{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T05:13:02Z","timestamp":1778735582488,"version":"3.51.4"},"reference-count":81,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T00:00:00Z","timestamp":1775001600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T00:00:00Z","timestamp":1776124800000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100021856","name":"Ministero dell\u2019Universit\u00e0 e della Ricerca","doi-asserted-by":"publisher","award":["P20228HZWR"],"award-info":[{"award-number":["P20228HZWR"]}],"id":[{"id":"10.13039\/501100021856","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100005389","name":"Universit\u00e0 degli Studi dell'Insubria","doi-asserted-by":"crossref","id":[{"id":"10.13039\/501100005389","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Math Imaging Vis"],"published-print":{"date-parts":[[2026,4]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>We propose a level set-based semi-Lagrangian method on graded adaptive Cartesian grids to address the problem of surface reconstruction from point clouds. The goal is to obtain an implicit, high-quality representation of real shapes that can subsequently serve as computational domain for partial differential equation models. The mathematical formulation is variational, incorporating a curvature constraint that minimizes the surface area while being weighted by the distance of the reconstructed surface from the input point cloud. Within the level set framework, this problem is reformulated as an advection\u2013diffusion equation, which we solve using a semi-Lagrangian scheme coupled with a local high-order interpolator. Building on the features of the level set and semi-Lagrangian method, we use quadtree and octree data structures to represent the grid and generate a mesh with the finest resolution near the zero level set and the point cloud data. The complete surface reconstruction workflow is described, including localization and reinitialization techniques, as well as strategies to handle complex and evolving topologies. A broad set of numerical tests in two and three dimensions is presented to assess the effectiveness of the method.<\/jats:p>","DOI":"10.1007\/s10851-026-01292-y","type":"journal-article","created":{"date-parts":[[2026,4,14]],"date-time":"2026-04-14T10:43:05Z","timestamp":1776163385000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Implicit Reconstruction from Point Cloud: An Adaptive Level Set-Based Semi-Lagrangian Method"],"prefix":"10.1007","volume":"68","author":[{"ORCID":"https:\/\/orcid.org\/0009-0003-8405-2245","authenticated-orcid":false,"given":"Silvia","family":"Preda","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2398-0828","authenticated-orcid":false,"given":"Matteo","family":"Semplice","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2026,4,14]]},"reference":[{"key":"1292_CR1","doi-asserted-by":"publisher","first-page":"479","DOI":"10.1007\/s11831-019-09320-4","volume":"27","author":"Q Wang","year":"2020","unstructured":"Wang, Q., Tan, Y., Mei, Z.: Computational methods of acquisition and processing of 3D point cloud data for construction applications. Arch. Comput. Methods Eng. 27, 479\u2013499 (2020)","journal-title":"Arch. Comput. Methods Eng."},{"key":"1292_CR2","doi-asserted-by":"publisher","first-page":"1104","DOI":"10.3390\/rs3061104","volume":"3","author":"F Remondino","year":"2011","unstructured":"Remondino, F.: Heritage recording and 3D modeling with photogrammetry and 3D scanning. Remote Sens. 3, 1104\u20131138 (2011)","journal-title":"Remote Sens."},{"key":"1292_CR3","doi-asserted-by":"publisher","first-page":"269","DOI":"10.1111\/j.1477-9730.2006.00383.x","volume":"21","author":"F Remondino","year":"2006","unstructured":"Remondino, F., El-Hakim, S.: Image-based 3D modelling: a review. Photogram. Rec. 21, 269\u2013291 (2006)","journal-title":"Photogram. Rec."