Alathari, Thamer

Bah, Mamadou T.

Nixon, Mark S.

English

Thamer S. Alathari

Mark S. Nixon

Mamadou T. Bah

Crossref

Femur Bone Segmentation Using a Pressure Analogy

Southampton (e-Prints Soton)

Femur Bone Segmentation using a Pressure Analogy                 Thamer S. Alathari, Mark S. Nixon School of Electronics and Computer Science University of Southampton, UK [tsa1g11|msn]@soton.ac.uk   Mamadou T. Bah Faculty of Engineering and the Environment  University of Southampton, UK msn@soton.ac.uk   Abstract— It has been recently shown that preclinical analysis of computed tomography 3D image volumes can provide essential information  to  find  the  optimal  position  of  an  implant  in  hip replacement procedures. In order to extract such data, proper segmentation is crucial. Many of the currently-available methods depend on manually segmented data as the first step. Inherent difficulties concern the similar density of adjacent structures, and that physically-separated structures appear to touch in scanned imagery. In this study, we describe a new technique  based on pressure analogy that depends on the local features of the image to accurately and automatically segment and visualize the femur bone and separate it from the acetabulum. The Dice coefficient was employed to study the similarity between the surface area of the segmentations compared with the manually segmented data, and  a  high  value  has  been  achieved.  The  same  method  also showed promising results in segmenting other limbs such as the pelvis, tibia and fibula bones.  Keywords—Visualization; Segmentation; 3D volume; Pressure; Analogy; Femur;  I.  INTRODUCTION Image segmentation is a valuable source of information for pre-clinical  procedures  often  aiding  hip  replacement. Osteoarthritis,  which  is  one  of  the  most  common  types  of arthritis,  is  a  disease  that  causes  the  distance  between  the femur bone and the acetabulum (pelvis socket) to become very small due to the degradation of the articular cartilage and the overgrowth of the bone. For successful implant placement, a proper  study  for  the  positioning  is  essential  to  get  the  best results and to distribute the forces exerted by the body weight.   The  problem  of  image  segmentation  in  this  scenario  is illustrated in Fig. 1, which shows one slice of a stack of CT-scanned images of the hip. The image shows the femoral head and the  acetabulum, together  with  some  surrounding tissue. We seek to process the whole volume image to visualize the femoral bone, and the image shows that the two bones appear to be connected.  Previous  research  has  tackled  this  problem  using  manual segmentation as prerequisite such as; statistical shape methods to describe the femur bone [1] [2], general Hough transform to construct the optimum model [3] and iterative deformable  Fig. 1. The intersection between the femoral head (blue) with the acetabulum (green) is circled sand labeled in (red)  model to match the femur shape [4]. Other methods relied on initial parameters chosen by an operator to refine boundary information between the acetabulum and the femoral bone [5]. There are two automated approaches to bone segmentation in the  literature,  one  is  based  on  the  graphcut  method  using statistical  analysis  and  morphology  [6]  and  the  other  one hinged on local adaptive thresholding conditioned on Bayesian rules [7].   In this work, we extend a new pressure analogy [8] to include segmentation  of  touching  objects  with  similar  density.  Pressure  is  used  as  a  volumetric  analogy  to  provide  an operator to analyze and refine features in volume data. Only the  principles  of  pressure  are  used  to  motivate  an  image analysis  operator:  precise  detail  is  not  needed.  Pressure domain data has been enhanced by a new mapping technique followed by morphological operations to expand the pressure mask  effect.  This  is  not  possible  using  conventional morphological operations (without the pressure analogy) since these are isotropic and lack capability to separate gaps whilst retaining overall shape. Logical operations are applied to the pressure  mask  to  separate  the  femur  bone  from  the acetabulum.  Labeling  has  been  aided  by  using  statistical operations. The proposed method is intuitive, anisotropic, non-iterative  and  requires  no  previous  knowledge  and  can automatically  separate  connected  structures  of  similar appearance (or density, in CT images). II.  