{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,21]],"date-time":"2026-02-21T03:21:10Z","timestamp":1771644070075,"version":"3.50.1"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T00:00:00Z","timestamp":1649289600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J. Imaging"],"abstract":"<jats:p>Three-dimensional surface reconstruction is a well-known task in medical imaging. In procedures for intervention or radiation treatment planning, the generated models should be accurate and reflect the natural appearance. Traditional methods for this task, such as Marching Cubes, use smoothing post processing to reduce staircase artifacts from mesh generation and exhibit the natural look. However, smoothing algorithms often reduce the quality and degrade the accuracy. Other methods, such as MPU implicits, based on adaptive implicit functions, inherently produce smooth 3D models. However, the integration in the implicit functions of both smoothness and accuracy of the shape approximation may impact the precision of the reconstruction. Having these limitations in mind, we propose a hybrid method for 3D reconstruction of MR images. This method is based on a parallel Marching Cubes algorithm called Flying Edges (FE) and Multi-level Partition of Unity (MPU) implicits. We aim to combine the robustness of the Marching Cubes algorithm with the smooth implicit curve tracking enabled by the use of implicit models in order to provide higher geometry precision. Towards this end, the regions that closely fit to the segmentation data, and thus regions that are not impacted by reconstruction issues, are first extracted from both methods. These regions are then merged and used to reconstruct the final model. Experimental studies were performed on a number of MRI datasets, providing images and error statistics generated from our results. The results obtained show that our method reduces the geometric errors of the reconstructed surfaces when compared to the MPU and FE approaches, producing a more accurate 3D reconstruction.<\/jats:p>","DOI":"10.3390\/jimaging8040103","type":"journal-article","created":{"date-parts":[[2022,4,7]],"date-time":"2022-04-07T13:39:51Z","timestamp":1649338791000},"page":"103","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["A Hybrid Method for 3D Reconstruction of MR Images"],"prefix":"10.3390","volume":"8","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1751-7762","authenticated-orcid":false,"given":"Loubna","family":"Lechelek","sequence":"first","affiliation":[{"name":"XLIM Laboratory, Joint Research Unit, National Center for Scientific Research (UMR CNRS) 7252, University of Poitiers, CEDEX 9, 86073 Poitiers, France"},{"name":"Common Laboratory Multi-Nuclear Multi-Organ Metabolic Imaging (I3M), CNRS-Siemens, University and Hospital of Poitiers, 86000 Poitiers, France"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9170-6513","authenticated-orcid":false,"given":"Sebastien","family":"Horna","sequence":"additional","affiliation":[{"name":"XLIM Laboratory, Joint Research Unit, National Center for Scientific Research (UMR CNRS) 7252, University of Poitiers, CEDEX 9, 86073 Poitiers, France"},{"name":"Common Laboratory Multi-Nuclear Multi-Organ Metabolic Imaging (I3M), CNRS-Siemens, University and Hospital of Poitiers, 86000 Poitiers, France"}]},{"given":"Rita","family":"Zrour","sequence":"additional","affiliation":[{"name":"XLIM Laboratory, Joint Research Unit, National Center for Scientific Research (UMR CNRS) 7252, University of Poitiers, CEDEX 9, 86073 Poitiers, France"},{"name":"Common Laboratory Multi-Nuclear Multi-Organ Metabolic Imaging (I3M), CNRS-Siemens, University and Hospital of Poitiers, 86000 Poitiers, France"}]},{"given":"Mathieu","family":"Naudin","sequence":"additional","affiliation":[{"name":"Common Laboratory Multi-Nuclear Multi-Organ Metabolic Imaging (I3M), CNRS-Siemens, University and Hospital of Poitiers, 86000 Poitiers, France"},{"name":"LMA Laboratory, Joint Research Unit, National Center for Scientific Research (UMR CNRS) 7348, University of Poitiers, CEDEX 9, 86073 Poitiers, France"}]},{"given":"Carole","family":"Guillevin","sequence":"additional","affiliation":[{"name":"Common Laboratory Multi-Nuclear Multi-Organ Metabolic Imaging (I3M), CNRS-Siemens, University and Hospital of Poitiers, 86000 Poitiers, France"},{"name":"LMA Laboratory, Joint Research Unit, National Center for Scientific Research (UMR CNRS) 7348, University of Poitiers, CEDEX 9, 86073 Poitiers, France"}]}],"member":"1968","published-online":{"date-parts":[[2022,4,7]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"903","DOI":"10.1001\/jamaneurol.2013.1062","article-title":"Cross-sectional and longitudinal analysis of the relationship between A\u03b2 deposition, cortical thickness, and memory in cognitively unimpaired individuals and in Alzheimer disease","volume":"70","author":"Villemagne","year":"2013","journal-title":"JAMA Neurol."