},{"key":"1292_CR4","doi-asserted-by":"crossref","unstructured":"Aregba\u00a0Driollet, D., Diele, F., Natalini, R.A.: mathematical model for the $${SO}_2$$ aggression to calcium carbonate stones: numerical approximation and asymptotic analysis. SIAM J. Appl. Math.64, 1636\u20131667 (2004)","DOI":"10.1137\/S003613990342829X"},{"key":"1292_CR5","doi-asserted-by":"publisher","first-page":"149","DOI":"10.1137\/070695125","volume":"69","author":"F Clarelli","year":"2008","unstructured":"Clarelli, F., Fasano, A., Natalini, R.: Mathematics and monument conservation: free boundary models of marble sulfation. SIAM J. Appl. Math. 69, 149\u2013168 (2008)","journal-title":"SIAM J. Appl. Math."},{"key":"1292_CR6","doi-asserted-by":"publisher","first-page":"4804","DOI":"10.1016\/j.apm.2014.03.040","volume":"38","author":"F Clarelli","year":"2014","unstructured":"Clarelli, F., De Filippo, B., Natalini, R.: Mathematical model of copper corrosion. Appl. Math. Model. 38, 4804\u20134816 (2014)","journal-title":"Appl. Math. Model."},{"key":"1292_CR7","doi-asserted-by":"crossref","unstructured":"Osher, S., Fedkiw, R.: Level set methods and dynamic implicit surfaces, Vol. 153 of Applied Mathematical Sciences, XIII, 273 (Springer New York, 2003)","DOI":"10.1007\/b98879"},{"key":"1292_CR8","doi-asserted-by":"publisher","first-page":"205","DOI":"10.1006\/jcph.2001.6977","volume":"176","author":"F Gibou","year":"2002","unstructured":"Gibou, F., Fedkiw, R.P., Cheng, L.-T., Kang, M.: A second-order-accurate symmetric discretization of the poisson equation on irregular domains. J. Comput. Phys. 176, 205\u2013227 (2002)","journal-title":"J. Comput. Phys."},{"key":"1292_CR9","doi-asserted-by":"publisher","first-page":"299","DOI":"10.1016\/j.jcp.2018.01.016","volume":"361","author":"A Coco","year":"2018","unstructured":"Coco, A., Russo, G.: Second order finite-difference ghost-point multigrid methods for elliptic problems with discontinuous coefficients on an arbitrary interface. J. Comput. Phys. 361, 299\u2013330 (2018)","journal-title":"J. Comput. Phys."},{"key":"1292_CR10","doi-asserted-by":"publisher","first-page":"20240072","DOI":"10.1515\/math-2024-0072","volume":"22","author":"A Coco","year":"2024","unstructured":"Coco, A., Russo, G.: High-order finite-difference ghost-point methods for elliptic problems in domains with curved boundaries. Open Math. 22, 20240072 (2024). https:\/\/doi.org\/10.1515\/math-2024-0072","journal-title":"Open Math."},{"key":"1292_CR11","doi-asserted-by":"crossref","unstructured":"Amenta, N., Bern, M., Kamvysselis, M., Cunningham, S., Bransford, W., Cohen, M.\u00a0F.: A new Voronoi-based surface reconstruction algorithm. In: Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques, SIGGRAPH 1998, 415 \u2013 422 (1998)","DOI":"10.1145\/280814.280947"},{"key":"1292_CR12","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-540-33259-6_6","volume-title":"Delaunay triangulation based surface reconstruction","author":"F Cazals","year":"2006","unstructured":"Cazals, F., Giesen, J.: Delaunay triangulation based surface reconstruction. Springer, Berlin Heidelberg (2006)"},{"key":"1292_CR13","unstructured":"Park, I.\u00a0K., Yun, I.\u00a0D., Lee, S.\u00a0U.: Constructing NURBS surface model from scattered and unorganized range data. In: Werner, B. (ed.) Second International Conference on 3-D Digital Imaging and Modeling (Cat. No.PR00062), 312\u2013320 (1999)"},{"key":"1292_CR14","unstructured":"Gregorski, B., Hamann, B., Joy, K.: Reconstruction of B-spline surfaces from scattered data points. In: Rawlinson, A. (ed.) Proceedings Computer Graphics International 2000, 163\u2013170 (2000)"},{"key":"1292_CR15","doi-asserted-by":"crossref","unstructured":"Carr, J., et\u00a0al.: Reconstruction and representation of 3D objects with radial basis functions. ACM SIGGRAPH (2001)","DOI":"10.1145\/383259.383266"},{"key":"1292_CR16","doi-asserted-by":"crossref","unstructured":"Carr, J., et\u00a0al.: Smooth surface reconstruction from noisy range data. In: Adcock, M., Gwilt, I., Tsui, L.