Document Zbl 1270.68345

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J. Comput. Vis.</a> <a href="/?q=in%3A317597" title="Articles in this Issue">103, No. 1, 22-59 (2013)</a>. </div> <div class="abstract">Summary: 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.</div> <div class="clear"></div> <br> <div class="citations"><div class="clear"><a href="/?q=rf%3A6199568">Cited in <strong>13</strong> Documents</a></div></div> <div class="classification"> <h3>MSC:</h3> <table><tr> <td> <a class="mono" href="/classification/?q=cc%3A68T45" title="MSC2020">68T45</a> </td> <td class="space"> Machine vision and scene understanding </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P99" title="MSC2020">62P99</a> </td> <td class="space"> Applications of statistics </td> </tr><tr> <td> <a class="mono" href="/classification/?q=cc%3A62P10" title="MSC2020">62P10</a> </td> <td class="space"> Applications of statistics to biology and medical sciences; meta analysis </td> </tr></table> </div><div class="keywords"> <h3>Keywords:</h3><a href="/?q=ut%3Alongitudinal+data">longitudinal data</a>; <a href="/?q=ut%3Astatistics">statistics</a>; <a href="/?q=ut%3Agrowth">growth</a>; <a href="/?q=ut%3Ashape+regression">shape regression</a>; <a href="/?q=ut%3Aspatiotemporal+registration">spatiotemporal registration</a>; <a href="/?q=ut%3Atime+warp">time warp</a></div> <div class="software"> <h3>Software:</h3><a href="/software/6286">LDDMM</a></div>  <div class="modal fade" id="metadataModal" tabindex="-1" role="dialog" aria-labelledby="myModalLabel"> <div class="modal-dialog" role="document"> <div class="modal-content"> <div class="modal-header"> <button type="button" class="close" data-dismiss="modal" aria-label="Close"><span aria-hidden="true">×</span></button> <h4 class="modal-title" id="myModalLabel">Cite</h4> </div> <div class="modal-body"> <div class="form-group"> <label for="select-output" class="control-label">Format</label> <select id="select-output" class="form-control" aria-label="Select Metadata format"></select> </div> <div class="form-group"> <label for="metadataText" class="control-label">Result</label> <textarea class="form-control" id="metadataText" rows="10" style="min-width: 100%;max-width: 100%"></textarea> </div> <div id="metadata-alert" class="alert alert-danger" role="alert" style="display: none;">  </div> </div> <div class="modal-footer"> <button type="button" class="btn btn-primary" onclick="copyMetadata()">Copy to clipboard</button> <button type="button" class="btn btn-default" data-dismiss="modal">Close</button> </div> </div> </div> </div> <div class="functions clearfix"> <div class="function">  <a type="button" class="btn btn-default btn-xs pdf" data-toggle="modal" data-target="#metadataModal" data-itemtype="Zbl" data-itemname="Zbl 1270.68345" data-ciurl="/ci/06199568" data-biburl="/bibtex/06199568.bib" data-amsurl="/amsrefs/06199568.bib" data-xmlurl="/xml/06199568.xml" > Cite </a> <a class="btn btn-default btn-xs pdf" data-container="body" type="button" href="/pdf/06199568.pdf" title="Zbl 1270.68345 as PDF">Review PDF</a> </div> <div class="fulltexts"> <span class="fulltext">Full Text:</span> <a class="btn btn-default btn-xs" type="button" href="https://doi.org/10.1007/s11263-012-0592-x" aria-label="DOI for “Toward a comprehensive framework for the spatiotemporal statistical analysis of longitudinal shape data”" title="10.1007/s11263-012-0592-x">DOI</a> </div> <div class="sfx" style="float: right;"> </div> </div> <div class="references"> <h3>References:</h3> <table><tr> <td>[1]</td> <td class="space">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. · <a href="https://doi.org/10.1016/j.neuroimage.2007.07.067" class="nowrap">doi:10.1016/j.neuroimage.2007.07.067</a></td> </tr><tr> <td>[2]</td> <td class="space">Allassonnière, S.,&amp; Kuhn, E. (2009). Stochastic algorithm for bayesian mixture effect template estimation. ESAIM Probability and Statistics (in press). · <a href="/1320.62045" class="nowrap">Zbl 1320.62045</a></td> </tr><tr> <td>[3]</td> <td class="space">Chandrashekara, R., Rao, A., Sanchez-Ortiz, G., Mohiaddin, R. H.,&amp; 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.</td> </tr><tr> <td>[4]</td> <td class="space">Courchesne, E., Campbell, K.,&amp; 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).</td> </tr><tr> <td>[5]</td> <td class="space">de Craene, M., Camara, O., Bijnens, B. H.,&amp; 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.