FEATURE EXTRACTION USING THE PRESSURE ANALOGY Extracting the  femur  bone  presents  a  great  challenge  for segmentation methods due to the existence of similar density bones  surrounding  and  touching  its  surface.  The  pressure analogy  presents  a  new  perspective  into  the  problem  of separating connected objects in volumetric images. Unlike the previous work, which depends on the small gradient between objects, this paper addresses the separation of objects which have a similar density and which appear to be touching in that the space between them is often small and occasionally zero. The  same  basis  as  the  original  pressure  approach  [8]  was adopted, one-sided threshold followed by a convolving cube to calculate  the  volume  of  the  background  to  obtain  pressure domain. The pressure domain provides valuable information about connected areas between the objects.  where     is  a  window  of  size  5×5×5,     is  the  volume thresholded  so  as  to  remove  background  data, retaining  the high  density  values,  and     is  the  pressure  domain.  The pressure data is then mapped using a high pass filter response to retain consistency and to provide a smooth transform. The filter  is  derived  by  arranging  the  pressure  levels    	in ascending  order  and  deriving  a  mapping  function  extracted from a high-pass filter:     =        +     (2)  where     = 180,    = − (1 2     ⁄ ),     = 1500  and C = 	1.06 × 10  	with  a  cut-off  frequency    	   	    = 100, for    ∈ [1,125],  so  the high  pressure  values  in  the top  25 levels are retained and emphasized. This mapping function is used to derive    =  (  ) which is then thresholded.    , ,  =  1												if	 ′ , ,  ≥ threshold	0																															otherwise  (3)  After that, connectivity check was applied on the thresholded mask; each element labeled defines a structured element    stored in 4D matrix ML. Each element is dilated three times to increase its mass and close the gap between elements using structure S of size 3×3×3 with all voxels turned on.   ′  =    ⊕    			∀	 	 ∈ 1:    	  	  	 ℎ 	4 ℎ	          (4)  The next  step is  to  erode  the  whole  mask in an attempt to minimize its effect.      =          		    ′ #              (5)        =      ⊖   (6)  The  final  mask          is  then  inverted  and  applied  to  the thresholded volume  , separating the objects.     , ,  = ¬	      	 , ,  ×   , ,   (7)  The objects were labeled individually to describe each object uniquely. The mask discards a small amount of data, which is implicit in these operations. To recover this data, the mask is multiplied by a logical thresholded volume to obtain only the areas in the mask (used to separate objects) and which do not exist in the background.     , ,  =	      	 , ,  × 	       (  , , )  (8)  Skeletonization [9] was applied as per slice on the recovery volume   to create small creek between the mask segments to aid the reconstruction process. The labeled mask is then grown on  those  areas  using  statistical  mode.  A  unique  label  now defines each object in volume	 , with no lost data.    , ,  =        , , ∈  				∀  , ,  ∈ foreground  (9)  Three morphological closing operations have been applied to every labeled object and close any open gaps in the detected object.        ,  =           ∀	 	 ∈ 1:Number	of	labels  (10)  where          is  a  4D  matrix  contain  the  volume  of  each segmented object. To analyse the validity of the results, the surface area was calculated for the proposed method results    and  the  manually  segmented  data    .  The  manual segmentation  took  place  by  thresholding  then  removing surrounding  bones  and  soft  tissue.  The  Dice  similarity coefficient (  ) [10] was used to compare the two results.     = 2       + a   ⁄   (11)  Our work describes a solution that is based  on the original basis of  the pressure analogy. Virtually the same advantages have  been  accrued  as  in  the  literature;  a  non-iterative, anisotropic  method  that  depends  on  local  features  of  the objects  in  the  scene.  The  novel  step  is  the  high  level refinement  and  the  extension  towards  separating  connected objects of similar density.    , ,  = 1     , ,  , , ∈   ∀  , ,  ∈ background  (1) III.  RESULTS As discussed previously, the method provides a mask that is used  to  separate  the  connected  objects.  