\u00a0Y. (eds.) Proceedings of the 1st International Conference on Computer Graphics and Interactive Techniques in Australasia and South East Asia, GRAPHITE \u201903, 119\u2013297 (2003)","DOI":"10.1145\/604471.604495"},{"key":"1292_CR17","doi-asserted-by":"publisher","DOI":"10.1016\/j.cagd.2021.102062","volume":"92","author":"Y Zeng","year":"2021","unstructured":"Zeng, Y., Zhu, Y.: Implicit surface reconstruction based on a new interpolation\/approximation radial basis function. Comput. Aided Geom. Des. 92, 102062 (2021)","journal-title":"Comput. Aided Geom. Des."},{"key":"1292_CR18","unstructured":"Cheng, Z.\u00a0Q., et\u00a0al.: A survey of methods for moving least squares surfaces. In: Hege, H.\u00a0C., Laidlaw, D., Pajarola, R., Staadt, O. (eds.) IEEE\/EG Symposium on Volume and Point-Based Graphics, 9\u201323 (2008)"},{"key":"1292_CR19","doi-asserted-by":"crossref","unstructured":"Hoppe, H., Derose, T., Duchamp, T., Mcdonald, J., Stuet-zle, W.: Surface reconstruction from unorganized point clouds. Comput. Graph. 71\u201378 (1992)","DOI":"10.1145\/133994.134011"},{"key":"1292_CR20","doi-asserted-by":"publisher","first-page":"12","DOI":"10.1016\/0021-9991(88)90002-2","volume":"79","author":"S Osher","year":"1988","unstructured":"Osher, S., Sethian, J.A.: Fronts propagating with curvature-dependent speed: algorithms based on Hamilton-Jacobi formulations. J. Comput. Phys. 79, 12\u201349 (1988)","journal-title":"J. Comput. Phys."},{"key":"1292_CR21","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1006\/jcph.1994.1155","volume":"114","author":"M Sussman","year":"1994","unstructured":"Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146\u2013159 (1994)","journal-title":"J. Comput. Phys."},{"key":"1292_CR22","unstructured":"Sethian, J.: Level set methods and fast marching methods. Evolving interfaces in computational geometry, fluid mechanics, computer vision, and materials science (Cambridge University Press, 1999)"},{"key":"1292_CR23","doi-asserted-by":"publisher","first-page":"295","DOI":"10.1006\/cviu.2000.0875","volume":"80","author":"HK Zhao","year":"2000","unstructured":"Zhao, H.K., Osher, S., Merriman, B., Kang, M.: Implicit and nonparametric shape reconstruction from unorganized data using a variational level set method. Comput. Vis. Image Underst. 80, 295\u2013314 (2000)","journal-title":"Comput. Vis. Image Underst."},{"key":"1292_CR24","unstructured":"Marcon, M., Piccarreta, L., Sarti, A., Tubaro, S.: Fast point-cloud wrapping through level-set evolution. In: Grau, O. (ed.) 1st European Conference on Visual Media Production (CVMP) 2004, 119\u2013125 (2004)"},{"key":"1292_CR25","doi-asserted-by":"crossref","unstructured":"Preda, S., Semplice, M.: Surface reconstruction from point cloud using a semi-Lagrangian scheme with local interpolator. SIAM J. Sci. Comput. 103 (2025)","DOI":"10.1007\/s10915-025-02843-y"},{"key":"1292_CR26","doi-asserted-by":"crossref","unstructured":"Coco, A., Preda, S., Semplice, M.: From point clouds to 3D simulations of marble sulfation. In: Bretti, G., Cavaterra, C., Solci, M., Spagnuolo, M. (eds.) Mathematical Modeling in Cultural Heritage, 153\u2013174 (Springer Nature Singapore, 2023)","DOI":"10.1007\/978-981-99-3679-3_10"},{"key":"1292_CR27","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2020.125503","volume":"386","author":"A Coco","year":"2020","unstructured":"Coco, A., Semplice, M., Serra Capizzano, S.: A level-set multigrid technique for nonlinear diffusion in the numerical simulation of marble degradation under chemical pollutants. Appl. Math. Comput. 