Journal of Digital Imaging

, Volume 26, Issue 3, pp 554–562 | Cite as

Automated, Foot-Bone Registration Using Subdivision-Embedded Atlases for Spatial Mapping of Bone Mineral Density

  • Lu Liu
  • Paul K. Commean
  • Charles Hildebolt
  • Dave Sinacore
  • Fred Prior
  • James P. Carson
  • Ioannis Kakadiaris
  • Tao Ju


We present an atlas-based registration method for bones segmented from quantitative computed tomography (QCT) scans, with the goal of mapping their interior bone mineral densities (BMDs) volumetrically. We introduce a new type of deformable atlas, called subdivision-embedded atlas, which consists of a control grid represented as a tetrahedral subdivision mesh and a template bone surface embedded within the grid. Compared to a typical lattice-based deformation grid, the subdivision control grid possesses a relatively small degree of freedom tailored to the shape of the bone, which allows efficient fitting onto subjects. Compared with previous subdivision atlases, the novelty of our atlas lies in the addition of the embedded template surface, which further increases the accuracy of the fitting. Using this new atlas representation, we developed an efficient and fully automated pipeline for registering atlases of 12 tarsal and metatarsal bones to a segmented QCT scan of a human foot. Our evaluation shows that the mapping of BMD enabled by the registration is consistent for bones in repeated scans, and the regional BMD automatically computed from the mapping is not significantly different from expert annotations. The results suggest that our improved subdivision-based registration method is a reliable, efficient way to replace manual labor for measuring regional BMD in foot bones in QCT scans.


Bone mineral density Registration Atlas Subdivision 



This work is supported in part by NIH grants (R21DK79457 and R21NS058553) and NSF grants (DBI-0743691 and CCF-0702662).