In  this  section,  we evaluate  the  performance  of  the  proposed  method  on  51 volumetric cropped images of femur bone acquired using CT scanner.     The  images  were  cropped  to  concentrate  the    z=25  z=33    z=38  z=42    z=53  z=58 Fig. 2. Different slice though the hip showing the contact area between the femoral head and the acetabulum   z=325  z=329  z=333    z=250  z=255  z=260 Fig. 3. Different slices showing the different contact areas between the femur bone and the surrounding veins           z=25  z=33    z=38  z=42    z=53  z=58 Fig. 5. Different slices though the hip showing the contact area between the femoral head and the acetabulum    (a)  (b) Fig. 4. A render of the final segmented image shown in Fig. 2 and Fig. 3  (a)Render showing the largest 6 objects, (b)The largest object labeled hence the femur bone. feature extraction process. To illustrate the problem, several slices of the connected areas between the acetabulum and the femoral head of one volume are shown Fig 2. In these images, the  connections  appear in different  places,  so  the technique requires  information  from  local  features.  Another  problem also arises, in that the multiple contact areas between the veins in the surrounding soft tissue touching the femur, especially when a contrast agent is present. However, veins have little impact on the total surface area, as in Fig 3.  A  rendering  of  the  final  labeled  objects,  with  each  label identified by a unique color, is shown in Fig. 4a. Once the femur bone is labelled and identified it can be extracted by choosing  the  desired  label  as  in  Fig.  4b.  Successive  slices through the segmented data are shown in Fig. 5.These show that the acetabulum is correctly identified as separate from the femur even when they are in contact and that the perimeters of the bones (the surfaces) are extracted correctly.        Fig. 6. Sample of four segmented femur bones using the proposed method  The  proposed  method  has  been  applied  to  the  51  femur volumes; random sample of the results is shown in Fig. 6. The segmentation proved to be successful and the femur bone was extracted properly. Nevertheless, some of the results showed less  than  perfect  segmentation as  in  Fig.  7.  In  some  cases, some segments of the femur head were joined with the hip, in other cases the whole head of the femur bone is lost and the worst was the difficulty of separating the hip and the femur bone.  A  histogram  provided  in  Fig.  8  showing  the performance of the proposed method on the 51 femur bones, the effects of veins have been omitted due to their minor effect on the total surface of the segmented femur bone. This shows that  a  clear  majority  of  the  femurs  have  been  successfully extracted  intact,  that  many  of  the  remainder  have  small segments  missing,  and  that  only  one  is  extracted  with connections remaining.  Due to the absence of the source code for the state of the art methods  such  as  [6]  and  [7]  a  fair  comparison  would  be difficult specially with variety of parameter choices available. The Dice coefficient of each sample of 9 volumetric images has been calculated. To verify the amount of loss in the total surface area in the results, the manual segmentation were used as the ground truth Fig. 9.  An average of dc = 0.907 has been calculated which indicate a minor loss in the total surface area and a successful segmentation.     (a)  (b)    (c)  (d) Fig. 7. Example of several situations where the proposed method did not perform well, (a) and (b) Some segments missing from the femoral head, (c) Femoral head completely lost, (d) Complete failure to separate the femur bone from the hip.                                       Percentage  Result Type Fig. 8. A histogram showing the performance of the proposed method  Dice Coefficient per Sample         Samples 1-3 Fully segmented femur bones    Samples 4-6 Femoral heads with lost bits    Samples 6-9 Femur bones with veins  Fig. 9. Dice coefficient for a sample of the results based on the total surface area compared to the surface area of the manually segmented data.  It is also worth noting that the Dice coefficients of the femur bone  extracted  together  with  veins  and  arteries  have introduced  false-positive  information.  