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A novel, fast, and complete 3D segmentation of vertebral bones

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A novel, fast, and complete 3D segmentation of vertebral bones
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  ANOVEL,FAST,ANDCOMPLETE3DSEGMENTATIONOFVERTEBRALBONES  Melih S. Aslan, Asem Ali, Ham Rara, Ben Arnold  ∗  , Rachid Fahmi, Aly A. Farag, and Ping Xiang ∗ University of Louisville  ∗ Image Analysis, Inc.Computer Vision and Image Processing Laboratory 1380 Burkesville St.Louisville, KY,40299USA Columbia, KY, 42728, USA ABSTRACT Bone mineral density (  BMD ) measurements and fractureanalysis of the spine bones are restricted to the Vertebralbodies ( VBs ), especially the trabecular bones ( TBs ). In thispaper, we propose a novel, fast, and robust 3D framework to segment  VBs  and trabecular bones in clinical computedtomography ( CT  ) images without any user intervention. TheMatched filter is employed to detect the  VB  region automat-ically. To segment the whole  VB , the graph cuts methodwhich integrates a linear combination of Gaussians (LCG)and Markov Gibbs Random Field (MGRF) is used. Then, thecortical and trabecular bones are segmented using local vol-ume growing methods. Validity was analyzed using groundtruths of data sets (expert segmentation) and the EuropeanSpine Phantom (  ESP ) as a known reference. Experiments onthe data sets show that the proposed segmentation approachis more accurate than other known alternatives.  Index Terms —  Spine Bone, Vertebral Body ( VB ), trabec-ular bone, graph cuts segmentation. 1. INTRODUCTION The spine bone consists of the  VB  and spinal processes. Inthispaper, weareprimarilyinterestedinvolumetriccomputedtomography (CT) images of the vertebral bone of spine col-umn with a particular focus on the lumbar spine. The primarygoal of the proposed work is in the field of spine densito-metry where bone mineral density (  BMD ) measurements arerestricted to the vertebral bodies, especially trabecular bones(see Fig. 1 for regions of spine bone).Various approaches have been introduced to tackle thesegmentation of skeletal structures in general and of verte-bral bodies in particular for the anatomical definition of a VB . For instance, Kang et al. [1] proposed a 3D segmen-tation method for skeletal structures from CT data. Theirmethod is a multi-step method that starts with a three dimen-sional region growing step using local adaptive thresholdsfollowed by a closing of boundary discontinuities and thenan anatomically-oriented boundary adjustment. Applicationsof this method to various anatomical bony structures are pre-sented and the segmentation accuracy was determined using Fig. 1 . Anatomy of a human vertebra (The image is adoptedfrom [4]).the European Spine Phantom (  ESP ) [2]. Later, Mastmeyer etal. [3] presented a hierarchical segmentation approach for thelumbar spine in order to measure bone mineral density. Thisapproach starts with separating the vertebrae from each other.Then, a two step segmentation using a deformable mesh fol-lowed by adaptive volume growing operations are employedin the segmentation. The authors conducted a performanceanalysis using two phantoms: a digital phantom based on anexpert manual segmentation and the  ESP . They also reportedthat their algorithm can be used to analyze three vertebrae inless than  10 min . This timing is far from the real time re-quired for clinical applications but it is a huge improvementcompared to the timing of   1 − 2 h  reported in [5]. Recently,in the context of evaluating the  Ankylosing Spondylitis , Tanet al. [6, 7] presented a technique to segment whole verte-brae with their syndesmophytes using a 3D multi-scale cas-cade of successive level sets. The seed placement was donemanually and