1,590
Views
4
CrossRef citations to date
0
Altmetric
Theory and Methods

Statistical Analysis of Functions on Surfaces, With an Application to Medical Imaging

&
Pages 1420-1434 | Received 28 Jun 2017, Accepted 09 May 2019, Published online: 14 Aug 2019

References

  • Audette, M. A., Ferrie, F. P., and Peters, T. M. (2000), “An Algorithmic Overview of Surface Registration Techniques for Medical Imaging,” Medical Image Analysis, 4, 201–217. DOI: 10.1016/S1361-8415(00)00014-1.
  • Bookstein, F. L. (1997a), “Shape and the Information in Medical Images: A Decade of the Morphometric Synthesis,” Computer Vision and Image Understanding, 66, 97–118. DOI: 10.1006/cviu.1997.0607.
  • Bookstein, F. L. (1997b), Morphometric Tools for Landmark Data: Geometry and Biology, Cambridge: Cambridge University Press.
  • Bruveris, M., Risser, L., and Vialard, F.-X. (2012), “Mixture of Kernels and Iterated Semidirect Product of Diffeomorphisms Groups,” Multiscale Modeling & Simulation, 10, 1344–1368. DOI: 10.1137/110846324.
  • Charlier, B., Charon, N., and Trouvé, A. (2017), “The Fshape Framework for the Variability Analysis of Functional Shapes,” Foundations of Computational Mathematics, 17, 287–357. DOI: 10.1007/s10208-015-9288-2.
  • Charon, N., and Trouvé, A. (2014), “Functional Currents: A New Mathematical Tool to Model and Analyse Functional Shapes,” Journal of Mathematical Imaging and Vision, 48, 413–431. DOI: 10.1007/s10851-012-0413-4.
  • Chavel, I. (2006), Riemannian Geometry: A Modern Introduction, Cambridge Studies in Advanced Mathematics (2nd ed.), Cambridge: Cambridge University Press.
  • Dupuis, P., Grenander, U., and Miller, M. I. (1998), “Variational Problems on Flows of Diffeomorphisms for Image Matching,” Quarterly of Applied Mathematics, 56, 1–20, 1998. DOI: 10.1090/qam/1632326.
  • Essen, D. V., Ugurbil, K., Auerbach, E., Barch, D., Behrens, T., Bucholz, R., Chang, A., Chen, L., Corbetta, M., Curtiss, S., Penna, S. D., Feinberg, D., Glasser, M., Harel, N., Heath, A., Larson-Prior, L., Marcus, D., Michalareas, G., Moeller, S., Oostenveld, R., Petersen, S., Prior, F., Schlaggar, B., Smith, S., Snyder, A., Xu, J., and Yacoub, E. (2012), “The Human Connectome Project: A Data Acquisition Perspective,” NeuroImage, 62, 2222–2231, 2012. DOI: 10.1016/j.neuroimage.2012.02.018.
  • Fischl, B., and Dale, A. M. (2000), “Measuring the Thickness of the Human Cerebral Cortex From Magnetic Resonance Images,” Proceedings of the National Academy of Sciences of the United States of America, 97, 11050–11055. DOI: 10.1073/pnas.200033797.
  • Fischl, B., Sereno, M. I., and Dale, A. M. (1999), “Cortical Surface-Based Analysis II: Inflation, Flattening, and a Surface-Based Coordinate System,” NeuroImage, 9, 195–207. DOI: 10.1006/nimg.1998.0396.
  • Glasser, M. F., Sotiropoulos, S. N., Wilson, J. A., Coalson, T. S., Fischl, B., Andersson, J. L., Xu, J., Jbabdi, S., Webster, M., Polimeni, J. R., Essen, D. C. V., and Jenkinson, M. (2013), “The Minimal Preprocessing Pipelines for the Human Connectome Project,” NeuroImage, 80, 105–124. DOI: 10.1016/j.neuroimage.2013.04.127.