  1. 1.
    Popp AW, Senn C, Franta O, Krieg MA, Perrelett R, Lippuner K: Tibial or hip BMD predict clinical fracture risk equally well: results from a prospective study in 700 elderly Swiss women. Osteoporos Int 20:1392–1399, 2009CrossRefGoogle Scholar
  2. 2.
    Engelke K, Adams JE, Armbrecht G, et al: Clinical use of quantitative computed tomography and peripheral quantitative computed tomography in the management of osteoporosis in adults: the 2007 ISCD Official Positions. J Clin Densitom 11:123–162, 2008PubMedCrossRefGoogle Scholar
  3. 3.
    Faulkner KG: Bone matters: are density increases necessary to reduce fracture risk? Journal of Bone and Mineral Research 15(2):183–187, 2000PubMedCrossRefGoogle Scholar
  4. 4.
    Liu L, Raber D, Nopachai D, Commean P, Sinacore D, Prior F, Pless R, Ju T: Interactive separation of segmented bones in ct volumes using graph cut. In: Proc. of the 11th international conference on Medical Image Computing and Computer-Assisted Intervention - Part I. 2008, 296–304Google Scholar
  5. 5.
    McInerney T, Terzopoulos D: Deformable models in medical image analysis: a survey. Medical Image Analysis 1(2):91–108, 1996PubMedCrossRefGoogle Scholar
  6. 6.
    Toga A: Brain Warping. Academic, 1998Google Scholar
  7. 7.
    Gain J, Bechmann D: A survey of spatial deformation from a user-centered perspective. ACM Trans. Graph. 27(107):1–107, 2008. 21CrossRefGoogle Scholar
  8. 8.
    Wells W, Viola P, Atsumi H, Nakajima S, Kikinis R: Multi-modal volume registration by maximization of mutual information. Medical Image Analysis 1(1):35–51, 1996PubMedCrossRefGoogle Scholar
  9. 9.
    Davatzikos C, Prince JL, Bryan RN: Image registration based on boundary mapping. IEEE Trans Med Imaging 15:112–115, 1996PubMedCrossRefGoogle Scholar
  10. 10.
    Johnson HJ, Christensen GE: Consistent landmark and intensity-based image registration. IEEE Trans Med Imaging 21(5):450–461, 2002PubMedCrossRefGoogle Scholar
  11. 11.
    Peckar W, Schnorr C, Rohr K, Stiehl HS: Two step parameter-free elastic image registration with prescribed point displacements. J Math Imaging Vision 10:143–162, 1999CrossRefGoogle Scholar
  12. 12.
    Zhang B, Arola DD, Roys S, Gullapalli RP: Three-dimensional elastic image registration based on strain energy minimization: application to prostate magnetic resonance imaging. Journal of Digital Imaging 24(4):573–585, 2011PubMedCrossRefGoogle Scholar
  13. 13.
    Christensen GE, Rabbit RD, Miller MI: Deformable templates using large deformation kinematics. IEEE Trans Image Process 5:1435–1447, 1996PubMedCrossRefGoogle Scholar
  14. 14.
    Thirion JP: Image matching as a diffusion process: an analogy with Maxwell’s demons. Med Image Anal 2:243–260, 1998PubMedCrossRefGoogle Scholar
  15. 15.
    Ju T, Carson J, Liu L, Warren J, Bello M, Kakadiaris I: Subdivision meshes for organizing spatial biomedical data. Methods 50(2):70–76, 2010PubMedCrossRefGoogle Scholar
  16. 16.
    Sederberg T, Parry S: Free-form deformation of solid geometric models. SIGGRAPH Comput. Graph 20:151–160, 1986CrossRefGoogle Scholar
  17. 17.
    MacCracken R, Joy K: Free-form deformations with lattices of arbitrary topology. In: Proc. of the 23rd annual conference on computer graphics and interactive techniques. SIGGRAPH ′96: 1996, 181–188Google Scholar
  18. 18.
    Bello M, Ju T, Carson J, Warren J, Chiu W, Kakadiaris I: Learning-based segmentation framework for tissue images containing gene expression data. IEEE Trans. Med. Imaging 26(5):728–744, 2007PubMedCrossRefGoogle Scholar
  19. 19.
    Commean PK, Ju T, Liu L, Sinacore DR, Hastings MK, Mueller MJ: Tarsal and metatarsal bone mineral density measurement using volumetric quantitative computed tomography. Journal of Digital Imaging 22:492–502, 2009PubMedCrossRefGoogle Scholar
  20. 20.
    Warren J, Weimer H: Subdivision methods for geometric design. Morgan-Kaufmann, 2002Google Scholar
  21. 21.
    Schaefer S, Hakenberg J, Warren J: Smooth subdivision of tetrahedral meshes. In: Proc. the Eurographics/ACM SIGGRAPH Symposium on Geometry Processing, Eurographics Association. 2004, 151–158Google Scholar
  22. 22.
    Ju T, Schaefer S, Warren J: Mean value coordinates for closed triangular meshes. In: ACM Transactions on Graphics. 24(3):561–566, 2005CrossRefGoogle Scholar
  23. 23.
    Lorensen W, Cline H: Marching cubes: a high resolution 3d surface construction algorithm. SIGGRAPH Comput. Graph 21:163–169, 1987CrossRefGoogle Scholar
  24. 24.
    Taubin G: A signal processing approach to fair surface design. In: SIGGRAPH ′95: Proc. of the 22nd Annual Conference on Computer Graphics and Interactive Techniques, New York, NY, USA, ACM. 1995, 351–358Google Scholar
  25. 25.
    Garland M, Heckbert P: Surface simplification using quadric error metrics. In: Proc. of the 24th Annual Conference on Computer Graphics and Interactive Techniques. SIGGRAPH ′97. 1997, 209–216Google Scholar
  26. 26.
    Commean PK, Kennedy JA, Bahow KA, Hildebolt CF, Liu L, Smith KE, Hastings MK, Ju T, Prior FW, Sinacore DR: Volumetric quantitative computed tomography measurement precision for volumes and densities of tarsal and metatarsal bones. J Clin Densitom. 14(3):313–320, 2011PubMedCrossRefGoogle Scholar
  27. 27.
    Smith KE, Whiting BR, Reiker GG, Commean PK, Sinacore DR, Prior FW: Assessment of technical and biological parameters of volumetric quantitative computed tomography in the foot: a phantom study. Osteoporosis International, In Press, 2012Google Scholar
  28. 28.
    Robb RA: Three Dimensional Biomedical Imaging: Principles and Practice. VCH, New York, 1995Google Scholar
  29. 29.
    Robb RA, Hanson DP, Karwoski RA, Larson AG, Workman EL, Stacy MC. Analyze: a comprehensive, operator-interactive software.Google Scholar
  30. 30.
    Russ JC: The Image Processing Handbook, 2nd edition. CRC, Boca Raton, FL, 1995Google Scholar
  31. 31.
    Rasband WS: ImageJ. In: National Institutes of Health; 1997.
  32. 32.
    Chintalapani G, Ellingsen L, Sadowsky O, Prince J, Taylor R: Statistical atlases of bone anatomy: construction, iterative improvement and validation. In Proc. MICCAI′07. 2007, 499–506Google Scholar
  33. 33.
    Lipman Y, Funkhouser T: Möbius voting for surface correspondence. ACM Trans. Graph. 28(3):72, 2009CrossRefGoogle Scholar

Copyright information

© Society for Imaging Informatics in Medicine 2012

Authors and Affiliations

  • Lu Liu
    • 1
  • Paul K. Commean
    • 2
  • Charles Hildebolt
    • 2
  • Dave Sinacore
    • 2
  • Fred Prior
    • 2
  • James P. Carson
    • 3
  • Ioannis Kakadiaris
    • 4
  • Tao Ju
    • 1
  1. 1.Department of Computer Science and EngineeringWashington UniversitySt. LouisUSA
  2. 2.Washington University School of MedicineSt. LouisUSA
  3. 3.Pacific Northwest National LaboratoryRichlandUSA
  4. 4.Department of Computer ScienceUniversity of HoustonHoustonUSA

Personalised recommendations