{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,8]],"date-time":"2026-07-08T18:05:30Z","timestamp":1783533930456,"version":"3.55.0"},"reference-count":48,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2013,11,20]],"date-time":"2013-11-20T00:00:00Z","timestamp":1384905600000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Discrete Comput Geom"],"published-print":{"date-parts":[[2014,1]]},"DOI":"10.1007\/s00454-013-9557-2","type":"journal-article","created":{"date-parts":[[2013,11,19]],"date-time":"2013-11-19T10:33:40Z","timestamp":1384857220000},"page":"221-267","source":"Crossref","is-referenced-by-count":47,"title":["Manifold Reconstruction Using Tangential Delaunay Complexes"],"prefix":"10.1007","volume":"51","author":[{"given":"Jean-Daniel","family":"Boissonnat","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Arijit","family":"Ghosh","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2013,11,20]]},"reference":[{"key":"9557_CR1","doi-asserted-by":"crossref","first-page":"481","DOI":"10.1007\/PL00009475","volume":"22","author":"N. Amenta","year":"1999","unstructured":"Amenta, N., Bern, M.: Surface reconstruction by Voronoi filtering. Discrete Comput. Geom. 22, 481\u2013504 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"9557_CR2","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1142\/S0218195902000773","volume":"12","author":"N. Amenta","year":"2002","unstructured":"Amenta, N., Choi, S., Dey, T.K., Leekha, N.: A simple algorithm for homeomorphic surface reconstruction. Int. J. Comput. Geom. Appl. 12, 125\u2013141 (2002)","journal-title":"Int. J. Comput. Geom. Appl."},{"issue":"2","key":"9557_CR3","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/0031-3203(84)90064-5","volume":"17","author":"F. Aurenhammer","year":"1984","unstructured":"Aurenhammer, F., Edelsbrunner, H.: An optimal algorithm for constructing the weighted Voronoi diagram in the plane. Pattern Recognit. 17(2), 251\u2013257 (1984)","journal-title":"Pattern Recognit."},{"issue":"1","key":"9557_CR4","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1137\/0216006","volume":"16","author":"F. Aurenhammer","year":"1987","unstructured":"Aurenhammer, F.: Power diagrams: properties, algorithms and applications. SIAM J. Comput. 16(1), 78\u201396 (1987)","journal-title":"SIAM J. Comput."},{"key":"9557_CR5","unstructured":"Boissonnat, J.-D., Dyer, R., Ghosh, A.: The stability of Delaunay triangulations. Int. J. Comput. Geom. Appl. (special issue for SoCG 2012) (to appear)"},{"key":"9557_CR6","doi-asserted-by":"crossref","first-page":"161","DOI":"10.1016\/S0010-4485(03)00059-9","volume":"36","author":"J.-D. Boissonnat","year":"2004","unstructured":"Boissonnat, J.-D., Fl\u00f6totto, J.: A coordinate system associated with points scattered on a surface. Comput. Aided Des. 36, 161\u2013174 (2004)","journal-title":"Comput. Aided Des."},{"issue":"1","key":"9557_CR7","doi-asserted-by":"crossref","first-page":"37","DOI":"10.1007\/s00454-009-9175-1","volume":"42","author":"J.-D. Boissonnat","year":"2009","unstructured":"Boissonnat, J.-D., Guibas, L.J., Oudot, S.Y.: Manifold reconstruction in arbitary dimensions using witness complexes. Discrete Comput. Geom. 42(1), 37\u201370 (2009)","journal-title":"Discrete Comput. Geom."},{"key":"9557_CR8","first-page":"585","volume-title":"Advances in Neural Information Processing Systems","author":"M. Belkin","year":"2002","unstructured":"Belkin, M., Niyogi, P.: Laplacian eigenmaps and spectral techniques for embedding and clustering. In: Advances in Neural Information Processing Systems, vol. 14, pp. 585\u2013591 (2002)"},{"issue":"2","key":"9557_CR9","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1007\/s00454-010-9256-1","volume":"44","author":"J.-D. Boissonnat","year":"2010","unstructured":"Boissonnat, J.-D., Nielsen, F., Nock, R.: Bregman Voronoi Diagrams. Discrete Comput. Geom. 44(2), 281\u2013307 (2010)","journal-title":"Discrete Comput. Geom."