Entropy-based particle correspondence for shape populations

  • Ipek Oguz
  • Josh Cates
  • Manasi Datar
  • Beatriz Paniagua
  • Thomas Fletcher
  • Clement Vachet
  • Martin Styner
  • Ross Whitaker
Review Article

Abstract

Purpose

Statistical shape analysis of anatomical structures plays an important role in many medical image analysis applications such as understanding the structural changes in anatomy in various stages of growth or disease. Establishing accurate correspondence across object populations is essential for such statistical shape analysis studies.

Methods

In this paper, we present an entropy-based correspondence framework for computing point-based correspondence among populations of surfaces in a groupwise manner. This robust framework is parameterization-free and computationally efficient. We review the core principles of this method as well as various extensions to deal effectively with surfaces of complex geometry and application-driven correspondence metrics.

Results

We apply our method to synthetic and biological datasets to illustrate the concepts proposed and compare the performance of our framework to existing techniques.

Conclusions

Through the numerous extensions and variations presented here, we create a very flexible framework that can effectively handle objects of various topologies, multi-object complexes, open surfaces, and objects of complex geometry such as high-curvature regions or extremely thin features.

Keywords

Correspondence Shape analysis Entropy 

References

  1. 1.
    Davies R (2002) Learning shape: optimal models for analysing shape variability. University of Manchester. Ph.D. thesisGoogle Scholar
  2. 2.
    Oguz I, Cates J, Fletcher T, Whitaker R, Cool D, Aylward S, Styner M (2008) Cortical correspondence using entropy-based particle systems and local features. In: 5th IEEE international symposium on biomedical imaging: from nano to macro. ISBI 2008, pp 1637–1640. doi:10.1109/ISBI.2008.4541327
  3. 3.
    Datar M, Gur Y, Paniagua B, Styner M, Whitaker R (2011) Geometric correspondence for ensembles of nonregular shapes. In: Fichtinger G, Martel A, Peters T (eds) Medical image computing and computer-assisted intervention MICCAI. Lecture notes in computer science, vol 6892. Springer, Heidelberg, pp 368–375. doi:10.1007/978-3-642-23629-7_45
  4. 4.
    Cates J, Meyer M, Fletcher T, Whitaker R (2006) Entropy-based particle systems for shape correspondence. In: Xavier P, Sarang J (eds) 1st MICCAI workshop on mathematical foundations of computational anatomy: geometrical, statistical and registration methods for modeling biological shape variability. Copenhagen, Denmark, pp 90–99Google Scholar
  5. 5.
    Cates J, Fletcher T, Warnock Z, Whitaker R (2008) A shape analysis framework for small animal phenotyping with application to mice with a targeted disruption of hoxd11. In: 5th IEEE international symposium on biomedical imaging: from nano to macro. ISBI 2008, pp 512–515. doi:10.1109/ISBI.2008.4541045
  6. 6.
    Cates J, Fletcher P.T, Styner M, Shenton M, Whitaker R (2007) Shape modeling and analysis with entropy-based particle systems. In: Karssemeijer N, Lelieveldt B (eds) Information processing in medical imaging. Lecture notes in computer science, vol 4584. Springer, Heidelberg, pp 333–345. doi:10.1007/978-3-540-73273-0_28
  7. 7.
    Oguz I, Niethammer M, Cates J, Whitaker R, Fletcher T, Vachet C, Styner M (2009) Cortical correspondence with probabilistic fiber connectivity. In: Jerry LP, Dzung LP, Kyle JM (eds) Information processing in medical imaging. Lecture notes in computer science, vol 5636. Springer, Heidelberg, pp 651–663. doi:10.1007/978-3-642-02498-6_54
  8. 8.
    Cates J, Fletcher T, Styner M, Hazlett H, Whitaker R (2008) Particle-based shape analysis of multi-object complexes. In: Metaxas D, Axel L, Fichtinger G, SzÃkely G (eds) Medical image computing and computer-assisted interventionâ–MICCAI. Lecture notes in computer science, vol 5241. Springer, Heidelberg, pp 477–485. doi:10.1007/978-3-540-85988-8_57
  9. 9.
    Datar M, Cates J, Fletcher T, Gouttard S, Gerig G, Whitaker R (2009) Particle based shape regression of open surfaces with applications to developmental neuroimaging. In: MICCAI, pp 167–174Google Scholar
  10. 10.
    Lee J, Lyu I, Oguz I, Styner M (2013) Particle-guided image registration. In: MICCAI, pp 1–8Google Scholar
  11. 11.
    Lyu I, Kim S, Seong J, Yoo S, Evans A, Shi Y, Sanchez M, Niethammer M, Styner M (2013) Group-wise cortical correspondence via sulcal curve-constrained entropy minimization. In: IPMI, pp 364–375Google Scholar
  12. 12.
    Datar M, Lyu I, Kim S, Cates J, Styner M, Whitaker R (2013) Geodesic distances to landmarks for dense correspondence on ensembles of complex shapes. In: MICCAI, pp 19–26Google Scholar
  13. 13.
    Dalal P, Shi F, Shen D, Wang S (2010) Multiple cortical surface correspondence using pairwise shape similarity. In: Jiang T, Navab N, Pluim JPW, Viergever MA (eds) Medical image computing and computer-assisted intervention–MICCAI. Lecture notes in computer science, vol 6361. Springer, Heidelberg, pp 349–356Google Scholar
  14. 14.
    Fischl B, Sereno M, Tootell R, Dale A (1999) High-resolution intersubject averaging and a coordinate system for the cortical surface. Hum Brain Mapp 8(4):272–284CrossRefPubMedGoogle Scholar
  15. 15.
    Goebel R, Esposito F, Formisano E (2006) Analysis of FIAC data with BrainVoyager QX: from single-subject to cortically aligned group general linear model analysis and self-organizing group independent component analysis. Hum Brain Mapp 27(5):392–401CrossRefPubMedGoogle Scholar
  16. 16.
    Meier D, Fisher E (2002) Parameter space warping: shape-based correspondence between morphologically different objects. IEEE Trans Med Imaging 21(1):31–47CrossRefPubMedGoogle Scholar
  17. 17.
    Brechbühler C, Gerig G, Kubler O (1995) Parametrization of closed surfaces for 3-D shape description. Comput Vis Image Underst 61(2):154–170CrossRefGoogle Scholar
  18. 18.
    Styner M, Oguz I, Xu S, Brechbühler C, Pantazis D, Levitt J, Shenton M, Gerig G (2006) Framework for the statistical shape analysis of brain structures using SPHARM-PDM. Insight J 1071:242–250Google Scholar
  19. 19.
    Tosun D, Prince J (2005) Cortical surface alignment using geometry driven multispectral optical flow. In: Christensen GE, Sonka M (eds) Information processing in medical imaging. Lecture notes in computer science, vol 3565. Springer, Heidelberg, pp 480–492. doi:10.1007/11505730_40
  20. 20.
    Wang Y, Peterson B, Staib L (2000) Shape-based 3D surface correspondence using geodesics and local geometry. In: IEEE conference on computer vision and pattern recognition, 2000, vol 2, pp 644–651. doi:10.1109/CVPR.2000.854933
  21. 21.
    Talairach J, Tournoux P (1988) Co-planar stereotaxic atlas of the human brain. 3D proportional system: an approach to cerebral imaging. Thieme Medical, StuttgartGoogle Scholar
  22. 22.
    Klein A, Andersson J, Ardekani B, Ashburner J, Avants B, Chiang M, Christensen G, Collins L, Gee J, Hellier P, Song J, Jenkinson M, Lepage C, Rueckert D, Thompson P, Vercauteren T, Woods R, Mann J, Parsey R (2009) Evaluation of 14 nonlinear deformation algorithms applied to human brain MRI registration. Neuroimage 46(3):786–802CrossRefPubMedPubMedCentralGoogle Scholar
  23. 23.
    Cootes T, Taylor C, Cooper D, Graham J (1995) Active shape models—their training and application. Comput Vis Image Understand 61:38–59CrossRefGoogle Scholar
  24. 24.
    Grenander U, Miller M (1998) Computational anatomy: an emerging discipline. Q Appl Math LVI(4):617–694Google Scholar
  25. 25.
    Bookstein F (1996) Landmark methods for forms without landmarks: morphometrics of group differences in outline shape. Med Image Anal 1:225–243CrossRefGoogle Scholar
  26. 26.
    Kotcheff A, Taylor C (1998) Automatic construction of eigenshape models by direct optimization. Med Image Anal 2(4):303–314CrossRefPubMedGoogle Scholar
  27. 27.
    Davies R, Twining C, Cootes T, Waterton J, Taylor C (2002) A minimum description length approach to statistical shape modeling. IEEE Trans Med Imaging 21(5):525–537CrossRefPubMedGoogle Scholar
  28. 28.
    Heimann T, Wolf I, Williams T, Meinzer H (2005) 3D active shape models using gradient descent optimization of description length. In: Christensen GE, Sonka M (eds) Information processing in medical imaging. Lecture notes in computer science, vol 3565. Springer, Heidelberg, pp 566–577. doi:10.1007/11505730_47
  29. 29.
    Twining C, Davies R, Taylor C (2007) Non-parametric surface-based regularisation for building statistical shape models. In: Karssemeijer N, Lelieveldt B (eds) Information processing in medical imaging. Lecture notes in computer science, vol 4584. Springer, Heidelberg, pp 738–750. doi:10.1007/978-3-540-73273-0_61
  30. 30.
    Ward A, Hamarneh G (2010) The groupwise medial axis transform for fuzzy skeletonization and pruning. IEEE Trans Pattern Anal Mach Intell. 32(6):1084–1096. doi:10.1109/TPAMI.2009.81
  31. 31.
    Styner M, Oguz I, Heimann T, Gerig G (2008) Minimum description length with local geometry. In: Biomedical imaging: from nano to macro, 2008. ISBI 2008. 5th IEEE International Symposium on, pp 1283–1286. doi:10.1109/ISBI.2008.4541238
  32. 32.
    Rueda S, Udupa J, Bai L (2010) Shape modeling via local curvature scale. Pattern Recognit Lett 31(4):324–336CrossRefGoogle Scholar
  33. 33.
    Ericsson A, Karlsson J (2007) Measures for benchmarking of automatic correspondence algorithms. J Math Imaging Vis 28(3):225–241CrossRefGoogle Scholar
  34. 34.
    Heimann T, Wolf I, Meinzer H (2007) Automatic generation of 3d statistical shape models with optimal landmark distributions. Methods Inf Med 46(3):275–281PubMedGoogle Scholar
  35. 35.
    Gu X, Yau S-T (2003) Global conformal surface parameterization. In: Proceedings of the 2003 Eurographics/ACM SIGGRAPH symposium on geometry processing. SGP ’03. Eurographics Association, Aachen, Germany, pp 127–137Google Scholar
  36. 36.
    Styner MA, Rajamani KT, Nolte L, Zsemlye G, Szekely G, Taylor C, Davies RH (2003) Evaluation of 3D correspondence methods for model building. In: Taylor C, Noble JA (eds) Information Processing in medical imaging. Lecture notes in computer science, vol 2732. Springer, Heidelberg, pp 63–75. doi:10.1007/978-3-540-45087-0_6
  37. 37.
    Cover T, Thomas J (1991) Elements of information theory. Wiley, HobokenGoogle Scholar
  38. 38.
    Meyer MD, George IP, Whitaker RT (2005) Robust particle systems for curvature dependent sampling of implicit surfaces. In: Shape modeling and applications, 2005 international conference, pp 124–133. doi:10.1109/SMI.2005.41
  39. 39.
    Vachet C, Cody HH, Niethammer M, Oguz I, Cates J, Whitaker R, Piven J, Styner M (2011) Group-wise automatic mesh-based analysis of cortical thickness. Proc SPIE. 7962:796227–796227. doi:10.1117/12.878300
  40. 40.
    Thodberg H (2003) Minimum description length shape and appearance models. In: Taylor C, Noble JA (eds) Information processing in medical imaging. Lecture notes in computer science. Springer, Heidelberg, pp 51–62. doi:10.1007/978-3-540-45087-0_5
  41. 41.
    Ericsson A, Åström K (2003) Minimizing the description length using steepest descent. In: Proc. British machine vision conference, Norwich, United Kingdom, vol 2, pp 93–102Google Scholar

Copyright information

© CARS 2015

Authors and Affiliations

  • Ipek Oguz
    • 1
  • Josh Cates
    • 2
  • Manasi Datar
    • 2
  • Beatriz Paniagua
    • 3
  • Thomas Fletcher
    • 2
  • Clement Vachet
    • 2
  • Martin Styner
    • 3
  • Ross Whitaker
    • 2
  1. 1.University of IowaIowa CityUSA
  2. 2.University of UtahSalt Lake CityUSA
  3. 3.University of North Carolina at Chapel HillChapel HillUSA

Personalised recommendations