results were validated using synthetic and realdata. Other techniques have been developed to segment skele-tal structures and can be found for instance in [8, 9] and thereferences therein.The  VB  consists of trabecular and cortical bones. Themain objective of our algorithm is to segment the  VB , andthen the trabecular bone. In this paper, we propose a novelautomatic  VB  segmentation approach that uses subsequently;i) the Matched filter which is used in automatic determinationof the  VB  region, ii) the LCG method to approximate the gray 654978-1-4244-4296-6/10/$25.00 ©2010 IEEE ICASSP 2010  (a) (b) (c) (d) Fig. 2 .  Typical challenges for vertebrae segmentation. (a) Innerboundaries. (b) Osteophytes. (c) Bone degenerative disease. (d)Double boundary. level distribution of the  VB  (object) and surrounding organs(background), and iii) the graph cuts to obtain the optimalsegmentation. First, we use the Matched filter to determinethe  VB  region in CT slice. In this method, no user interac-tion is needed. Also, this method helps the LCG method toinitialize the gray level distributions more accurately. Afterthe LCG method initializes the labels, graph cuts segmenta-tion method is employed in the segmentation. Because the VB  and surrounding organs have very close gray level infor-mation and there are no strong edges in some CT images, wedepend on both the volume gray level information and spatialrelationships of voxels in order to overcome any region inho-mogeneity existing in CT images as shown in the Fig. 2. Inthis study, the interpolation and level set methods using var-ious post-processing steps are tested and compared with theproposed algorithm. After we segment the  VB , cortex and tra-becular bones are extracted from each other using the localadaptive region growing algorithm.Section 2 discusses the background of Matched filter,graph cuts method, and local adaptive region growing meth-ods. Section 3 describes the alternative methods, explain theexperiments, and compare the results. 2. PROPOSED FRAMEWORK2.1. Matched Filter In the first step, the Matched filter [10] is employed to detectthe  VB  automatically. This procedure eliminates the userinteraction and improves the segmentation accuracy. Let f  ( x,y )  and  g ( x,y )  be the reference and test images, respec-tively. To compare the two images for various possible shifts τ  x  and  τ  y , one can compute the cross-correlation  c ( τ  x ,τ  y )  as c ( τ  x ,τ  y ) =     g ( x,y ) f  ( x − τ  x ,y − τ  y ) dxdy.  (1)where the limits of integration are dependent on  g ( x,y ) .Equation 1 can also be written as c ( τ  x ,τ  y ) =  FT  − 1 ( G ( f  x ,f  y ) F  ∗ ( f  x ,f  y ))  (2) =     G ( f  x ,f  y ) F  ∗ ( f  x ,f  y )  e ( j 2 π ( f  x τ  x + f  y τ  y )) df  x df  y . where  G ( f  x ,f  y )  and  F  ( f  x ,f  y )  are the 2-D FTs of   g ( x,y ) and  f  ( x,y ) , respectively with  f  x  and  f  y  demoting the spatialfrequencies. The test image g ( x,y )  is filtered by H  ( f  x ,f  y ) = F  ∗ ( f  x ,f  y )  to produce the output  c ( τ  x ,τ  y ) . Hence,  H  ( f  x ,f  y ) is the correlation filter which is complex conjugate of the  2 -DFT of the reference image  f  ( x,y ) . 2.2. Graph Cuts Segmentation Framework In the graph cuts method, a  VB  (object) and surrounding or-gans (background) are represented using a gray level distribu-tion models which are approximated by a linear combinationof Gaussians (LCG) to better specify region borders betweentwo classes (object and background). Initial segmentationbased on the LCG models is then iteratively refined by usingMGRF with analytically estimated potentials. In this step, thegraph cuts is used as a global optimization algorithm to findthe segmented data that minimize a certain energy function,which integrates the LCG model and the MGRF