  • Hadjipantelis, P. Z., Aston, J. A. D., Müller, H. G., and Evans, J. P. (2015), “Unifying Amplitude and Phase Analysis: A Compositional Data Approach to Functional Multivariate Mixed-Effects Modeling of Mandarin Chinese,” Journal of the American Statistical Association, 110, 545–559. DOI: 10.1080/01621459.2015.1006729.
  • Hagler, D. J., Saygin, A. P., and Sereno, M. I. (2006), “Smoothing and Cluster Thresholding for Cortical Surface-Based Group Analysis of FMRI Data,” NeuroImage, 33, 1093–1103. DOI: 10.1016/j.neuroimage.2006.07.036.
  • Huang, Y., Teng, Z., Elkhawad, M., Tarkin, J. M., Joshi, N., Boyle, J. R., Buscombe, J. R., Fryer, T. D., Zhang, Y., Park, A. Y., Wilkinson, I. B., Newby, D. E., Gillard, J. H., and Rudd, J. H. F. (2016), “High Structural Stress and Presence of Intraluminal Thrombus Predict Abdominal Aortic Aneurysm 18F-FDG Uptake: Insights From Biomechanics,” Circulation: Cardiovascular Imaging, 9, e004656. DOI: 10.1161/CIRCIMAGING.116.004656.
  • Im, K., Lee, J. M., Lyttelton, O., Kim, S. H., Evans, A. C., and Kim, S. I. (2008), “Brain Size and Cortical Structure in the Adult Human Brain,” Cerebral Cortex, 18, 2181–2191. DOI: 10.1093/cercor/bhm244.
  • Joshi, S., and Miller, M. (2000), “Landmark Matching via Large Deformation Diffeomorphisms,” IEEE Transactions on Image Processing, 9, 1357–1370. DOI: 10.1109/83.855431.
  • Kneip, A., and Ramsay, J. O. (2008), “Combining Registration and Fitting for Functional Models,” Journal of the American Statistical Association, 103, 1155–1165. DOI: 10.1198/016214508000000517.
  • Lerch, J. P., and Evans, A. C. (2005), “Cortical Thickness Analysis Examined Through Power Analysis and a Population Simulation,” NeuroImage, 24, 163–173. DOI: 10.1016/j.neuroimage.2004.07.045.
  • Lila, E., and Aston, J. A. D. (2017), “Statistical Analysis of Functions on Surfaces, With an Application to Medical Imaging,” arXiv no. 1707.00453. DOI: 10.1080/01621459.2019.1635479.
  • Lila, E., Aston, J. A. D., and Sangalli, L. M. (2016), “Smooth Principal Component Analysis Over Two-Dimensional Manifolds With an Application to Neuroimaging,” The Annals of Applied Statistics, 10, 1854–1879. DOI: 10.1214/16-AOAS975.
  • Maguire, E. A., Woollett, K., and Spiers, H. J. (2006), “London Taxi Drivers and Bus Drivers: A Structural MRI and Neuropsychological Analysis,” Hippocampus, 16, 1091–1101. DOI: 10.1002/hipo.20233.
  • Marron, J. S., Ramsay, J. O., Sangalli, L. M., and Srivastava, A. (2015), “Functional Data Analysis of Amplitude and Phase Variation,” Statistical Science, 30, 468–484. DOI: 10.1214/15-STS524.
  • Miller, M. I., Trouvé, A., and Younes, L. (2006), “Geodesic Shooting for Computational Anatomy,” Journal of Mathematical Imaging and Vision, 24, 209–228. DOI: 10.1007/s10851-005-3624-0.
  • Panaretos, V. M., and Zemel, Y. (2016), “Amplitude and Phase Variation of Point Processes,” The Annals of Statistics, 44, 771–812. DOI: 10.1214/15-AOS1387.