386, 125503 (2020)","journal-title":"Appl. Math. Comput."},{"key":"1292_CR28","unstructured":"K\u00f3sa, B., Hali\u010dkov\u00e1-Brehovsk\u00e1, J.: New efficient numerical method for 3D point cloud surface reconstruction by using level set methods. In: Mikula, K., \u0160ev\u010dovi\u010d, D., Urb\u00e1n, J. (eds.) Proceedings of Equadiff 2017 Conference, 387\u2013396 (2017)"},{"key":"1292_CR29","unstructured":"Zhao, H.\u00a0K., Osher, S., Fedkiw, R.: Fast surface reconstruction using the level set method. In: Williams, A.\u00a0D. (ed.) Proceedings of IEEE Workshop on Variational and Level Set Methods in Computer Vision, 194\u2013201 (2001)"},{"key":"1292_CR30","doi-asserted-by":"publisher","first-page":"103","DOI":"10.1007\/s00791-016-0274-2","volume":"18","author":"E Carlini","year":"2017","unstructured":"Carlini, E., Ferretti, R.: A Semi-Lagrangian scheme with radial basis approximation for surface reconstruction. Comput. Vis. Sci. 18, 103\u2013112 (2017)","journal-title":"Comput. Vis. Sci."},{"key":"1292_CR31","doi-asserted-by":"crossref","unstructured":"He, Y., Huska, M., Kang, S.\u00a0H., Liu, H.: Fast algorithms for surface reconstruction from point cloud. In: Li, M., Han, X. Cheng, J. (eds.) Springer Proceedings in Mathematics and Statistics, Vol. 360, 61\u201380 (2021)","DOI":"10.1007\/978-981-16-2701-9_4"},{"key":"1292_CR32","doi-asserted-by":"publisher","first-page":"243","DOI":"10.1002\/cpa.3160050303","volume":"5","author":"R Courant","year":"1952","unstructured":"Courant, R., Isaacson, E., Rees, M.: On the solution of nonlinear hyperbolic differential equations by finite differences. Comm. Pure Appl. Math. 5, 243\u2013255 (1952)","journal-title":"Comm. Pure Appl. Math."},{"key":"1292_CR33","doi-asserted-by":"crossref","unstructured":"Falcone., M., Ferretti, R.: Semi-Lagrangian approximation schemes for linear and Hamilton-Jacobi equations. In: Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, (2014)","DOI":"10.1137\/1.9781611973051"},{"key":"1292_CR34","doi-asserted-by":"publisher","first-page":"A2458","DOI":"10.1137\/140969713","volume":"36","author":"L Bonaventura","year":"2014","unstructured":"Bonaventura, L., Ferretti, R.: Semi-Lagrangian methods for parabolic problems in divergence form. SIAM J. Sci. Comput. 36, A2458\u2013A2477 (2014)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR35","doi-asserted-by":"crossref","unstructured":"Bonaventura, L., Calzola, E., Carlini, E., Ferretti, R.: Second order Fully Semi-Lagrangian discretizations of advection-diffusion-reaction systems. J. Sci. Comput. 88 (2021)","DOI":"10.1007\/s10915-021-01518-8"},{"key":"1292_CR36","doi-asserted-by":"publisher","first-page":"498","DOI":"10.1006\/jcph.1999.6194","volume":"151","author":"J Strain","year":"1999","unstructured":"Strain, J.: Semi-Lagrangian methods for level set equations. J. Comput. Phys. 151, 498\u2013533 (1999)","journal-title":"J. Comput. Phys."},{"key":"1292_CR37","doi-asserted-by":"publisher","first-page":"656","DOI":"10.1137\/S1064827599359461","volume":"22","author":"D Levy","year":"2000","unstructured":"Levy, D., Puppo, G., Russo, G.: Compact central WENO schemes for multidimensional conservation laws. SIAM J. Sci. Comput. 22, 656\u2013672 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR38","doi-asserted-by":"publisher","DOI":"10.1016\/j.jcp.2019.109062","volume":"404","author":"DS Balsara","year":"2020","unstructured":"Balsara, D.S., Garain, S., Florinski, V., Boscheri, W.: An efficient class of WENO schemes with adaptive order for unstructured meshes. J. Comput. Phys. 404, 109062 (2020)","journal-title":"J. Comput. Phys."},{"key":"1292_CR39","doi-asserted-by":"publisher","first-page":"110","DOI":"10.1016\/j.jcp.2016.05.010","volume":"318","author":"J Zhu","year":"2016","unstructured":"Zhu, J., Qiu, J.: A new fifth order finite difference WENO scheme for solving hyperbolic conservation laws. J. Comput. Phys. 318, 110\u2013121 (2016)","journal-title":"J. Comput. Phys."