</td> </tr><tr> <td>[6]</td> <td class="space">Davis, B., Fletcher, P., Bullitt, E.,&amp; Joshi, S. (2007). Population shape regression from random design data. In Proceedings of international conference on computer vision (ICCV), pp. 1–7.</td> </tr><tr> <td>[7]</td> <td class="space">Declerck, J., Feldman, J.,&amp; 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.</td> </tr><tr> <td>[8]</td> <td class="space">de Waal, F. B. M. (1995). Bonobo sex and society. Scientific American, 272, 82–88.</td> </tr><tr> <td>[9]</td> <td class="space">Dupuis, P., Grenander, U.,&amp; Miller, M. (1998). Variational problems on flows of diffeomorphisms for image matching. Quaterly of Applied Mathematics, 56(3), 587–600. · <a href="/0949.49002" class="nowrap">Zbl 0949.49002</a></td> </tr><tr> <td>[10]</td> <td class="space">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.</td> </tr><tr> <td>[11]</td> <td class="space">Durrleman, S., Pennec, X., Trouvé, A.,&amp; Ayache, N. (2009a). Statistical models of sets of curves and surfaces based on currents. Medical Image Analysis, 13(5), 793–808. · <a href="https://doi.org/10.1016/j.media.2009.07.007" class="nowrap">doi:10.1016/j.media.2009.07.007</a></td> </tr><tr> <td>[12]</td> <td class="space">Durrleman, S., Pennec, X., Trouvé, A., Gerig, G.,&amp; 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.</td> </tr><tr> <td>[13]</td> <td class="space">Durrleman, S., Fillard, P., Pennec, X., Trouvé, A.,&amp; Ayache, N. (2011). Registration, atlas estimation and variability analysis of white matter fiber bundles modeled as currents. NeuroImage, 55(3), 1073–1090. · <a href="https://doi.org/10.1016/j.neuroimage.2010.11.056" class="nowrap">doi:10.1016/j.neuroimage.2010.11.056</a></td> </tr><tr> <td>[14]</td> <td class="space">Ehrhardt, J., Werner, R., Schmidt-Richberg, A., Schulz, B.,&amp; 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.</td> </tr><tr> <td>[15]</td> <td class="space">Fishbaugh, J., Durrleman, S.,&amp; 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).</td> </tr><tr> <td>[16]</td> <td class="space">Gerber, S., Tasdizen, T., Fletcher, T. P.,&amp; 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).</td> </tr><tr> <td>[17]</td> <td class="space">Gerig, G., Davis, B., Lorenzen, P., Xu, S., Jomier, M., Piven, J.,&amp; 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).</td> </tr><tr> <td>[18]</td> <td class="space">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 .</td> </tr><tr> <td>[19]</td> <td class="space">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. · <a href="https://doi.org/10.1073/pnas.0806485105" class="nowrap">doi:10.1073/pnas.0806485105</a></td> </tr><tr> <td>[20]</td> <td class="space">Grenander, U., Srivastava, A.,&amp; Saini, S. (2007). A pattern-theoretic characterization of biological growth. IEEE Transactions on Medical Imaging, 26(5), 648–659. · <a href="https://doi.org/10.1109/TMI.2006.891500" class="nowrap">doi:10.1109/TMI.2006.891500</a></td> </tr><tr> <td>[21]</td> <td class="space">Hart, G., Shi, Y., Zhu, H., Sanchez, M., Styner, M.,&amp; 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.</td> </tr><tr> <td>[22]</td> <td class="space">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. · <a href="https://doi.org/10.1001/archpsyc.62.12.1366" class="nowrap">doi:10.1001/archpsyc.62.12.1366</a></td> </tr><tr> <td>[23]</td> <td class="space">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. · <a href="https://doi.org/10.1001/archgenpsychiatry.2011.39" class="nowrap">doi:10.1001/archgenpsychiatry.2011.39</a></td> </tr><tr> <td>[24]</td> <td class="space">Jian, B.,&amp; 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 .</td> </tr><tr> <td>[25]</td> <td class="space">Joshi, S.,&amp; Miller, M. (2000). Landmark matching via large deformation diffeomorphisms. IEEE Transaction on Image Processing, 9(8), 1357–1370. · <a href="/0965.37065" class="nowrap">Zbl 0965.37065</a> · <a href="https://doi.org/10.1109/83.855431" class="nowrap">doi:10.1109/83.855431</a></td> </tr><tr> <td>[26]</td> <td class="space">Kano, T. (1992). The last ape: Pygmy chimpanzee behavior and ecology. Stanford: Stanford University Press.</td> </tr><tr> <td>[27]</td> <td class="space">Khan, A.,&amp; 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).</td> </tr><tr> <td>[28]</td> <td class="space">Kinzey, W. G. (1984). The dentition of the pygmy chimpanzee, Pan paniscus. New York: Plenum.