},{"key":"9557_CR10","series-title":"Graduate Text in Mathematics","volume-title":"Topology and Geometry","author":"G.E. Bredon","year":"1994","unstructured":"Bredon, G.E.: Topology and Geometry. Graduate Text in Mathematics. Springer, Berlin (1994)"},{"key":"9557_CR11","first-page":"278","volume-title":"Proc. ACM Symp. on Computational Geometry","author":"M. Belkin","year":"2008","unstructured":"Belkin, M., Sun, J., Wang, Y.: Discrete Laplace operator on meshed surfaces. In: Proc. ACM Symp. on Computational Geometry, pp. 278\u2013287 (2008)"},{"key":"9557_CR12","first-page":"270","volume-title":"Proc. ACM Symp. on Computational Geometry","author":"J.-D. Boissonnat","year":"2008","unstructured":"Boissonnat, J.-D., Wormser, C., Yvinec, M.: Locally uniform anisotropic meshing. In: Proc. ACM Symp. on Computational Geometry, pp. 270\u2013277 (2008)"},{"key":"9557_CR13","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9781139172998","volume-title":"Algorithmic Geometry","author":"J.-D. Boissonnat","year":"1998","unstructured":"Boissonnat, J.-D., Yvinec, M.: Algorithmic Geometry. Cambridge University Press, Cambridge (1998)"},{"key":"9557_CR14","doi-asserted-by":"crossref","first-page":"883","DOI":"10.1145\/355483.355487","volume":"47","author":"S.-W. Cheng","year":"2000","unstructured":"Cheng, S.-W., Dey, T.K., Edelsbrunner, H., Facello, M.A., Teng, S.-H.: Sliver Exudation. J. ACM 47, 883\u2013904 (2000)","journal-title":"J. ACM"},{"key":"9557_CR15","first-page":"1018","volume-title":"Proc. ACM-SIAM Symp. Discrete Algorithms","author":"S.-W. Cheng","year":"2005","unstructured":"Cheng, S.-W., Dey, T.K., Ramos, E.A.: Manifold Reconstruction from Point Samples. In: Proc. ACM-SIAM Symp. Discrete Algorithms, pp. 1018\u20131027 (2005)"},{"key":"9557_CR16","volume-title":"Effective Computational Geometry for Curve and Surfaces","author":"F. Cazals","year":"2006","unstructured":"Cazals, F., Giesen, J.: Delaunay triangulation based surface reconstruction. In: Boissonnat, J.D., Teillaud, M. (eds.) Effective Computational Geometry for Curve and Surfaces. Springer, Berlin (2006)"},{"key":"9557_CR17","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1007\/BF02573985","volume":"10","author":"B. Chazelle","year":"1993","unstructured":"Chazelle, B.: An optimal convex hull algorithm in any fixed dimension. Discrete Comput. Geom. 10, 377\u2013409 (1993)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"9557_CR18","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1007\/s11263-007-0056-x","volume":"76","author":"G. Carlsson","year":"2008","unstructured":"Carlsson, G., Ishkhanov, T., de Silva, V., Zomorodian, A.: On the local behavior of spaces of natural images. Int. J. Comput. Vis. 76(1), 1\u201312 (2008)","journal-title":"Int. J. Comput. Vis."},{"key":"9557_CR19","doi-asserted-by":"crossref","first-page":"156","DOI":"10.1016\/j.comgeo.2007.07.001","volume":"40","author":"F. Chazal","year":"2008","unstructured":"Chazal, F., Lieutier, A.: Smooth manifold reconstruction from noisy and non-uniform approximation with guarantees. Comput. Geom. 40, 156\u2013170 (2008)","journal-title":"Comput. Geom."},{"key":"9557_CR20","first-page":"232","volume-title":"Proc. ACM Symp. on Computational Geometry","author":"F. Chazal","year":"2008","unstructured":"Chazal, F., Oudot, S.Y.: Towards persistence-based reconstruction in Euclidean spaces. In: Proc. ACM Symp. on Computational Geometry, pp. 232\u2013241 (2008)"},{"key":"9557_CR21","doi-asserted-by":"crossref","first-page":"387","DOI":"10.1007\/BF02187740","volume":"4","author":"K.L. Clarkson","year":"1989","unstructured":"Clarkson, K.L., Shor, P.W.: Applications of random sampling in computational geometry. II. Discrete Comput. Geom. 4, 387\u2013421 (1989)","journal-title":"Discrete Comput. Geom."},{"key":"9557_CR22","doi-asserted-by":"crossref","first-page":"4","DOI":"10.1007\/s00371-003-0217-z","volume":"20","author":"D. Cohen-Steiner","year":"2004","unstructured":"Cohen-Steiner, D., Da, T.K.F.: A greedy Delaunay based surface reconstruction algorithm. Vis. Comput. 20, 4\u201316 (2004)","journal-title":"Vis. Comput."},{"issue":"5","key":"9557_CR23","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1142\/S0218195908002702","volume":"18","author":"S.-W. Cheng","year":"2008","unstructured":"Cheng, S.-W., Wang, Y., Wu, Z.: Provable dimension detection using principle component analysis. Int. J. Comput. Geom. Appl. 18(5), 415\u2013440 (2008)","journal-title":"Int. J. Comput. Geom. Appl."