},{"key":"1292_CR40","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1007\/s10915-018-0773-z","volume":"78","author":"A Baeza","year":"2019","unstructured":"Baeza, A., B\u00fcrger, R., Mulet, P., Zor\u00edo, D.: Central WENO schemes through a global average weight. J. Sci. Comput. 78, 499\u2013530 (2019)","journal-title":"J. Sci. Comput."},{"key":"1292_CR41","doi-asserted-by":"publisher","first-page":"770","DOI":"10.1016\/j.amc.2007.09.017","volume":"198","author":"J Zhou","year":"2008","unstructured":"Zhou, J., Cai, L., Zhou, F.-Q.: New high-resolution scheme for three-dimensional nonlinear hyperbolic conservation laws. Appl. Math. Comp. 198, 770\u2013786 (2008)","journal-title":"Appl. Math. Comp."},{"key":"1292_CR42","doi-asserted-by":"publisher","first-page":"A2564","DOI":"10.1137\/17M1111036","volume":"39","author":"M Dumbser","year":"2017","unstructured":"Dumbser, M., Boscheri, W., Semplice, M., Russo, G.: Central weighted ENO schemes for hyperbolic conservation laws on fixed and moving unstructured meshes. SIAM J. Sci. Comput. 39, A2564\u2013A2591 (2017)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR43","doi-asserted-by":"publisher","first-page":"1095","DOI":"10.1002\/num.22133","volume":"33","author":"J Zhu","year":"2017","unstructured":"Zhu, J., Qiu, J.: A new fifth order finite difference WENO scheme for Hamilton-Jacobi equations. Numer. Meth. for PDEs 33, 1095\u20131113 (2017)","journal-title":"Numer. Meth. for PDEs"},{"key":"1292_CR44","doi-asserted-by":"publisher","first-page":"53","DOI":"10.1016\/j.compfluid.2019.02.010","volume":"183","author":"F Zheng","year":"2019","unstructured":"Zheng, F., Shu, C.W., Qiu, J.: High order finite difference hermite WENO schemes for the Hamilton-Jacobi equations on unstructured meshes. Comp. Fluids 183, 53\u201365 (2019)","journal-title":"Comp. Fluids"},{"key":"1292_CR45","doi-asserted-by":"publisher","first-page":"897","DOI":"10.4208\/cicp.OA-2018-0156","volume":"27","author":"J Zhu","year":"2020","unstructured":"Zhu, J., Qiu, J.: A New Type of High-Order WENO Schemes for Hamilton-Jacobi Equations on Triangular Meshes. Comm. Comput. Phys. 27, 897\u2013920 (2020)","journal-title":"Comm. Comput. Phys."},{"key":"1292_CR46","doi-asserted-by":"publisher","first-page":"1689","DOI":"10.1090\/mcom\/3273","volume":"87","author":"I Cravero","year":"2018","unstructured":"Cravero, I., Puppo, G., Semplice, M., Visconti, G.: CWENO: uniformly accurate reconstructions for balance laws. Math. Comp. 87, 1689\u20131719 (2018)","journal-title":"Math. Comp."},{"key":"1292_CR47","doi-asserted-by":"publisher","first-page":"2328","DOI":"10.1137\/18M1228232","volume":"57","author":"I Cravero","year":"2019","unstructured":"Cravero, I., Semplice, M., Visconti, G.: Optimal definition of the nonlinear weights in multidimensional Central WENOZ reconstructions. SIAM J. Numer. Anal. 57, 2328\u20132358 (2019)","journal-title":"SIAM J. Numer. Anal."},{"key":"1292_CR48","doi-asserted-by":"crossref","unstructured":"Semplice, M., Visconti, G.: Efficient implementation of adaptive order reconstructions. J. Sci. Comput. 83 (2020)","DOI":"10.1007\/s10915-020-01156-6"},{"key":"1292_CR49","doi-asserted-by":"publisher","first-page":"410","DOI":"10.1006\/jcph.1999.6345","volume":"155","author":"D Peng","year":"1999","unstructured":"Peng, D., Merriman, B., Osher, S., Zhao, H.K., Kang, M.: A PDE-based fast local level set method. J. Comput. Phys. 155, 410\u2013438 (1999)","journal-title":"J. Comput. Phys."},{"key":"1292_CR50","doi-asserted-by":"publisher","first-page":"107","DOI":"10.2140\/camcos.2014.9.107","volume":"9","author":"R Saye","year":"2014","unstructured":"Saye, R.: High-order methods for computing distances to implicitly defined surfaces. Commun. Appl. Math. Comput. Sci. 9, 107\u2013141 (2014)","journal-title":"Commun. Appl. Math. Comput. Sci."