</td> </tr><tr> <td>[29]</td> <td class="space">Kuroda, S. (1989). Developmental retardation and behavioural characteristics of pygmy chimpanzees. Cambridge: Harvard University Press.</td> </tr><tr> <td>[30]</td> <td class="space">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.</td> </tr><tr> <td>[31]</td> <td class="space">Miller, I. M., Trouvé, A.,&amp; Younes, L. (2002). On the metrics and euler-lagrange equations of computational anatomy. Annual Review of Biomedical Engineering, 4, 375–405. · <a href="https://doi.org/10.1146/annurev.bioeng.4.092101.125733" class="nowrap">doi:10.1146/annurev.bioeng.4.092101.125733</a></td> </tr><tr> <td>[32]</td> <td class="space">Miller, M., Trouvé, A.,&amp; Younes, L. (2006). Geodesic shooting for computational anatomy. Journal of Mathematical Imaging and Vision, 24(2), 209–228. · <a href="/1478.92084" class="nowrap">Zbl 1478.92084</a> · <a href="https://doi.org/10.1007/s10851-005-3624-0" class="nowrap">doi:10.1007/s10851-005-3624-0</a></td> </tr><tr> <td>[33]</td> <td class="space">Pennec, X., Fillard, P.,&amp; Ayache, N. (2006). A Riemannian framework for tensor computing. International Journal of Computer Vision, 66(1), 41–66. · <a href="/1287.53031" class="nowrap">Zbl 1287.53031</a> · <a href="https://doi.org/10.1007/s11263-005-3222-z" class="nowrap">doi:10.1007/s11263-005-3222-z</a></td> </tr><tr> <td>[34]</td> <td class="space">Perperidis, D., Mohiaddin, R. H.,&amp; Rueckert, D. (2005). Spatio-temporal free-form registration of cardiac MRI sequences. Medical Image Analysis, 9(5), 441–456. · <a href="https://doi.org/10.1016/j.media.2005.05.004" class="nowrap">doi:10.1016/j.media.2005.05.004</a></td> </tr><tr> <td>[35]</td> <td class="space">Peyrat, J. M., Delingette, H., Sermesant, M., Pennec, X., Xu, C.,&amp; 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.</td> </tr><tr> <td>[36]</td> <td class="space">Qiu, A., Younes, L., Miller, M.,&amp; 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. · <a href="https://doi.org/10.1016/j.neuroimage.2007.11.041" class="nowrap">doi:10.1016/j.neuroimage.2007.11.041</a></td> </tr><tr> <td>[37]</td> <td class="space">Qiu, A., Albert, M., Younes, L.,&amp; Miller, M. I. (2009). Time sequence diffeomorphic metric mapping and parallel transport track time-dependent shape changes. NeuroImage, 45(1 Supplement 1), S51–S60. · <a href="https://doi.org/10.1016/j.neuroimage.2008.10.039" class="nowrap">doi:10.1016/j.neuroimage.2008.10.039</a></td> </tr><tr> <td>[38]</td> <td class="space">Shea, B. (1989). Heterochrony in human evolution: The case for neoteny reconsidered. Yearbook of Physical Anthropology, 32, 69–101. · <a href="https://doi.org/10.1002/ajpa.1330320505" class="nowrap">doi:10.1002/ajpa.1330320505</a></td> </tr><tr> <td>[39]</td> <td class="space">Thompson, P. M., Giedd, J. N., Woods, R. P., MacDonald, D., Evans, A. C.,&amp; Toga, A. W. (2000). Growth patterns in the developing human brain detected by using continuum-mechanical tensor maps. Nature, 404, 6774. · <a href="https://doi.org/10.1038/35004593" class="nowrap">doi:10.1038/35004593</a></td> </tr><tr> <td>[40]</td> <td class="space">Trouvé, A. (1998). Diffeomorphisms groups and pattern matching in image analysis. International Journal of Computer Vision, 28(3), 213–221. · <a href="https://doi.org/10.1023/A:1008001603737" class="nowrap">doi:10.1023/A:1008001603737</a></td> </tr><tr> <td>[41]</td> <td class="space">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 . · <a href="/1259.65104" class="nowrap">Zbl 1259.65104</a></td> </tr><tr> <td>[42]</td> <td class="space">Vaillant, M., Miller, M., Younes, L.,&amp; Trouvé, A. (2004). Statistics on diffeomorphisms via tangent space representations. NeuroImage, 23, 161–169. · <a href="https://doi.org/10.1016/j.neuroimage.2004.07.023" class="nowrap">doi:10.1016/j.neuroimage.2004.07.023</a></td> </tr><tr> <td>[43]</td> <td class="space">Xie, Y., Ho, J.,&amp; 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.</td> </tr><tr> <td>[44]</td> <td class="space">Yushkevich, P. A., Piven, J., Ho, S., Gee, J. C.,&amp; Gerig, G. (2006). User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability. Neuroimage, 31(3), 1116–1128. · <a href="https://doi.org/10.1016/j.neuroimage.2006.01.015" class="nowrap">doi:10.1016/j.neuroimage.2006.01.015</a></td> </tr></table> <div class="reference_disclaimer"> This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. 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