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1145\/37402.37422","article-title":"Marching cubes: A high resolution 3D surface construction algorithm","volume":"21","author":"Lorensen","year":"1987","journal-title":"ACM Siggraph Comput. Graph."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1186\/s13173-019-0086-6","article-title":"An extended triangulation to the Marching Cubes 33 algorithm","volume":"25","author":"Custodio","year":"2019","journal-title":"J. Braz. Comput. Soc."},{"key":"ref_4","unstructured":"Bourgeois, D., Wolf, M., and Moreland, K. (2018). Isosurface Visualization Miniapplication, Technical Report, Tech. Rep. SAND2018-2780O."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Schroeder, W., Maynard, R., and Geveci, B. (2015, January 25\u201326). Flying edges: A high-performance scalable isocontouring algorithm. Proceedings of the 2015 IEEE 5th Symposium on Large Data Analysis and Visualization (LDAV), Chicago, IL, USA.","DOI":"10.1109\/LDAV.2015.7348069"},{"key":"ref_6","unstructured":"Moench, T., Adler, S., and Preim, B. (2010, January 1\u20132). Staircase-aware smoothing of medical surface meshes. Proceedings of the 2nd Eurographics Conference on Visual Computing for Biology and Medicine, Leipzig, Germany."},{"key":"ref_7","first-page":"95","article-title":"Contour-Based Surface Reconstruction using Implicit Curve Fitting, and Distance Field Filtering and Interpolation","volume":"2006","author":"Marker","year":"2006","journal-title":"Vol. Graph."},{"key":"ref_8","unstructured":"Pihuit, A., Palombi, O., and Cani, M.P. (2009). Reconstruction Implicite de Surfaces 3D \u00e0 Partir de R\u00e9gions 2D dans des Plans Parall\u00e8les, AFIG 2009-22e Journ\u00e9es de l\u2019Association Fran\u00e7aise d\u2019Informatique Graphique."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"934","DOI":"10.1016\/j.cad.2011.03.002","article-title":"Three-dimensional surface reconstruction of human bone using a B-spline based interpolation approach","volume":"43","author":"Yoo","year":"2011","journal-title":"Comput.-Aided Des."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/j.gmod.2006.09.007","article-title":"Contour-based surface reconstruction using mpu implicit models","volume":"69","author":"Braude","year":"2007","journal-title":"Graph. Model."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"243","DOI":"10.1145\/378267.378271","article-title":"Re: Additional reference to \u201cmarching cubes\u201d","volume":"22","year":"1988","journal-title":"ACM SIGGRAPH Comput. Graph."},{"key":"ref_12","first-page":"83","article-title":"The asymptotic decider: Resolving the ambiguity in Marching Cubes","volume":"91","author":"Nielson","year":"1991","journal-title":"IEEE Vis."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"52","DOI":"10.1007\/BF01900699","article-title":"On generating topologically consistent isosurfaces from uniform samples","volume":"11","author":"Natarajan","year":"1994","journal-title":"Vis. Comput."},{"key":"ref_14","unstructured":"Chernyaev, E. (2022, March 30). Marching Cubes 33: Construction of Topologically Correct Isosurfaces, Available online: https:\/\/www.cs.jhu.edu\/~misha\/ReadingSeminar\/Papers\/Chernyaev96.pdf."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"283","DOI":"10.1109\/TVCG.2003.1207437","article-title":"On Marching Cubes","volume":"9","author":"Nielson","year":"2003","journal-title":"IEEE Trans. Vis. Comput. Graph."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1080\/10867651.2003.10487582","article-title":"Efficient implementation of marching cubes\u2019 cases with topological guarantees","volume":"8","author":"Lewiner","year":"2003","journal-title":"J. Graph. Tools"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"840","DOI":"10.1016\/j.cag.2013.04.004","article-title":"Practical considerations on Marching Cubes 33 topological correctness","volume":"37","author":"Custodio","year":"2013","journal-title":"Comput. Graph."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1111\/cgf.12975","article-title":"Construction of topologically correct and manifold isosurfaces","volume":"35","author":"Grosso","year":"2016","journal-title":"Comput. Graph. Forum"},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"791","DOI":"10.1111\/j.1467-8659.2008.01209.x","article-title":"Quality isosurface mesh generation using an extended marching cubes lookup table","volume":"27","author":"Raman","year":"2008","journal-title":"Comput. Graph. Forum"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"524","DOI":"10.1006\/gmip.1996.0044","article-title":"Arbitrary topology shape reconstruction from planar cross sections","volume":"58","author":"Bajaj","year":"1996","journal-title":"Graph. Model. Image Process."