},{"key":"1292_CR51","doi-asserted-by":"publisher","first-page":"603","DOI":"10.1090\/S0025-5718-04-01678-3","volume":"74","author":"HK Zhao","year":"2005","unstructured":"Zhao, H.K.: A fast sweeping method for Eikonal equations. Math. Comput. 74, 603\u2013627 (2005)","journal-title":"Math. Comput."},{"key":"1292_CR52","doi-asserted-by":"crossref","unstructured":"Falcone, M., Ferretti, R.: Consistency of a large time-step scheme for mean curvature motion. In: Brezzi, F., Buffa, A., Corsaro, S., Murli, A. (eds.) Numerical Mathematics and Advanced Applications, 495\u2013502 (Springer Milan, 2003)","DOI":"10.1007\/978-88-470-2089-4_46"},{"key":"1292_CR53","doi-asserted-by":"publisher","first-page":"409","DOI":"10.4171\/ifb\/240","volume":"12","author":"E Carlini","year":"2010","unstructured":"Carlini, E., Falcone, M., Ferretti, R.: Convergence of a large time-step scheme for mean curvature motion. Interfaces Free Bound. 12, 409\u2013411 (2010)","journal-title":"Interfaces Free Bound."},{"key":"1292_CR54","doi-asserted-by":"publisher","first-page":"2328","DOI":"10.1137\/18M1228232","volume":"57","author":"I Cravero","year":"2019","unstructured":"Cravero, I., Semplice, M., Visconti, G.: Optimal definition of the nonlinear weights in multidimensional Central WENOZ reconstructions. SIAM J. Numer. Anal. 57, 2328\u20132358 (2019)","journal-title":"SIAM J. Numer. Anal."},{"key":"1292_CR55","doi-asserted-by":"publisher","DOI":"10.1007\/s42967-025-00482-6","volume-title":"A CWENO Large Time-Step Scheme for Hamilton-Jacobi Equations","author":"E Carlini","year":"2025","unstructured":"Carlini, E., Ferretti, R., Preda, S., Semplice, M.: A CWENO Large Time-Step Scheme for Hamilton-Jacobi Equations. Commun. Appl. Math, Comput (2025)"},{"key":"1292_CR56","doi-asserted-by":"publisher","first-page":"202","DOI":"10.1006\/jcph.1996.0130","volume":"126","author":"GS Jiang","year":"1996","unstructured":"Jiang, G.S., Shu, C.W.: Efficient implementation of weighted ENO schemes. J. Comput. Phys. 126, 202\u2013228 (1996)","journal-title":"J. Comput. Phys."},{"key":"1292_CR57","doi-asserted-by":"publisher","first-page":"97","DOI":"10.1006\/jcph.1998.6165","volume":"150","author":"C Hu","year":"1999","unstructured":"Hu, C., Shu, C.W.: Weighted essentially non-oscillatory schemes on triangular meshes. J. Comput. Phys. 150, 97\u2013127 (1999)","journal-title":"J. Comput. Phys."},{"key":"1292_CR58","doi-asserted-by":"publisher","first-page":"2126","DOI":"10.1137\/S106482759732455X","volume":"21","author":"G-S Jiang","year":"2000","unstructured":"Jiang, G.-S., Peng, D.: Weighted ENO schemes for Hamilton-Jacobi equations. SIAM J. Sci. Comput. 21, 2126\u20132143 (2000)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR59","doi-asserted-by":"crossref","unstructured":"Falcone, M., Paolucci, G., Tozza, S.: Multidimensional smoothness indicators for first-order Hamilton-Jacobi equations. J. Comput. Phys. 409 (2020)","DOI":"10.1016\/j.jcp.2020.109360"},{"key":"1292_CR60","doi-asserted-by":"publisher","first-page":"1528","DOI":"10.1109\/9.412624","volume":"40","author":"JN Tsitsiklis","year":"1995","unstructured":"Tsitsiklis, J.N.: Efficient algorithms for globally optimal trajectories. IEEE Trans. Autom. Control 40, 1528\u20131538 (1995)","journal-title":"IEEE Trans. Autom. Control"},{"key":"1292_CR61","doi-asserted-by":"publisher","first-page":"1591","DOI":"10.1073\/pnas.93.4.1591","volume":"93","author":"JA Sethian","year":"1996","unstructured":"Sethian, J.A.: A fast marching level set method for monotonically advancing fronts. Proc. Natl. Acad. Sci. 93, 1591\u20131595 (1996)","journal-title":"Proc. Natl. Acad. Sci."