Skip to main content

3D Anatomical Shape Atlas Construction Using Mesh Quality Preserved Deformable Models

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 7599))

Abstract

The construction of 3D anatomical shape atlas has been extensively studied in medical image analysis research for a variety of applications. Among the multiple steps of shape atlas construction, establishing anatomical correspondences across subjects is probably the most critical and challenging one. The adaptive focus deformable model (AFDM) [16] was proposed to tackle this problem by exploiting cross-scale geometry characteristics of 3D anatomy surfaces. Although the effectiveness of AFDM has been proved in various studies, its performance is highly dependent on the quality of 3D surface meshes. In this paper, we propose a new framework for 3D anatomical shape atlas construction. Our method aims to robustly establish correspondences across different subjects and simultaneously generate high-quality surface meshes without removing shape detail. Mathematically, a new energy term is embedded into the original energy function of AFDM to preserve surface mesh qualities during the deformable surface matching. Shape details and smoothness constraints are encoded into the new energy term using the Laplacian representation An expectation-maximization style algorithm is designed to optimize multiple energy terms alternatively until convergence. We demonstrate the performance of our method via two diverse applications: 3D high resolution CT cardiac images and rat brain MRIs with multiple structures.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   49.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Baldwin, M., Langenderfer, J., Rullkoetter, P., Laz, P.: Development of subject-specific and statistical shape models of the knee using an efficient segmentation and mesh-morphing approach. Computer Methods and Programs in Biomedicine 97(3), 232–240 (2010)

    Article  Google Scholar 

  2. Busaryev, O., Dey, T.K., Levine, J.A.: Repairing and meshing imperfect shapes with delaunay refinement. In: 2009 SIAM/ACM Joint Conference on Geometric and Physical Modeling, SPM 2009, pp. 25–33. ACM (2009)

    Google Scholar 

  3. Chen, T., Rangarajan, A., Eisenschenk, S.J., Vemuri, B.C.: Construction of Neuroanatomical Shape Complex Atlas from 3D Brain MRI. In: Jiang, T., Navab, N., Pluim, J.P.W., Viergever, M.A. (eds.) MICCAI 2010, Part III. LNCS, vol. 6363, pp. 65–72. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  4. Cootes, T.F., Twining, C.J., Babalola, K.O., Taylor, C.J.: Diffeomorphic statistical shape models. IVC 26, 326–332 (2008)

    Article  Google Scholar 

  5. Cootes, T., Taylor, C., Cooper, D., Graham, J.: Active shape model - their training and application. Computer Vision and Image Understanding 61, 38–59 (1995)

    Article  Google Scholar 

  6. Durrleman, S., Pennec, X., Trouvé, A., Gerig, G., Ayache, N.: Spatiotemporal Atlas Estimation for Developmental Delay Detection in Longitudinal Datasets. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009, Part I. LNCS, vol. 5761, pp. 297–304. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Fletcher, P.T., Lu, C., Pizer, S.M., Joshi, S.: Principal geodesic analysis for the study of nonlinear statistics of shape. TMI 23, 995–1005 (2004)

    Google Scholar 

  8. Gao, M., Huang, J., Zhang, S., Qian, Z., Voros, S., Metaxas, D., Axel, L.: 4D Cardiac Reconstruction Using High Resolution CT Images. In: Metaxas, D.N., Axel, L. (eds.) FIMH 2011. LNCS, vol. 6666, pp. 153–160. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  9. Gerber, S., Tasdizen, T., Joshi, S., Whitaker, R.: On the Manifold Structure of the Space of Brain Images. In: Yang, G.-Z., Hawkes, D., Rueckert, D., Noble, A., Taylor, C. (eds.) MICCAI 2009, Part I. LNCS, vol. 5761, pp. 305–312. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  10. Langs, G., Lashkari, D., Sweet, A., Tie, Y., Rigolo, L., Golby, A.J., Golland, P.: Learning an Atlas of a Cognitive Process in Its Functional Geometry. In: Székely, G., Hahn, H.K. (eds.) IPMI 2011. LNCS, vol. 6801, pp. 135–146. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Lorenzo-Valdes, M., Sanchez-Ortiz, G.I., Elkington, A.G., Mohiaddin, R.H., Rueckert, D.: Segmentation of 4D cardiac MR images using a probabilistic atlas and the em algorithm. Medical Image Analysis 8(3), 255–265 (2004)