model.To segment a  VB , the volume is initially labeled based onits gray level probabilistic model. Then we create a weightedundirected graph with vertices corresponding to the set of vol-ume voxels  P  , and a set of edges connecting these vertices.Each edge is assigned a nonnegative weight. The graph alsocontains two special terminal vertices  s  (source) “ VB ”, and  t (sink) “background”. Consider a neighborhood system in  P  ,which is represented by a set  N   of all unordered pairs  {  p,q  } of neighboring voxels in P  . Let L the set of labels { “0”, “1” } ,correspond to  VB  and background regions respectively. La-beling is a mapping from  P   to  L , and we denote the set of labeling by  f   =  { f  1 ,...,f   p ,...,f  |P| } . In other words, thelabel  f   p , which is assigned to the voxel  p  ∈ P  , segments itinto  VB  or background region. Now our goal is to find theoptimal segmentation, best labeling  f  , by minimizing the fol-lowing energy function: E  ( f  ) =   p ∈P  D  p ( f   p ) +  {  p,q }∈N  V   ( f   p ,f  q ) ,  (3)where  D  p ( f   p ) , measures how much assigning a label  f   p  tovoxel  p  disagrees with the voxel intensity,  I   p .  D  p ( f   p ) = − ln P  ( I   p  |  f   p )  is formulated to represent the regional prop-erties of segments. The second term is the pairwise interac-tion model which represents the penalty for the discontinuitybetween voxels  p  and  q  .To initially label the  VB  volume and to compute the datapenalty term D  p ( f   p ) , we use the modified EM [11] to approx-imate the gray level marginal density of each class  f   p ,  VB  andbackground region, using a LCG with  C  + f  p positive and  C  − f  p negative components as follows: P  ( I   p | f   p ) = C  + f p  r =1 w + f  p ,r ϕ ( I   p | θ + f  p ,r ) − C  − f p  l =1 w − f  p ,l ϕ ( I   p | θ − f  p ,l ) , (4)where  ϕ ( . | θ )  is a Gaussian density with parameter  θ  ≡ ( µ,σ 2 )  with mean  µ  and variance  σ 2 .  w + f  p ,r  means the  r th 655  (a)(b) (c) (d) Fig. 3 .  Steps of the proposed algorithm. (a) The clinical CT dataset, (b) the Matched filter determines the VB region, (c) LCG initial-ization, and (d) the final result using the graph cuts. positive weight in class  f   p  and  w − f  p ,l  means the  l th nega-tive weight in class  f   p . These weights have a restriction  C  + f p r =1  w + f  p ,r  −  C  − f p l =1  w − f  p ,l  = 1 .The simplest model of spatial interaction is the MarkovGibbsrandomfield(MGRF)withthenearest6-neighborhood.Therefore, for this specific model the Gibbs potential,  γ  , canbe obtained analytically using our maximum likelihood es-timator (MLE) for a generic MGRF in [12, 13]. So, theresulting approximate MLE of   γ   is: γ  ∗ =  K   −  K  2 K   − 1 f  neq ( f  )   .  (5)where  K   = 2  is the number of classes in the volume and f  neq ( f  )  denotes the relative frequency of the not equal labelsin the voxel pairs. To segment a  VB  volume, we use a 3Dgraph where each vertex in this graph represents a voxel inthe  VB  volume. Then we define the weight of each edge asshown in table 2.2. After that, we get the optimal segmen-tation surface between the  VB  and its background by findingthe minimum cost cut on this graph. The minimum cost cut iscomputed exactly in polynomial time for two terminal graphcuts with positive edges weights via  s/t  Min-Cut/Max-Flowalgorithm [14].Edge Weight for {  p,q  }  γ f   p   =  f  q 0  f   p  =  f  q { s,p } − ln [ P  ( I   p  |  “1”)]  p  ∈ P {  p,t } − ln [ P  ( I   p  |  “0”)]  p  ∈ P  2.3. Local Adaptive Volume Growing Method Starting from the segmented  VB , check every voxel on itsouter surface. If the intensity value or Hounsfield units (HU)of this voxel is greater than a local threshold then it will beused to initiate a local volume growing. This volume growingclassification is based on the mean intensity value,  µ , and itsstandard deviation,  σ , in the  26 -neighborhood of the consid-(a) (b) Fig. 4 .  