},{"key":"1292_CR62","doi-asserted-by":"publisher","first-page":"230","DOI":"10.1137\/S106482750037617X","volume":"23","author":"DL Chopp","year":"2001","unstructured":"Chopp, D.L.: Some Improvements of the Fast Marching Method. SIAM J. Sci. Comput. 23, 230\u2013244 (2001)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR63","doi-asserted-by":"publisher","first-page":"673","DOI":"10.1137\/S0036142901396533","volume":"41","author":"Y-HR Tsai","year":"2003","unstructured":"Tsai, Y.-H.R., Cheng, L.-T., Osher, S., Zhao, H.-K.: Fast Sweeping Algorithms for a Class of Hamilton-Jacobi Equations. SIAM J. Numer. Anal. 41, 673\u2013694 (2003)","journal-title":"SIAM J. Numer. Anal."},{"key":"1292_CR64","volume-title":"A Domain Decomposition Parallelization of the Fast Marching Method","author":"M Herrmann","year":"2003","unstructured":"Herrmann, M.: A Domain Decomposition Parallelization of the Fast Marching Method. Tech. Rep, DTIC Document (2003)"},{"key":"1292_CR65","unstructured":"Tugurlan, M.\u00a0C.: Fast marching methods\u2014parallel implementation and analysis. Ph.D. thesis (2008)"},{"key":"1292_CR66","first-page":"421","volume":"25","author":"H Zhao","year":"2007","unstructured":"Zhao, H.: Parallel implementations of the fast sweeping method. J. Comput. Math. 25, 421\u2013429 (2007)","journal-title":"J. Comput. Math."},{"key":"1292_CR67","doi-asserted-by":"publisher","first-page":"A156","DOI":"10.1137\/12088197X","volume":"37","author":"A Chacon","year":"2015","unstructured":"Chacon, A., Vladimirsky, A.: A parallel two-scale method for Eikonal equations. SIAM J. Sci. Comput. 37, A156\u2013A180 (2015)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR68","doi-asserted-by":"publisher","first-page":"2512","DOI":"10.1137\/060670298","volume":"30","author":"WK Jeong","year":"2008","unstructured":"Jeong, W.K., Whitaker, R.T.: A fast iterative method for Eikonal equations. SIAM J. Sci. Comput. 30, 2512\u20132534 (2008)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR69","doi-asserted-by":"publisher","first-page":"83","DOI":"10.1137\/050627083","volume":"45","author":"J Qian","year":"2007","unstructured":"Qian, J., Zhang, Y., Zhao, H.: Fast sweeping methods for Eikonal equations on triangular meshes. SIAM J. Numer. Anal. 45, 83\u2013107 (2007)","journal-title":"SIAM J. Numer. Anal."},{"key":"1292_CR70","doi-asserted-by":"crossref","unstructured":"Chen, X., Cao, D., Fu, X.: A fast sweeping method based on coordinate transformation for eikonal equation on unstructured triangular meshes. In: Fourth International Meeting for Applied Geoscience & Energy of SEG Technical Program Expanded Abstracts (2024)","DOI":"10.1190\/image2024-4100642.1"},{"key":"1292_CR71","doi-asserted-by":"publisher","first-page":"179","DOI":"10.1006\/jcph.1996.0167","volume":"127","author":"H-K Zhao","year":"1996","unstructured":"Zhao, H.-K., Chan, T., Merriman, B., Osher, S.: A variational level set approach to multiphase motion. J. Comput. Phys. 127, 179\u2013195 (1996)","journal-title":"J. Comput. Phys."},{"key":"1292_CR72","doi-asserted-by":"crossref","unstructured":"Li, C., Xu, C., Gui, C., Fox, M.\u00a0D.: Level set evolution without re-initialization: a new variational formulation. In: Schmid, C., Soatto, S., Tomasi, C. (eds.) 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR\u201905), Vol.\u00a01, 430\u2013436 (2005)","DOI":"10.1109\/CVPR.2005.213"},{"key":"1292_CR73","doi-asserted-by":"crossref","unstructured":"Wu, W., Wu, Y., Huang, Q.: An improved distance regularized level set evolution without re-initialization. In: IEEE 2012 IEEE Fifth International Conference on Advanced Computational Intelligence (ICACI), 631\u2013636 (2012)","DOI":"10.1109\/ICACI.2012.6463242"},{"key":"1292_CR74","doi-asserted-by":"publisher","first-page":"497","DOI":"10.1137\/18M1231432","volume":"13","author":"M Falcone","year":"2020","unstructured":"Falcone, M., Paolucci, G., Tozza, S.: A high-order scheme for image segmentation via a modified level-set method. SIAM J. Imaging Sci. 13, 497\u2013534 (2020)","journal-title":"SIAM J. Imaging Sci."