LIU Ke-cheng SINGH S et al. Shape recovery algorithms using level sets in 2-D /3-D medical imagery a state-of-the-art review J. IEEE Trans on Information Technology in Biomedicine HEIMANN T MEINZER H P. Statistical shape models for 3D medical image segmentation a review J. Medical Image Analysis CREMERS D ROUSSON M DERICHE R. A review of statistical approaches to level set segmentation integrating color texture motion and shape J. International Journal of Computer Vision PARAGIOS N. A level set approach for shape-driven segmentation and tracking of the left ventricle J. IEEE Trans on Medical Imaging SETHIAN J A. Level set methods and fast marching methods evolving interfaces in computational geometry fluid mechanics computer vision and materials science M. S. l. Cambridge University Press ARFKEN G. Mathematical methods for physicists M. 3rd ed. S. l. Academic Press MUMFORD D SHAH J. Optimal approximation by piece-wise smooth functions and associated variational problems J. Communication Pure Applied Mathematics

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