Two dimensional view of the separation of trabecular andcortical bones. (a) Integral segmented  VB  including trabecular andcortical bones. (b) ROI outline of the trabecular bone. ered voxel,  v , as follows:  if   I  ( v )  ≥  µ − ασ,  label  v  as cortical , if   I  ( v )  < µ − ασ,  label  v  as trabecular , (6)with  α  being a small positive real number. In our experiment,we accept that  α  = 1 . 3. EXPERIMENTS AND DISCUSSION To assess the accuracy and robustness of our proposed frame-work, we tested it using clinical data sets, as well as, the phan-tom (  ESP ), which is an accepted standard for quality con-trol [2] in bone densitometry. The real data sets were scannedat  120 kV and  2 . 5 mm slice thickness. The  ESP  was scannedat  120 kV and  0 . 75 mm slice thickness. All algorithms are runon a PC 3Ghz AMD Athlon 64 X2 Dual, and 3GB RAM. Allimplementations are in C++.To compare the proposed method with other alternatives, VBs  are subsequently segmented using the spline interpola-tion and level sets method including some post-processingsteps. Finally, segmentation accuracy is measured for eachmethod using the ground truths (expert segmentation). M1represents the proposed algorithm. The alternative meth-ods used in the experiments are represented as M2 (forspline-based interpolation), M3 (for level sets with mor-phological closing post-process), M4 (for level sets withoutany post-process), and M5 (for level sets with interpolationpost-process).To evaluate the results we calculate the percentage seg-mentation error as follows: error % = 100 ∗ Number of misclassified voxelsTotalnumber of   VB  voxels .  (7)Preliminary results are very encouraging and the test re-sults was achieved for 10 data sets and the  ESP . The statisti-cal analysis of our method is shown in the Table 1. In thistable the results of the proposed segmentation method andother four alternatives are shown. The average error of the VB  segmentation on  10  clinical  3 D image sets is  5 . 6%  forthe proposed method. The average error of in the trabecularbone segmentation is  2 . 14% . It is worth mentioning that thesegmentation step is extremely fast thanks to automatically 656  (M1) (M2) (M3) (M4) (M5) Fig. 5 .  3D results of one clinical data sets using different methods.(M1) The result of the proposed method, (M2-M5) The results of alternative methods. Red color shows the segmentation errors. Fig. 6 .  Some 3D results of the proposed framework. detection of the  VOI   step using the Matched Filter. The seg-mentation time is much faster than that reported in [3, 5] andother alternatives tested in our experiment. The spline basedinterpolation method, represented as M2, has the closest seg-mentation accuracy for the clinical data set as shown in theTable 1. An example that shows 3D segmentation results of all tested methods for a clinical data set is shown in Fig 5.In this figure, the red color represents the misclassified vox-els. The result of M1 has less misclassified voxels than othermethods. Some 3D results of the proposed method are shownin the Fig. 6.The Figure 7 shows some CT images of the  ESP  used inour experiment. Because clinical CT images have gray levelinhomogeneity, noise, andweakedgesinsomeslices, the  ESP was scanned with the same problems to validate the robust-ness of the method. The  VB  segmentation error on the  ESP  is 3 . 0%  for the proposed method. The level set method withoutany post-processing has the closest (but not less) segmenta-tion error which is  9 . 9% . The Fig. 8 shows 3D segmentationresults for the  ESP  using M1 (proposed method) and M4. Be-causetheproposedalgorithmusesbothgraylevelinformationand spatial interaction between the voxels, it is superior thanother alternatives. 