},{"key":"1292_CR75","doi-asserted-by":"publisher","first-page":"146","DOI":"10.1006\/jcph.1994.1155","volume":"114","author":"M Sussman","year":"1994","unstructured":"Sussman, M., Smereka, P., Osher, S.: A level set approach for computing solutions to incompressible two-phase flow. J. Comput. Phys. 114, 146\u2013159 (1994)","journal-title":"J. Comput. Phys."},{"key":"1292_CR76","doi-asserted-by":"publisher","first-page":"345","DOI":"10.1016\/j.jcp.2016.06.017","volume":"322","author":"M Mirzadeh","year":"2016","unstructured":"Mirzadeh, M., Guittet, A., Burstedde, C., Gibou, F.: Parallel level-set methods on adaptive tree-based grids. J. Comput. Phys. 322, 345\u2013364 (2016)","journal-title":"J. Comput. Phys."},{"key":"1292_CR77","doi-asserted-by":"publisher","first-page":"300","DOI":"10.1016\/j.jcp.2006.11.034","volume":"225","author":"C Min","year":"2007","unstructured":"Min, C., Gibou, F.: A second order accurate level set method on non-graded adaptive cartesian grids. J. Comput. Phys. 225, 300\u2013321 (2007)","journal-title":"J. Comput. Phys."},{"key":"1292_CR78","unstructured":"AIM@SHAPE & VISIONAIR. VISIONAIR shape repository. http:\/\/visionair.ge.imati.cnr.it\/ontologies\/shapes\/ (2022). http:\/\/visionair.ge.imati.cnr.it\/ontologies\/shapes\/view.jsp?id=268-frog_-_merged. Accessed March 2022"},{"key":"1292_CR79","unstructured":"Laboratory, S. U. C.\u00a0G.: The Stanford 3D Scanning Repository. http:\/\/graphics.stanford.edu\/data\/3Dscanrep\/. Accessed March 2022"},{"key":"1292_CR80","doi-asserted-by":"publisher","first-page":"1103","DOI":"10.1137\/100791634","volume":"33","author":"C Burstedde","year":"2011","unstructured":"Burstedde, C., Wilcox, L.C., Ghattas, O.: p4est: Scalable Algorithms for Parallel Adaptive Mesh Refinement on Forests of Octrees. SIAM J. Sci. Comput. 33, 1103\u20131133 (2011)","journal-title":"SIAM J. Sci. Comput."},{"key":"1292_CR81","doi-asserted-by":"publisher","first-page":"04016007","DOI":"10.1061\/(ASCE)SU.1943-5428.0000159","volume":"142","author":"J Hali\u010dkov\u00e1","year":"2016","unstructured":"Hali\u010dkov\u00e1, J., Mikula, K.: Level set method for surface reconstruction and its application in surveying. J. Surveying Engrg. 142, 04016007 (2016)","journal-title":"J. Surveying Engrg."}],"container-title":["Journal of Mathematical Imaging and Vision"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-026-01292-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s10851-026-01292-y","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s10851-026-01292-y.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T04:50:34Z","timestamp":1778734234000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s10851-026-01292-y"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,4]]},"references-count":81,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2026,4]]}},"alternative-id":["1292"],"URL":"https:\/\/doi.org\/10.1007\/s10851-026-01292-y","relation":{},"ISSN":["0924-9907","1573-7683"],"issn-type":[{"value":"0924-9907","type":"print"},{"value":"1573-7683","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,4]]},"assertion":[{"value":"6 November 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"24 March 2026","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"14 April 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}},{"order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Declarations"}},{"value":"The authors declare that they have no conflict of interest.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}},{"value":"The authors declare no conflict of interest.","order":3,"name":"Ethics","group":{"name":"EthicsHeading","label":"Conflict of interest"}}],"article-number":"14"}}