{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,20]],"date-time":"2026-04-20T13:35:00Z","timestamp":1776692100190,"version":"3.51.2"},"reference-count":35,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2009,4,28]],"date-time":"2009-04-28T00:00:00Z","timestamp":1240876800000},"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":[[2009,7]]},"DOI":"10.1007\/s00454-009-9175-1","type":"journal-article","created":{"date-parts":[[2009,4,27]],"date-time":"2009-04-27T11:19:34Z","timestamp":1240831174000},"page":"37-70","source":"Crossref","is-referenced-by-count":33,"title":["Manifold Reconstruction in Arbitrary Dimensions Using Witness Complexes"],"prefix":"10.1007","volume":"42","author":[{"given":"Jean-Daniel","family":"Boissonnat","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Leonidas J.","family":"Guibas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Steve Y.","family":"Oudot","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2009,4,28]]},"reference":[{"issue":"4","key":"9175_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(4), 481\u2013504 (1999)","journal-title":"Discrete Comput. Geom."},{"key":"9175_CR2","doi-asserted-by":"crossref","first-page":"125","DOI":"10.1006\/gmip.1998.0465","volume":"60","author":"N. Amenta","year":"1998","unstructured":"Amenta, N., Bern, M., Eppstein, D.: The crust and the \u03b2-skeleton: combinatorial curve reconstruction. Graph. Models Image Process. 60, 125\u2013135 (1998)","journal-title":"Graph. Models Image Process."},{"key":"9175_CR3","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."},{"key":"9175_CR4","doi-asserted-by":"crossref","unstructured":"Attali, D., Edelsbrunner, H., Harer, J., Mileyko, Y.: Alpha\u2013beta witness complexes. In: Proc. 10th Workshop on Algorithms and Data Structures, pp. 386\u2013397 (2007)","DOI":"10.1007\/978-3-540-73951-7_34"},{"key":"9175_CR5","doi-asserted-by":"crossref","unstructured":"Attali, D., Edelsbrunner, H., Mileyko, Y.: Weak witnesses for Delaunay triangulations of submanifolds. In: Proc. ACM Sympos. on Solid and Physical Modeling, pp. 143\u2013150 (2007)","DOI":"10.1145\/1236246.1236267"},{"issue":"1\u20133","key":"9175_CR6","doi-asserted-by":"crossref","first-page":"209","DOI":"10.1023\/B:MACH.0000033120.25363.1e","volume":"56","author":"M. Belkin","year":"2004","unstructured":"Belkin, M., Niyogi, P.: Semi-supervised learning on Riemannian manifolds. Mach. Learn. 56(1\u20133), 209\u2013239 (2004)","journal-title":"Mach. Learn."},{"key":"9175_CR7","doi-asserted-by":"crossref","unstructured":"Boissonnat, J.-D., Oudot, S.: Provably good sampling and meshing of Lipschitz surfaces. In: Proc. 22nd Annu. Sympos. Comput. Geom., pp. 337\u2013346 (2006)","DOI":"10.1145\/1137856.1137906"},{"key":"9175_CR8","doi-asserted-by":"crossref","first-page":"231","DOI":"10.1007\/978-3-540-33259-6_6","volume-title":"Effective Computational Geometry for Curves 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 Curves and Surfaces, pp. 231\u2013273. Springer, Berlin (2006)"},{"key":"9175_CR9","doi-asserted-by":"crossref","unstructured":"Chazal, F., Lieutier, A.: Weak feature size and persistent homology: computing homology of solids in \u211d n from noisy data samples. In: Proc. 21st Annual ACM Symposium on Computational Geometry, pp. 255\u2013262 (2005)","DOI":"10.1145\/1064092.1064132"},{"key":"9175_CR10","doi-asserted-by":"crossref","unstructured":"Chazal, F., Lieutier, A.: Topology guaranteeing manifold reconstruction using distance function to noisy data. In: Proc. 22nd Annu. Sympos. on Comput. Geom., pp. 112\u2013118 (2006)","DOI":"10.1145\/1137856.1137876"},{"key":"9175_CR11","doi-asserted-by":"crossref","unstructured":"Chazal, F., Oudot, S.Y.: Towards persistence-based reconstruction in Euclidean spaces. In: Proc. 24th ACM Sympos. Comput. Geom., pp. 232\u2013241 (2008)","DOI":"10.1145\/1377676.1377719"},{"key":"9175_CR12","doi-asserted-by":"crossref","unstructured":"Chazal, F., Cohen-Steiner, D., Lieutier, A.: A sampling theory for compact sets in Euclidean space. In: Proc. 22nd Annu. Sympos. Comput. Geom., pp. 319\u2013326 (2006)","DOI":"10.1145\/1137856.1137904"},{"issue":"5","key":"9175_CR13","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. Assoc. Comput. Mach. 47(5), 883\u2013904 (2000)","journal-title":"J. Assoc. Comput. Mach."