},{"key":"9557_CR24","first-page":"793","volume":"7","author":"B. Delaunay","year":"1934","unstructured":"Delaunay, B.: Sur la sph\u00e8re vide. Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk 7, 793\u2013800 (1934)","journal-title":"Izv. Akad. Nauk SSSR, Otdelenie Matematicheskii i Estestvennyka Nauk"},{"key":"9557_CR25","doi-asserted-by":"crossref","DOI":"10.1017\/CBO9780511546860","volume-title":"Curve and Surface Reconstruction: Algorithms with Mathematical Analysis","author":"T.K. Dey","year":"2006","unstructured":"Dey, T.K.: Curve and Surface Reconstruction: Algorithms with Mathematical Analysis. Cambridge University Press, Cambridge (2006)"},{"key":"9557_CR26","doi-asserted-by":"crossref","first-page":"5591","DOI":"10.1073\/pnas.1031596100","volume":"100","author":"D.L. Donohu","year":"2003","unstructured":"Donohu, D.L., Grimes, C.: Hessian eigenmaps: new locally linear embedding techniques for high dimensional data. Proc. Acad. Nat. Sci. 100, 5591\u20135596 (2003)","journal-title":"Proc. Acad. Nat. Sci."},{"issue":"3","key":"9557_CR27","doi-asserted-by":"crossref","first-page":"418","DOI":"10.1090\/S0002-9947-1959-0110078-1","volume":"93","author":"H. Federer","year":"1959","unstructured":"Federer, H.: Curvature measures. Trans. Am. Math. Soc. 93(3), 418\u2013491 (1959)","journal-title":"Trans. Am. Math. Soc."},{"key":"9557_CR28","volume-title":"Geometric Measure Theory","author":"H. Federer","year":"1969","unstructured":"Federer, H.: Geometric Measure Theory. Springer, New York (1969)"},{"key":"9557_CR29","unstructured":"Fl\u00f6totto, J.: A coordinate system associated to a point cloud issued from a manifold: definition, properties and applications. Ph.D. thesis, Universit\u00e9 of Nice Sophia-Antipolis (2003)"},{"key":"9557_CR30","first-page":"781","volume-title":"Proc. ACM-SIAM Symp. Discrete Algorithms","author":"S. Funke","year":"2002","unstructured":"Funke, S., Ramos, E.: Smooth-surface reconstruction in near-linear time. In: Proc. ACM-SIAM Symp. Discrete Algorithms, pp. 781\u2013790 (2002)"},{"key":"9557_CR31","doi-asserted-by":"crossref","unstructured":"Freedman, D.: Efficient simplicial reconstructions of manifolds from their samples. IEEE Trans. Pattern Anal. Mach. Intell. 24(10) (2002)","DOI":"10.1109\/TPAMI.2002.1039206"},{"key":"9557_CR32","first-page":"117","volume":"37","author":"J.H.G. Fu","year":"1993","unstructured":"Fu, J.H.G.: Convergence of curvature in secant approximations. J. Differ. Geom. 37, 117\u2013190 (1993)","journal-title":"J. Differ. Geom."},{"key":"9557_CR33","unstructured":"Ghosh, A.: Piecewise linear reconstruction and meshing of submanifolds of Euclidean space. Ph.D. thesis, INRIA Sophia Antipolis & Universit\u00e9 of Nice Sophia-Antipolis (2012)"},{"key":"9557_CR34","first-page":"363","volume-title":"Proc. Eurographics","author":"M. Gopi","year":"2000","unstructured":"Gopi, M., Khrisnan, S., Silva, C.T.: Surface reconstruction based on lower dimensional localized Delaunay triangulation. In: Proc. Eurographics, pp. 363\u2013371 (2000)"},{"issue":"2","key":"9557_CR35","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1007\/s00454-004-1120-8","volume":"32","author":"J. Giesen","year":"2004","unstructured":"Giesen, J., Wagner, U.: Shape dimension and intrinsic metric from samples of manifolds. Discrete Comput. Geom. 32(2), 245\u2013267 (2004)","journal-title":"Discrete Comput. Geom."},{"issue":"1","key":"9557_CR36","doi-asserted-by":"crossref","first-page":"145","DOI":"10.1016\/S0304-3975(02)00437-1","volume":"296","author":"X.-Y. Li","year":"2003","unstructured":"Li, X.-Y.: Generating well-shaped d-dimensional Delaunay meshes. Theor. Comput. Sci. 296(1), 145\u2013165 (2003)","journal-title":"Theor. Comput. Sci."},{"key":"9557_CR37","doi-asserted-by":"crossref","first-page":"1393","DOI":"10.1109\/TPAMI.2006.184","volume":"28","author":"S. Lafon","year":"2006","unstructured":"Lafon, S., Lee, A.B.: Diffusion maps and coarse-graining: a unified framework for dimensionality reduction, graph partitioning, and data set parameterization. IEEE Trans. Pattern Anal. Mach. Intell. 