{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:53:03Z","timestamp":1787323983294,"version":"build-2736575974"},"reference-count":59,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Imaging Sci."],"published-print":{"date-parts":[[2019,1]]},"abstract":"<jats:p>In this work we demonstrate how Finsler geometry---and specifically the related geodesic tracto-graphy---can be levied to analyze structural connections between different brain regions. We present new theoretical developments which support the definition of a novel Finsler metric and associated connectivity measures, based on closely related works on the Riemannian framework for diffusion MRI. Using data from the Human Connectome Project, as well as population data from an autism spectrum disorder study, we demonstrate that this new Finsler metric, together with the new connectivity measures, results in connectivity maps that are much closer to known tract anatomy compared to previous geodesic connectivity methods. Our implementation can be used to compute geodesic distance and connectivity maps for segmented areas and is publicly available.<\/jats:p>","DOI":"10.1137\/18m1209428","type":"journal-article","created":{"date-parts":[[2019,3,26]],"date-time":"2019-03-26T14:22:51Z","timestamp":1553610171000},"page":"551-575","source":"Crossref","is-referenced-by-count":5,"title":["Structural Connectivity Analysis Using Finsler Geometry"],"prefix":"10.1137","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3507-3288","authenticated-orcid":true,"given":"Tom","family":"Dela Haije","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Peter","family":"Savadjiev","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Andrea","family":"Fuster","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Robert T.","family":"Schultz","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Ragini","family":"Verma","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Luc","family":"Florack","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Carl-Fredrik","family":"Westin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2019,3,26]]},"reference":[{"key":"atypb1","doi-asserted-by":"publisher","DOI":"10.1109\/ISBI.2009.5193327"},{"key":"atypb2","doi-asserted-by":"publisher","DOI":"10.1016\/S1053-8119(03)00336-7"},{"key":"atypb3","doi-asserted-by":"publisher","DOI":"10.1007\/s11263-010-0377-z"},{"key":"atypb4","first-page":"642","author":"Astola L.","year":"2007","journal-title":"New York"},{"key":"atypb5","doi-asserted-by":"crossref","unstructured":"D. Bao, S.S. Chern, and Z. Shen,\n                      An Introduction to Riemann-Finsler Geometry\n                      , Springer, New York, 2000.","DOI":"10.1007\/978-1-4612-1268-3"},{"key":"atypb6","doi-asserted-by":"publisher","DOI":"10.1006\/jmrb.1994.1037"},{"key":"atypb7","doi-asserted-by":"publisher","DOI":"10.1006\/jmrb.1996.0086"},{"key":"atypb8","doi-asserted-by":"publisher","DOI":"10.1002\/nbm.782"},{"key":"atypb9","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.38.8.716"},{"key":"atypb10","doi-asserted-by":"publisher","DOI":"10.1148\/radiology.182.3.1535892"},{"key":"atypb11","doi-asserted-by":"publisher","DOI":"10.1038\/nrn2575"},{"key":"atypb12","doi-asserted-by":"crossref","unstructured":"P. T. Callaghan,\n                      Principles of Nuclear Magnetic Resonance Microscopy\n                      , Clarendon Press, Oxford, UK, 1991.","DOI":"10.1093\/oso\/9780198539445.001.0001"},{"key":"atypb13","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2014.10.009"},{"key":"atypb14","doi-asserted-by":"publisher","DOI":"10.1016\/j.cortex.2008.05.004"},{"key":"atypb15","doi-asserted-by":"publisher","DOI":"10.1006\/nimg.1998.0395"},{"key":"atypb16","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2010.12.012"},{"key":"atypb17","unstructured":"T. C. J. Dela Haije,\n                      Finsler Geometry and Diffusion MRI\n                      , Ph.D. thesis, Eindhoven University of Technology, Eindhoven, 2017."},{"key":"atypb18","unstructured":"M. Descoteaux,\n                      High Angular Resolution Diffusion MRI: From Local Estimation to Segmentation and Tractography\n                      , Ph.D. thesis, Universit\u00e9 de Nice Sophia Antipolis, Nice, 2008."},{"key":"atypb19","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2006.01.021"},{"key":"atypb20","doi-asserted-by":"publisher","DOI":"10.1093\/cercor\/bhg087"},{"key":"atypb21","doi-asserted-by":"publisher","DOI":"10.1006\/nimg.1998.0396"},{"key":"atypb22","first-page":"346","author":"Fletcher P. T.","year":"2007","journal-title":"New York"},{"key":"atypb23","first-page":"189","author":"Florack L. M. J.","year":"2014","journal-title":"New York"},{"key":"atypb24","doi-asserted-by":"publisher","DOI":"10.1007\/s10851-015-0586-8"},{"key":"atypb25","first-page":"97","author":"Fuster A.","year":"2014","journal-title":"New York"},{"key":"atypb26","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2013.04.127"},{"key":"atypb27","first-page":"13","author":"Hao X.","year":"2011","journal-title":"New York"},{"key":"atypb28","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2013.10.007"},{"key":"atypb29","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2003.11.007"},{"key":"atypb30","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142902419600"},{"key":"atypb31","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.21725"},{"key":"atypb32","doi-asserted-by":"crossref","unstructured":"C. Lenglet, R. Deriche, and