4. CONCLUSION In this paper, we have presented a novel, fast, and robust 3D seg-mentation framework for  VBs  and  TBs  in clinical CT images. Userinteraction is completely eliminated using the Matched filter which Table 1 .  Accuracy and time performance of our  VB  segmentationon 10 data sets. Average volume 512x512x14. M1 M2 M3 M4 M5 Min. error, % 2.1 3.5 7.3 8.2 7.2Max. error, % 12.6 8.6 34.3 41.4 37.2Mean error, % 5.6 6.3 13.7 15.5 14.5Stand. dev.,% 4.3 2.4 11.5 14.5 12.8Average time,sec 7.5 34.5 12.5 6.9 43.6 Fig. 7 .  CT images from the  ESP  data set.   (a) (b) Fig. 8 .  3D Results for the  ESP . (a) The result of the proposed algo-rithm, (b) The result of M4 which has closest result to the proposedalgorithm. Red color shows the misclassified area.detects the  VB  region automatically. This step also improves thesegmentation accuracy of the graph Cuts method. Validity was ana-lyzed using ground truths of data sets and the European Spine Phan-tom (  ESP ) as a known reference. Experiments on the data sets showthat the proposed segmentation approach is more accurate and robustthan other known alternatives. 5. REFERENCES [1]  Y. Kang, K. Engelke, and W. A. Kalender, New accurate and precise3D segmentation method for skeletal structures in volumetric CT data,TMI, vol. 22, no. 5, pp. 586-598, 2003.[2] W. A. Kalender, D. Felsenberg, H. Genant, M. Fischer, J. Dequeker, andJ. Reeve, The European Spine Phantom - a tool for standardization andquality control in spinal bone measurements by DXA and QCT Euro-pean J. Radiology, vol. 20, pp. 83-92, 1995.[3] A. Mastmeyer, K. Engelke, C. Fuchs, and W. A. Kalender, A hierarchi-cal 3D segmentation method and the definition of vertebral body coor-dinate systems for QCT of the lumbar spine, Medical Image Analysis,vol. 10, no. 4, pp. 560-577, 2006.[4] www.back.com.[5] J. Kaminsky, P. Klinge, M. Bokemeyer, W. Luedemann, and M Samii,Specially adapted interactive tools for an improved 3D-segmentation of the spine, Computerized Medical Imaging and Graphics, vol. 28, no. 3,pp. 119-127, 2004.[6] S. Tan, J. Yao, M. M. Ward, L. Yao, and R. M. Summers, Computeraided evaluation of Ankylosing Spondylitis, (ISBI’06) pp. 339-342,2006.[7] S. Tan, J. Yao, M. M. Ward, L. Yao, and R. M. Summers, ComputerAidedEvaluationofAnkylosingSpondylitisUsingHigh-ResolutionCT,TMI, vol. 27, no. 9, pp. 1252-1267, 2008.[8] T. B. Sebastiana, H. Teka, J. J. Criscob, and B. B. Kimia, Segmentationof carpal bones from CT images using skeletally coupled deformablemodels, Medical Image Analysis, vol.7, no.1, pp. 21-45, 2003.[9] R.A.Zoroofi, Y.Sato, T.Sasama, T.Nishii, N.Sugano, K.Yonenobu, H.Yoshikawa, T. Ochi, and S. Tamura Automated segmentation of acetab-ulum and femoral head from 3-D CT images, IEEE Trans Inf TechnolBiomed, vol. 7, no. 4, pp. 329-343, 2003.[10] B. V. K. V. Kumar, M. Savvides, and C. Xie, Correlation pattern recog-nition for face recognition, Proceedings of the IEEE, vol. 94, no. 11,pp. 1963-1976, 2006.[11] A.A. Farag, A. El-Baz, and G. Gimelfarb, Density estimation usingmodified expectation maximization for a linear combination of gaus-sians, ICIP’04, vol. 3, pp. 1871-1874, 2004.[12] A. M. Ali and A. A. Farag, Automatic Lung Segmentation of Volu-metric Low-Dose CT Scans Using Graph Cuts, ISVC’08, pp. 258-267,2008.[13] M. S. Aslan, A. M. Ali, B. Arnold, R. Fahmi, A. A. Farag, and PingXiang, Segmentation of trabecular bones from vertebral bodies in volu-metric CT spina images, ICIP’09, 2009, (Accepted to appear).[14] Y. Boykol and V. Kolmogorov, An experiment comparison of min-cut/max-flowalgorithms for energy minimization in vision, IEEE Trans-action on Pattern Analysis and Machine Intelligence, vol. 26, pp. 1124-1137, 2004. 657
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