28, 1393\u20131403 (2006)","journal-title":"IEEE Trans. Pattern Anal. Mach. Intell."},{"key":"9557_CR38","series-title":"Graduate Texts in Mathematics","volume-title":"Algebraic Topology: An Introduction","author":"W.S. Massey","year":"1967","unstructured":"Massey, W.S.: Algebraic Topology: An Introduction. Graduate Texts in Mathematics, vol. 56. Springer, Berlin (1967)"},{"key":"9557_CR39","volume-title":"Advances in Neural Information Processing Systems","author":"B. Nadler","year":"2005","unstructured":"Nadler, B., Lafon, S., Coifman, R.R., Kevrekidis, I.G.: Diffusion maps, spectral clustering and eigenfunctions of Fokker-Planck operators. In: Advances in Neural Information Processing Systems, vol.\u00a018 (2005)"},{"issue":"1","key":"9557_CR40","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00454-008-9053-2","volume":"39","author":"P. Niyogi","year":"2008","unstructured":"Niyogi, P., Smale, S., Weinberger, S.: Finding the homology of submanifolds with high confidence from random samples. Discrete Comput. Geom. 39(1), 419\u2013441 (2008)","journal-title":"Discrete Comput. Geom."},{"key":"9557_CR41","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-81735-9","volume-title":"Introduction to Piecewise-Linear Topology","author":"C.P. Rourke","year":"1972","unstructured":"Rourke, C.P., Sanderson, B.J.: Introduction to Piecewise-Linear Topology. Springer, Berlin (1972)"},{"key":"9557_CR42","doi-asserted-by":"crossref","first-page":"2323","DOI":"10.1126\/science.290.5500.2323","volume":"290","author":"S.T. Roweis","year":"2000","unstructured":"Roweis, S.T., Saul, L.K.: Nonlinear dimensionality reduction by locally linear embedding. Science 290, 2323\u20132326 (2000)","journal-title":"Science"},{"key":"9557_CR43","first-page":"237","volume-title":"Proc. ACM Symp. on Computational Geometry","author":"J. Shewchuk","year":"2005","unstructured":"Shewchuk, J.: Star splaying: an algorithm for repairing Delaunay triangulations and convex hulls. In: Proc. ACM Symp. on Computational Geometry, pp. 237\u2013246 (2005)"},{"key":"9557_CR44","doi-asserted-by":"crossref","first-page":"2268","DOI":"10.1126\/science.290.5500.2268","volume":"290","author":"H.S. Seung","year":"2000","unstructured":"Seung, H.S., Lee, D.D.: The manifold ways of perception. Science 290, 2268\u20132269 (2000)","journal-title":"Science"},{"key":"9557_CR45","doi-asserted-by":"crossref","first-page":"2319","DOI":"10.1126\/science.290.5500.2319","volume":"290","author":"J.B. Tenenbaum","year":"2000","unstructured":"Tenenbaum, J.B., de Silva, V., Langford, J.C.: A global geometric framework for nonlinear dimensionality reduction. Science 290, 2319\u20132323 (2000)","journal-title":"Science"},{"key":"9557_CR46","doi-asserted-by":"crossref","DOI":"10.1515\/9781400877577","volume-title":"Geometric Integration Theory","author":"H. Whitney","year":"1957","unstructured":"Whitney, H.: Geometric Integration Theory. Princeton University Press, Princeton (1957)"},{"key":"9557_CR47","unstructured":"Zeeman, E.C.: In: Seminar on Combinatorial Topology. Institut des Hautes \u00c9tudes Scientifiques (Paris) and University of Warwick (Coventry), Notes, pp. 1963\u20131966"},{"issue":"1","key":"9557_CR48","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1137\/S1064827502419154","volume":"26","author":"Z. Zhang","year":"2004","unstructured":"Zhang, Z., Zha, H.: Principal manifolds and nonlinear dimension reduction via local tangent space alignment. SIAM J. Sci. Comput. 26(1), 313\u2013338 (2004)","journal-title":"SIAM J. Sci. Comput."}],"container-title":["Discrete & Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-013-9557-2.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-013-9557-2\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-013-9557-2","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T19:50:38Z","timestamp":1559073038000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-013-9557-2"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2013,11,20]]},"references-count":48,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2014,1]]}},"alternative-id":["9557"],"URL":"https:\/\/doi.org\/10.1007\/s00454-013-9557-2","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2013,11,20]]}}}