  • Patrangenaru, V., and Ellingson, L. (2015), Nonparametric Statistics on Manifolds and Their Applications to Object Data Analysis (1st ed.), Boca Raton, FL: CRC Press, Inc., ISBN 1439820503, 9781439820506.
  • Ramsay, J. O., and Silverman, B. W. (2005), Functional Data Analysis, Springer Series in Statistics (2nd ed.), New York: Springer, ISBN 038740080X.
  • Tang, R., and Muller, H.-G. (2008), “Pairwise Curve Synchronization for Functional Data,” Biometrika, 95, 875–889. DOI: 10.1093/biomet/asn047.
  • Thirion, J.-P. (1995), “Fast Non-Rigid Matching of 3D Medical Images,” Research Report RR-2547, INRIA, 1995.
  • Thirion, J.-P. (1998), “Image Matching as a Diffusion Process: An Analogy With Maxwell’s Demons,” Medical Image Analysis, 2, 243–260.
  • Treece, G., and Gee, A. (2015), “Independent Measurement of Femoral Cortical Thickness and Cortical Bone Density Using Clinical CT,” Medical Image Analysis, 20, 249–264. DOI: 10.1016/j.media.2014.11.012.
  • Trouvé, A., and Younes, L. (2005), “Metamorphoses Through Lie Group Action,” Foundations of Computational Mathematics, 5, 173–198. DOI: 10.1007/s10208-004-0128-z.
  • Tward, D., Miller, M., Trouvé, A., and Younes, L. (2017), “Parametric Surface Diffeomorphometry for Low Dimensional Embeddings of Dense Segmentations and Imagery,” IEEE Transactions on Pattern Analysis and Machine Intelligence, 39, 1195–1208. DOI: 10.1109/TPAMI.2016.2578317.
  • Vaillant, M., and Glaunès, J. (2005), “Surface Matching via Currents,” Information Processing in Medical Imaging: Proceedings of the… Conference, 19, 381–392.
  • Vaillant, M., Miller, M. I., Younes, L., and Trouvé, A. (2004), “Statistics on Diffeomorphisms via Tangent Space Representations,” NeuroImage, 23, S161–S169. DOI: 10.1016/j.neuroimage.2004.07.023.
  • Vaillant, M., Qiu, A., Glaunès, J., and Miller, M. I. (2007), “Diffeomorphic Metric Surface Mapping in Subregion of the Superior Temporal Gyrus,” NeuroImage, 34, 1149–1159. DOI: 10.1016/j.neuroimage.2006.08.053.
  • Vercauteren, T., Pennec, X., Perchant, A., and Ayache, N. (2009), “Diffeomorphic Demons: Efficient Non-parametric Image Registration,” NeuroImage, 45, S61–S72. Mathematics in Brain Imaging. DOI: 10.1016/j.neuroimage.2008.10.040.
  • Yao, K. D., Patrangenaru, V., and Lester, D. (2017), “3D Mean Projective Shape Difference for Face Differentiation From Multiple Digital Camera Images,” arXiv no. 1704.03106.
  • Yeo, B., Sabuncu, M., Vercauteren, T., Ayache, N., Fischl, B., and Golland, P. (2010), “Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration,” IEEE Transactions on Medical Imaging, 29, 650–668. DOI: 10.1109/TMI.2009.2030797.
  • Younes, L. (2010), Shapes and Diffeomorphisms (Vol. 171, 1st ed.), Berlin, Heidelberg: Springer, ISBN 3642120547.
  • Zaetz, J., and Kurtek, S. (2015), “A Novel Riemannian Framework for Shape Analysis of Annotated Surfaces,” in Proceedings of International Workshop on Differential Geometry in Computer Vision for Analysis of Shapes, Images and Trajectories, BMVA Press, pp. 3.1–3.11.
  • Zitová, B., and Flusser, J. (2003), “Image Registration Methods: A Survey,” Image and Vision Computing, 21, 977–1000. DOI: 10.1016/S0262-8856(03)00137-9.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.