This  arises  from  the larger  surface  area  of  the  combination  of  bone  with  blood vessels  and  could lead  the  Dice  coefficient to  exceed  unity which  has  not  occurred  here  (some  segments  have  been omitted, but cannot be observed in these renderings).  As anticipated, the proposed method showed promising results in segmenting and visualizing other bones such as the tibia and fibula bones in Fig. 10 where the only variable changed is the threshold used for the pressure (Eq. 3). Figure 11 shows images of the complete pelvis, Fig. 11a includes some blood vessels, two femoral heads and the lower lumbar region. Fig. 11b shows the labelled pelvis extracted alone from this data. Again, the only variable changed is the pressure threshold and the remainder of the technique is wholly automatic.  IV.  DISCUSSION AND CONCLUSIONS Segmenting and visualizing the femur bone is the first step for future preclinical analysis in arthritis. The literature flourishes with machine learning techniques that depends on manually segmented  data.   The  problem  with  those  techniques  is  the general problem of machine learning, they are data oriented. Morphology operations alone would introduce or neglect some of the valuable information by acting in an isotropic manner, which would result in undesirable results. On the other hand, the new pressure analogy depends on local image features; it is anisotropic, non-iterative. The technique could even provide a mask without the need for training or learning. The proposed method  based  on  the  pressure  analogy  carries  of  the  same advantages,  and  can  handle  similar  density  connection between the objects. This would benefit the automation of the other techniques discussed in literature such as providing an automatic  large  set  of  data  for  machine  learning  and presenting  the  general  Hough  transform  with  a  standard template.  The  results  can  also  be  of  great  help  to  the preclinical studies of hip replacement, and help determining the optimum positioning of the femur bone implant to achieve a  perfect  fit.  The  proposed  method  has  shown  encouraging results for separating touching objects with the same density in computer tomography volumes. In future, more local features will be taken into account to reveal more information about the object of interest.    (a)  (b)    (c)  (d) Fig. 10. Other bones segmented using the proposed method, (a) and (c) Rendering of segmented tibia bone, (b) and (d) Rendering of segmented fibula bone. 010203040506070Femur bones with Femoral headFemur bones without errorsFemur bones with missing bits from Femoral headFemur bones connected to pelvis0.20.40.60.811 2 3 4 5 6 7 8 9Dice CoefficientSample Number(a)  (b) Fig. 11. Other bones segmented using the proposed method  (a) Rendering of the hip area including some blood vessels, two femoral heads and the lower lumbar region, (b) Rendering of the final segmented pelvis.    ACKNOWLEDGMENTS The  authors  would  like  to  thank  the  Public  Authority  for Applied Education and Training in Kuwait for providing the financial support and studentship of T Alathari.  REFERENCES [1]  J. Schmid, J. Kim, and N. Magnenat-Thalmann, “Robust Statistical Shape Models for MRI Bone Segmentation in Presence of Small Field of View,” Med. Image Anal., vol. 15, no. 1, pp. 155–68, Feb. 2011. [2]  F. Yokota, T. Okada, M. Takao, N. Sugano, Y. Tada, and Y. Sato, “Automated Segmentation of The Femur and Pelvis from 3D CT Data of Diseased Hip Using Hierarchical Statistical Shape Model of Joint Structure,” Med. Image Comput. Comput. Assist. Interv., vol. 12, no. Pt 2, pp. 811–8, Jan. 2009. [3]  H. Seim, D. Kainmueller, and M. 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S. Alathari and M. S. Nixon, “Segmenting Objects in 3d Images by Volumetric Analysis,” Proc. ISVC 2013, LNCS, 8033, pp. 238–245, 2013. [9]  L. Lam, S.-W. Lee, and C. Y. Suen, “Thinning Methodologies-A Comprehensive Survey,” IEEE Trans. Pattern Anal. Mach. Intell., vol. 14, no. 9, p. 879, 1992. [10]  T. Sørensen, “A method of Establishing Groups of Equal Amplitude in Plant Sociology Based on Similarity of Species and its Application to Analyses of the Vegetation on Danish Commons,” Biol. Skr., vol. 5, pp. 1–34, 1948.                                   

A method of Establishing Groups of Equal Amplitude in Plant Sociology Based on Similarity of Species and its Application to

Femur bone segmentation using a pressure analogy

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Southampton (e-Prints Soton)