    Article  Google Scholar 

  12. Nealen, A., Igarashi, T., Sorkine, O., Alexa, M.: Laplacian mesh optimization. In: International Conference on Computer Graphics and Interactive Techniques in Australasia and Southeast Asia, pp. 381–389 (2006)

    Google Scholar 

  13. Park, J., Shontz, S., Drapaca, C.: A combined level set/mesh warping algorithm for tracking brain and cerebrospinal fluid evolution in hydrocephalic patients. In: Image-Based Geometric Modeling and Mesh Generation, pp. 107–141 (2012)

    Google Scholar 

  14. Pinkall, U., Polthier, K.: Computing discrete minimal surfaces and their conjugates. Experimental Mathematics 2, 15–36 (1993)

    Article  MATH  MathSciNet  Google Scholar 

  15. Sastry, S., Kim, J., Shontz, S., Craven, B., Lynch, F., Manning, K., Panitanarak, T.: Patient-specific model generation and simulation for pre-operative surgical guidance for pulmonary embolism treatment. Image-Based Geometric Modeling and Mesh Generation pp. 223–249

    Google Scholar 

  16. Shen, D., Davatzikos, C.: An adaptive-focus deformable model using statistical and geometric information. PAMI 22(8), 906–913 (2000)

    Article  Google Scholar 

  17. Sigal, I., Hardisty, M., Whyne, C.: Mesh-morphing algorithms for specimen-specific finite element modeling. Journal of Biomechanics 41(7), 1381–1389 (2008)

    Article  Google Scholar 

  18. Sigal, I., Whyne, C.: Mesh morphing and response surface analysis: quantifying sensitivity of vertebral mechanical behavior. Annals of Biomedical Engineering 38(1), 41–56 (2010)

    Article  Google Scholar 

  19. Sigal, I., Yang, H., Roberts, M., Downs, J.: Morphing methods to parameterize specimen-specific finite element model geometries. Journal of Biomechanics 43(2), 254–262 (2010)

    Article  Google Scholar 

  20. Styner, M., Gerig, G., Lieberman, J., Jones, D., Weinberger, D.: Statistical shape analysis of neuroanatomical structures based on medial models. Medical Image Analysis 7, 207–220 (2003)

    Article  Google Scholar 

  21. Thompson, P.M., Toga, A.W.: Detection, visualization and animation of abnormal anatomic structure with a deformable probabilistic brain atlas based on random vector field transformations. Medical Image Analysis 1(4), 271–294 (1997)

    Article  Google Scholar 

  22. Zhan, Y., Shen, D.: Deformable segmentation of 3D ultrasound prostate images using statistical texture matching method. TMI 25(3), 256–272 (2006)

    MathSciNet  Google Scholar 

  23. Zhang, S., Zhan, Y., Dewan, M., Huang, J., Metaxas, D., Zhou, X.: Towards robust and effective shape modeling: Sparse shape composition. Medical Image Analysis, 265–277 (2012)

    Google Scholar 

  24. Zhang, Y., Xu, G., Bajaj, C.: Quality meshing of implicit solvation models of biomolecular structures. Computer Aided Geometric Design 23(6), 510–530 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  25. Zhang, Y., Bajaj, R., Xu, G.: Surface smoothing and quality improvement of quadrilateral/hexahedral meshes with geometric flow. In: Proceedings, 14th International Meshing Roundtable, pp. 449–468. John Wiley and Sons (2005)

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cui, X., Zhang, S., Zhan, Y., Gao, M., Huang, J., Metaxas, D.N. (2012). 3D Anatomical Shape Atlas Construction Using Mesh Quality Preserved Deformable Models. In: Levine, J.A., Paulsen, R.R., Zhang, Y. (eds) Mesh Processing in Medical Image Analysis 2012. MeshMed 2012. Lecture Notes in Computer Science, vol 7599. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33463-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-33463-4_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33462-7

  • Online ISBN: 978-3-642-33463-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics