International Journal of Computer Vision

, Volume 103, Issue 1, pp 22–59

Toward a Comprehensive Framework for the Spatiotemporal Statistical Analysis of Longitudinal Shape Data

  • Stanley Durrleman
  • Xavier Pennec
  • Alain Trouvé
  • José Braga
  • Guido Gerig
  • Nicholas Ayache
Article
  • 1.1k Downloads

Abstract

This paper proposes an original approach for the statistical analysis of longitudinal shape data. The proposed method allows the characterization of typical growth patterns and subject-specific shape changes in repeated time-series observations of several subjects. This can be seen as the extension of usual longitudinal statistics of scalar measurements to high-dimensional shape or image data. The method is based on the estimation of continuous subject-specific growth trajectories and the comparison of such temporal shape changes across subjects. Differences between growth trajectories are decomposed into morphological deformations, which account for shape changes independent of the time, and time warps, which account for different rates of shape changes over time. Given a longitudinal shape data set, we estimate a mean growth scenario representative of the population, and the variations of this scenario both in terms of shape changes and in terms of change in growth speed. Then, intrinsic statistics are derived in the space of spatiotemporal deformations, which characterize the typical variations in shape and in growth speed within the studied population. They can be used to detect systematic developmental delays across subjects. In the context of neuroscience, we apply this method to analyze the differences in the growth of the hippocampus in children diagnosed with autism, developmental delays and in controls. Result suggest that group differences may be better characterized by a different speed of maturation rather than shape differences at a given age. In the context of anthropology, we assess the differences in the typical growth of the endocranium between chimpanzees and bonobos. We take advantage of this study to show the robustness of the method with respect to change of parameters and perturbation of the age estimates.

Keywords

Longitudinal data Statistics Growth  Shape regression Spatiotemporal registration Time warp 

Supplementary material

11263_2012_592_MOESM1_ESM.mov (743 kb)
Supplementary material 1 (mov 742 KB)
11263_2012_592_MOESM2_ESM.wmv (2.5 mb)
Supplementary material 2 (wmv 2593 KB)
11263_2012_592_MOESM3_ESM.wmv (1.8 mb)
Supplementary material 3 (wmv 1857 KB)
11263_2012_592_MOESM4_ESM.wmv (353 kb)
Supplementary material 4 (wmv 353 KB)

References

  1. Aljabar, P., Bhatia, K., Murgasova, M., Hajnal, J., Boardman, J., Srinivasan, L., et al. (2008). Assessment of brain growth in early childhood using deformation-based morphometry. NeuroImage, 39(1), 348–358.CrossRefGoogle Scholar
  2. Allassonnière, S.,& Kuhn, E. (2009). Stochastic algorithm for bayesian mixture effect template estimation. ESAIM Probability and Statistics (in press).Google Scholar
  3. Chandrashekara, R., Rao, A., Sanchez-Ortiz, G., Mohiaddin, R. H.,& Rueckert, D. (2003). Construction of a statistical model for cardiac motion analysis using nonrigid image registration. In Information processing in medical imaging (Vol. 2732, pp. 599–610). Springer, Lecture Notes in Computer Science.Google Scholar
  4. Courchesne, E., Campbell, K.,& Solso, S. (2011). Brain growth across the life span in autism: Age-specific changes in anatomical pathology. Brain Research, 1380, 138–145 (the Emerging Neuroscience of Autism Spectrum Disorders).Google Scholar
  5. de Craene, M., Camara, O., Bijnens, B. H.,& Frangi, A. F. (2009). Large diffeomorphic FFD registration for motion and strain quantification from 3D-US sequences. In Proceedings of functional imaging and modeling of the heart (Vol. 5528, pp. 437–446). Spinger, LNCS.Google Scholar
  6. Davis, B., Fletcher, P., Bullitt, E.,& Joshi, S. (2007). Population shape regression from random design data. In Proceedings of international conference on computer vision (ICCV), pp. 1–7.Google Scholar
  7. Declerck, J., Feldman, J.,& Ayache, N. (1998). Definition of a 4D continuous planispheric transformation for the tracking and the analysis of LV motion. Medical Image Analysis, 4(1), 1–17. Google Scholar
  8. de Waal, F. B. M. (1995). Bonobo sex and society. Scientific American, 272, 82–88.CrossRefGoogle Scholar
  9. Dupuis, P., Grenander, U.,& Miller, M. (1998). Variational problems on flows of diffeomorphisms for image matching. Quaterly of Applied Mathematics, 56(3), 587–600.MathSciNetMATHGoogle Scholar
  10. Durrleman, S. (2010). Statistical models of currents for measuring the variability of anatomical curves, surfaces and their evolution. Thèse de sciences (phd thesis), Université de Nice-Sophia Antipolis.Google Scholar
  11. Durrleman, S., Pennec, X., Trouvé, A.,& Ayache, N. (2009a). Statistical models of sets of curves and surfaces based on currents. Medical Image Analysis, 13(5), 793–808.CrossRefGoogle Scholar
  12. Durrleman, S., Pennec, X., Trouvé, A., Gerig, G.,& Ayache, N. (2009b) Spatiotemporal atlas estimation for developmental delay detection in longitudinal datasets. In Medical image computing and computer-assisted intervention—MICCAI (Vol. 5761, pp. 297–304). Springer, LNCS.Google Scholar
  13. Durrleman, S., Fillard, P., Pennec, X., Trouvé, A.,& Ayache, N. (2011). Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents. NeuroImage, 55(3), 1073–1090.CrossRefGoogle Scholar
  14. Ehrhardt, J., Werner, R., Schmidt-Richberg, A., Schulz, B.,& Handels, H. (2008). Generation of a mean motion model of the lung using 4D-CT image data. In Proceedings of eurographics workshop on visual computing for biomedicine (pp. 69–76). Eurographics Association.Google Scholar
  15. Fishbaugh, J., Durrleman, S.,& Gerig, G. (2011). Estimation of smooth growth trajectories with controlled acceleration from time series shape data. In Medical image computing and computer-assisted intervention—MICCAI. Springer, LNCS (to appear).Google Scholar
  16. Gerber, S., Tasdizen, T., Fletcher, T. P.,& Whitaker, R. (2010). Manifold modeling for brain population analysis. Medical Image Analysis 14(5), 643–653 (special Issue on the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention (MICCAI) 2009).Google Scholar
  17. Gerig, G., Davis, B., Lorenzen, P., Xu, S., Jomier, M., Piven, J.,& Joshi, S. (2006). Computational anatomy to assess longitudinal trajectory of brain growth. In Third international symposium on 3D data processing, visualization, and transmission (pp. 1041–1047).Google Scholar
  18. Glaunès, J. (2005). Transport par difféomorphismes de points, de mesures et de courants pour la comparaison de formes et l’anatomie numérique. PhD thesis, Université Paris 13, http://cis.jhu.edu/joan/TheseGlaunes.pdf.
  19. Gogtay, N., Lu, A., Leow, A., Klunder, A., Lee, A., Chavez, A., et al. (2008). 3D growth pattern abnormalities visualized in childhood-onset schizophrenia using tensor-based morphometry. Proceedings of the National Academy of Sciences, 105(41), 15979–15984.CrossRefGoogle Scholar
  20. Grenander, U., Srivastava, A.,& Saini, S. (2007). A pattern-theoretic characterization of biological growth. IEEE Transactions on Medical Imaging, 26(5), 648–659.CrossRefGoogle Scholar
  21. Hart, G., Shi, Y., Zhu, H., Sanchez, M., Styner, M.,& Niethammer, M. (2010). DTI longitudinal atlas construction as an average of growth models. In Proceedings of international workshop on spatio-temporal image analysis for longitudinal and time-series image data.Google Scholar
  22. Hazlett, H., Poe, M., Gerig, G., Smith, R., Provenzale, J., Ross, A., et al. (2005). Magnetic resonance imaging and head circumference study of brain size in autism. The Archives of General Psychiatry, 62, 1366–1376.CrossRefGoogle Scholar
  23. Hazlett, H., Poe, M., Styner, M., Chappell, C., Smith, R., Vachet, C., et al. (2011). Early brain overgrowth in autism associated with an increase in cortical surface area before age 2 years. Journal of Archives of General Psychiatry, 68(5), 467–476.CrossRefGoogle Scholar
  24. Jian, B.,& Vemuri, B. C. (2005). A robust algorithm for point set registration using mixture of Gaussians. In: 10th IEEE international conference on computer vision (ICCV 2005), 17–20 October 2005, Beijing, China, pp. 1246–1251. http://gmmreg.googlecode.com.
  25. Joshi, S.,& Miller, M. (2000). Landmark matching via large deformation diffeomorphisms. IEEE Transaction on Image Processing, 9(8), 1357–1370.MathSciNetMATHCrossRefGoogle Scholar
  26. Kano, T. (1992). The last ape: Pygmy chimpanzee behavior and ecology. Stanford: Stanford University Press.Google Scholar
  27. Khan, A.,& Beg, M. (2008). Representation of time-varying shapes in the large deformation diffeomorphic framework. In 5th IEEE international symposium on biomedical imaging ISBI (pp. 1521–1524).Google Scholar
  28. Kinzey, W. G. (1984). The dentition of the pygmy chimpanzee, Pan paniscus. New York: Plenum.Google Scholar
  29. Kuroda, S. (1989). Developmental retardation and behavioural characteristics of pygmy chimpanzees. Cambridge: Harvard University Press.Google Scholar
  30. Mansi, T., Durrleman, S., Bernhardt, B., Sermesant, M., Delingette, H., Voigt, I., et al. (2009). A statistical model of right ventricle in tetralogy of fallot for prediction of remodelling and therapy planning. In Proceedings of medical image computing and computer assisted intervention (MICCAI) (Vol. 5761, pp. 214–221). Springer, LNCS.Google Scholar
  31. Miller, I. M., Trouvé, A.,& Younes, L. (2002). On the metrics and euler-lagrange equations of computational anatomy. Annual Review of Biomedical Engineering, 4, 375–405.CrossRefGoogle Scholar
  32. Miller, M., Trouvé, A.,& Younes, L. (2006). Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision, 24(2), 209–228.MathSciNetCrossRefGoogle Scholar
  33. Pennec, X., Fillard, P.,& Ayache, N. (2006). A Riemannian framework for tensor computing. International Journal of Computer Vision, 66(1), 41–66.MathSciNetCrossRefGoogle Scholar
  34. Perperidis, D., Mohiaddin, R. H.,& Rueckert, D. (2005). Spatio-temporal free-form registration of cardiac MRI sequences. Medical Image Analysis, 9(5), 441–456.CrossRefGoogle Scholar
  35. Peyrat, J. M., Delingette, H., Sermesant, M., Pennec, X., Xu, C.,& Ayache, N. (2008). Registration of 4D time-series of cardiac images with multichannel diffeomorphic demons. In Proceedings of medical image computing and computer assisted intervention (MICCAI) (Vol. 5242, pp. 972–979). Springer, LNCS.Google Scholar
  36. Qiu, A., Younes, L., Miller, M.,& Csernansky, J. (2008). Parallel transport in diffeomorphisms distinguishes the time-dependent pattern of hippocampal surface deformation due to healthy aging and the dementia of the Alzheimer’s type. NeuroImage, 40, 68–76.CrossRefGoogle Scholar
  37. Qiu, A., Albert, M., Younes, L.,& Miller, M. I. (2009). Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes. NeuroImage, 45(1 Supplement 1), S51–S60.CrossRefGoogle Scholar
  38. Shea, B. (1989). Heterochrony in human evolution: The case for neoteny reconsidered. Yearbook of Physical Anthropology, 32, 69–101.CrossRefGoogle Scholar
  39. Thompson, P. M., Giedd, J. N., Woods, R. P., MacDonald, D., Evans, A. C.,& Toga, A. W. (2000). Growth patterns in the developing human brain detected by using continuum-mechanical tensor maps. Nature, 404, 6774.CrossRefGoogle Scholar
  40. Trouvé, A. (1998). Diffeomorphisms groups and pattern matching in image analysis. International Journal of Computer Vision, 28(3), 213–221.CrossRefGoogle Scholar
  41. Trouvé, A., Vialard, F. X. (2010). Shape splines and stochastic shape evolutions: A second order point of view. Quaterly of Applied Mathematics (to appear). http://arxiv.org/abs/1003.3895.
  42. Vaillant, M., Miller, M., Younes, L.,& Trouvé, A. (2004). Statistics on diffeomorphisms via tangent space representations. NeuroImage, 23, 161–169.CrossRefGoogle Scholar
  43. Xie, Y., Ho, J.,& Vemuri, B. C. (2010). Image atlas construction via intrinsic averaging on the manifold of images. In The twenty-third IEEE conference on computer vision and pattern recognition, CVPR 2010 (pp. 2933–2939). San Francisco, CA, USA: IEEE.Google Scholar
  44. Yushkevich, P. A., Piven, J., Ho, S., Gee, J. C.,& Gerig, G. (2006). User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability. Neuroimage, 31(3), 1116–1128.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Stanley Durrleman
    • 2
    • 3
    • 1
  • Xavier Pennec
    • 2
  • Alain Trouvé
    • 3
  • José Braga
    • 4
  • Guido Gerig
    • 1
  • Nicholas Ayache
    • 2
  1. 1.Scientific Computing and Imaging (SCI) InstituteSalt Lake CityUSA
  2. 2.Asclepios team-projectINRIA Sophia AntipolisSophia AntipolisFrance
  3. 3.Centre de Mathématiques et Leurs Applications (CMLA)CNRS-ENS CachanCachanFrance
  4. 4.Laboratoire de paléoanthropologie assistée par ordinateurCNRS-Université de Toulouse (Paul Sabatier)ToulouseFrance

Personalised recommendations