29 7 2012 7 Application Research of Computers Vol. 29 No. 7 Jul. 2012 * 201203 TP391. 41 doi 10. 3969 /j. issn. 1001-3695. 2012. 07. 086 A 1001-3695 2012 07-2715-04 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 201203 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 1 2 13 ~ 1 15 5 ~ 7 1 ~ 4 5 ~ 8 9 C-V 5 10 ~ 12 2011-11-07 2011-12-29 10DZ1500600 2011ZX02505-002 1976- aysyf@ 126. com 1974-1975-.
2716 29 Hessian 9 6 F 10 12 14 = - 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 2 3 1 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 4 5 6 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 11 11 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 +
7 2717 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 2 1 - H dx ^σ 2 1 - H dx b = 13 1 - 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 2 2 - I - μ b 2 9 2 + 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 1 0.8 0.6 0.4 0.2 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 70 60 50 40 30 20 10 0 REMAC C 鄄 V GAC 10 20 30 40 50 60 70 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 100 150 滋 o 200 250 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
2718 29 5500 TTO Philips Sonos 7500 2 5 6 Visual Studio C + + 2008 3. 4 GHz 4 REMAC 1 mm = 1. 68 pixels 1 0. 714 8 1. 764 3 0. 519 9 2 0. 833 9 2. 668 5 0. 604 0 3 0. 655 2 1. 502 9 0. 472 6 4 (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 1995 17 2 158-175. 180 60 3 COHEN L D. On active contour models and balloons J. Computer Vision Graphics and Image Processing 1991 53 2 211-218. 1 000 240 256 12 8 4 6 14 REMAC 100 2. 5 15 0 3. 4 GHz 4 10 s 1 CASELLES V KIMMEL R SAPIRO G. Geodesic active contours J. International Journal of Computer Vision 1997 22 1 61-79. 2 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 1993 15 11 1131-1147. 5 CHAN T F VESE L A. Active contours without edges J. IEEE Trans on Image Processing 2001 10 2 266-277. 6 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 208 144 160 1996 18 9 884-900. 40 50% 17 1 7 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 2005 14 7 910-80 2. 5 924. 15 0 8 MUKHERJEE D P RAY N ACTON S T. Level set analysis for leukocyte detection and tracking J. IEEE Trans on Image Proces- 3. 4 GHz 4 8 s REMAC sing 2004 13 4 562-572. 9 LORIGO L M FAUGERAS O D GRIMSON W E L et al. CURVES curve evolution for vessel segmentation J. Medical Image Analysis 2001 5 3 195-206. 1 2 10 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 2002 50 3 295-313. 1 REMAC 1 mm = 2. 43 pixels 11 CHEN Yun-mei TAGARE H D THIRUVENKADAM S et al. Using prior shapes in geometric active contours in a variational framework 1 0. 701 2 2. 767 3 0. 510 7 J. International Journal of Computer Vision 2002 50 3 315-2 0. 618 8 1. 964 6 0. 471 5 328. 2729
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