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0734-189X(88)80028-8","article-title":"Shape reconstruction from planar cross sections","volume":"44","author":"Boissonnat","year":"1988","journal-title":"Comput. Vision Graph. Image Process."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"693","DOI":"10.1145\/359842.359846","article-title":"Optimal surface reconstruction from planar contours","volume":"20","author":"Fuchs","year":"1977","journal-title":"Commun. ACM"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1006\/gmip.1999.0494","article-title":"Shape reconstruction from contours using isotopic deformation","volume":"61","author":"Fujimura","year":"1999","journal-title":"Graph. Model. Image Process."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1145\/965145.801264","article-title":"A new general triangulation method for planar contours","volume":"16","author":"Ganapathy","year":"1982","journal-title":"ACM Siggraph Comput. Graph."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"228","DOI":"10.1145\/130881.131213","article-title":"Surfaces from contours","volume":"11","author":"Meyers","year":"1992","journal-title":"ACM Trans. Graph. (TOG)"},{"key":"ref_26","first-page":"94151R","article-title":"Reconstruction of surfaces from planar contours through contour interpolation","volume":"Volume 9415","author":"Sunderland","year":"2015","journal-title":"Medical Imaging 2015: Image-Guided Procedures, Robotic Interventions, and Modeling"},{"key":"ref_27","first-page":"139","article-title":"Fast surface reconstruction from contours using implicit surfaces","volume":"98","author":"Galin","year":"1998","journal-title":"Implicit Surf."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1111\/1467-8659.1330075","article-title":"A new approach to the construction of surfaces from contour data","volume":"13","author":"Jones","year":"1994","journal-title":"Comput. Graph. Forum"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1093\/imanum\/6.2.173","article-title":"Multidimensional reconstruction by set-valued approximations","volume":"6","author":"Levin","year":"1986","journal-title":"IMA J. Numer. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","unstructured":"Ohtake, Y., Belyaev, A., Alexa, M., Turk, G., and Seidel, H.P. (2003). Multi-level partition of unity implicits. ACM Trans. Graph. (SIGGRAPH Proc.), Available online: https:\/\/faculty.cc.gatech.edu\/~turk\/my_papers\/mpu_implicits.pdf.","DOI":"10.1145\/1201775.882293"},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Jolesz, F.A. (2014). 3D Slicer: A Platform for Subject-Specific Image Analysis, Visualization, and Clinical Support. Intraoperative Imaging and Image-Guided Therapy, Springer.","DOI":"10.1007\/978-1-4614-7657-3"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Schroeder, W.J., Lorensen, B., and Martin, K. (2004). The Visualization Toolkit: An Object-Oriented Approach to 3D Graphics, Kitware.","DOI":"10.1016\/B978-012387582-2\/50003-4"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Taubin, G., Zhang, T., and Golub, G. (1996, January 5\u201318). Optimal surface smoothing as filter design. Proceedings of the European Conference on Computer Vision, Cambridge, UK.","DOI":"10.1007\/BFb0015544"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1002\/hbm.10062","article-title":"Fast robust automated brain extraction","volume":"17","author":"Smith","year":"2002","journal-title":"Hum. Brain Mapp."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1109\/42.906424","article-title":"Segmentation of brain MR images through a hidden Markov random field model and the expectation-maximization algorithm","volume":"20","author":"Zhang","year":"2001","journal-title":"IEEE Trans. Med. Imaging"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"179","DOI":"10.1006\/nimg.1998.0395","article-title":"Cortical surface-based analysis. I. Segmentation and surface reconstruction","volume":"9","author":"Dale","year":"1999","journal-title":"Neuroimage"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1142\/S0218195920500028","article-title":"Computing the Hausdorff distance of two sets from their distance functions","volume":"30","author":"Kraft","year":"2020","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"774","DOI":"10.1016\/j.neuroimage.2012.01.021","article-title":"FreeSurfer","volume":"62","author":"Fischl","year":"2012","journal-title":"Neuroimage"}],"container-title":["Journal of Imaging"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2313-433X\/8\/4\/103\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:49:40Z","timestamp":1760136580000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2313-433X\/8\/4\/103"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,4,7]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["jimaging8040103"],"URL":"https:\/\/doi.org\/10.3390\/jimaging8040103","relation":{},"ISSN":["2313-433X"],"issn-type":[{"value":"2313-433X","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,4,7]]}}}