O. Faugeras,\n                      Inferring white matter geometry from diffusion tensor MRI: Application to connectivity mapping\n                      , in Computer Vision-ECCV 2004, T. Kanade, J. Kittler, J. M. Kleinberg, F. Mattern, J. C. Mitchell, O. Nierstrasz, C. Pandu Rangan, B. Steffen, M. Sudan, D. Terzopoulos, D. Tygar, M. Y. Vardi, G. Weikum, T. Pajdla, and J. Matas, eds., Lecture Notes in Comput. Sci. 3024, Springer, New York, 2004, pp. 127-140.","DOI":"10.1007\/978-3-540-24673-2_11"},{"key":"atypb33","doi-asserted-by":"publisher","DOI":"10.1137\/070710986"},{"key":"atypb34","doi-asserted-by":"publisher","DOI":"10.3389\/fnhum.2013.00845"},{"key":"atypb35","doi-asserted-by":"publisher","DOI":"10.1038\/s41467-017-01285-x"},{"key":"atypb36","doi-asserted-by":"crossref","unstructured":"J. Melonakos, V. Mohan, M. Niethammer, K. Smith, M. Kubicki, and A. Tannenbaum,\n                      Finsler tractography for white matter connectivity analysis of the cingulum bundle\n                      , in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2007, Lecture Notes in Comput. Sci. 4791, Springer, 2007, pp. 36-43.","DOI":"10.1007\/978-3-540-75757-3_5"},{"key":"atypb37","doi-asserted-by":"publisher","DOI":"10.1109\/TPAMI.2007.70713"},{"key":"atypb38","doi-asserted-by":"publisher","DOI":"10.1016\/j.media.2015.10.011"},{"key":"atypb39","doi-asserted-by":"crossref","unstructured":"L. O'Donnell, S. Haker, and C.F. Westin,\n                      New approaches to estimation of white matter connectivity in diffusion tensor MRI: Elliptic PDEs and geodesics in a tensor-warped space\n                      , in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2002, T. Dohi and R. Kikinis, eds., Lecture Notes in Comput. Sci. 2488, Springer, New York, 2002, pp. 459-466.","DOI":"10.1007\/3-540-45786-0_57"},{"key":"atypb40","doi-asserted-by":"crossref","unstructured":"M. P\u00e9chaud, M. Descoteaux, and R. Keriven,\n                      Brain connectivity using geodesics in HARDI\n                      , Medical Image Computing and Computer-Assisted Intervention-MICCAI 2009, Lecture Notes in Comput. Sci. 5761, Springer, New York, 2009, pp. 482-489.","DOI":"10.1007\/978-3-642-04271-3_59"},{"key":"atypb41","first-page":"180","author":"Pichon E.","year":"2005","journal-title":"International Conference on Medical Image Computing and Computer-Assisted Intervention"},{"key":"atypb42","first-page":"1076","author":"Prados E.","year":"2006","journal-title":"IEEE"},{"key":"atypb43","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2009.10.003"},{"key":"atypb44","doi-asserted-by":"publisher","DOI":"10.1016\/j.nicl.2012.11.006"},{"key":"atypb45","unstructured":"H. Rund,\n                      The Hamilton-Jacobi Theory in the Calculus of Variations: Its Role in Mathematics and Physics\n                      , D. Van Nostrand, London, 1966."},{"key":"atypb46","doi-asserted-by":"crossref","unstructured":"M. Schober, N. Kasenburg, A. Feragen, P. Hennig, and S. Hauberg,\n                      Probabilistic shortest path tractography in DTI using Gaussian process ODE solvers\n                      , in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2014, Lecture Notes in Comput. Sci. 8675, Springer, New York, 2014, pp. 265-272.","DOI":"10.1007\/978-3-319-10443-0_34"},{"key":"atypb47","doi-asserted-by":"publisher","DOI":"10.3389\/fnana.2015.00098"},{"key":"atypb48","doi-asserted-by":"publisher","DOI":"10.1137\/110824395"},{"key":"atypb49","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2012.06.005"},{"key":"atypb50","doi-asserted-by":"publisher","DOI":"10.1063\/1.1695690"},{"key":"atypb51","doi-asserted-by":"publisher","DOI":"10.1002\/nbm.3017"},{"key":"atypb52","doi-asserted-by":"crossref","unstructured":"A. Trist\u00e1n-Vega and S. Aja-Fern\u00e1ndez,\n                      Joint LMMSE estimation of DWI data for DTI processing\n                      , in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2008, Lecture Notes in Comput. Sci. 5242, Springer, New York, 2008, pp. 27-34.","DOI":"10.1007\/978-3-540-85990-1_4"},{"key":"atypb53","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.20279"},{"key":"atypb54","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.10268"},{"key":"atypb55","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2013.05.041"},{"key":"atypb56","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2016.01.011"},{"key":"atypb57","doi-asserted-by":"publisher","DOI":"10.1016\/j.neuroimage.2007.02.049"},{"key":"atypb58","doi-asserted-by":"publisher","DOI":"10.1002\/mrm.20411"},{"key":"atypb59","doi-asserted-by":"publisher","DOI":"10.1090\/S0025-5718-04-01678-3"}],"container-title":["SIAM Journal on Imaging Sciences"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/18M1209428","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T14:16:51Z","timestamp":1787321811000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/18M1209428"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,1]]},"references-count":59,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2019,1]]}},"alternative-id":["10.1137\/18M1209428"],"URL":"https:\/\/doi.org\/10.1137\/18m1209428","relation":{"has-preprint":[{"id-type":"doi","id":"10.1101\/424150","asserted-by":"object"}]},"ISSN":["1936-4954"],"issn-type":[{"value":"1936-4954","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,1]]}}}