},{"key":"9175_CR14","unstructured":"Cheng, S.-W., Dey, T.K., Ramos, E.A.: Manifold reconstruction from point samples. In: Proc. 16th Sympos. Discrete Algorithms, pp. 1018\u20131027 (2005)"},{"key":"9175_CR15","unstructured":"Cheng, S.-W., Dey, T.K., Ramos, E.A.: Manifold reconstruction from point samples. Journal version of [14]"},{"key":"9175_CR16","doi-asserted-by":"crossref","unstructured":"Cohen-Steiner, D., Edelsbrunner, H., Harer, J.: Stability of persistence diagrams. In: Proc. 21st ACM Sympos. Comput. Geom., pp. 263\u2013271 (2005)","DOI":"10.1145\/1064092.1064133"},{"issue":"1","key":"9175_CR17","doi-asserted-by":"crossref","first-page":"39","DOI":"10.1007\/s10711-008-9261-1","volume":"135","author":"V. Silva de","year":"2008","unstructured":"de Silva, V.: A weak characterisation of the Delaunay triangulation. Geom. Dedic. 135(1), 39\u201364 (2008)","journal-title":"Geom. Dedic."},{"key":"9175_CR18","unstructured":"de Silva, V., Carlsson, G.: Topological estimation using witness complexes. In: Proc. Sympos. Point-Based Graphics, pp. 157\u2013166 (2004)"},{"key":"9175_CR19","first-page":"580","volume":"5","author":"D. DeMers","year":"1993","unstructured":"DeMers, D., Cottrell, G.: Nonlinear dimensionality reduction. Adv. Neural Inf. Process. Syst. 5, 580\u2013587 (1993)","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"9175_CR20","unstructured":"Dey, T.K., Kumar, P.: A simple provable algorithm for curve reconstruction. In: Proc. 10th ACM\u2013SIAM Sympos. Discrete Algorithms, pp. 893\u2013894 (1999)"},{"key":"9175_CR21","doi-asserted-by":"crossref","first-page":"419","DOI":"10.1007\/s00454-002-2838-9","volume":"29","author":"T.K. Dey","year":"2003","unstructured":"Dey, T.K., Giesen, J., Goswami, S., Zhao, W.: Shape dimension and approximation from samples. Discrete Comput. Geom. 29, 419\u2013434 (2003)","journal-title":"Discrete Comput. Geom."},{"key":"9175_CR22","series-title":"EATCS Monographs on Theoretical Computer Science","doi-asserted-by":"crossref","DOI":"10.1007\/978-3-642-61568-9","volume-title":"Algorithms in Combinatorial Geometry","author":"H. Edelsbrunner","year":"1987","unstructured":"Edelsbrunner, H.: Algorithms in Combinatorial Geometry. EATCS Monographs on Theoretical Computer Science, vol. 10. Springer, Berlin (1987)"},{"key":"9175_CR23","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1007\/s00454-002-2885-2","volume":"28","author":"H. Edelsbrunner","year":"2002","unstructured":"Edelsbrunner, H., Letscher, D., Zomorodian, A.: Topological persistence and simplification. Discrete Comput. Geom. 28, 511\u2013533 (2002)","journal-title":"Discrete Comput. Geom."},{"key":"9175_CR24","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, 418\u2013491 (1959)","journal-title":"Trans. Am. Math. Soc."},{"key":"9175_CR25","unstructured":"Gao, J., Guibas, L.J., Oudot, S.Y., Wang, Y.: Geodesic Delaunay triangulation and witness complex in the plane. In: Proc. 18th ACM\u2013SIAM Sympos. on Discrete Algorithms, pp. 571\u2013580 (2008)"},{"key":"9175_CR26","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 with high co-dimension. Discrete Comput. Geom. 32, 245\u2013267 (2004)","journal-title":"Discrete Comput. Geom."},{"key":"9175_CR27","doi-asserted-by":"crossref","first-page":"325","DOI":"10.1007\/s00454-008-9094-6","volume":"40","author":"L.J. Guibas","year":"2008","unstructured":"Guibas, L.J., Oudot, S.Y.: Reconstruction using witness complexes. Discrete Comput. Geom. 40, 325\u2013356 (2008)","journal-title":"Discrete Comput. Geom."},{"issue":"1\u20133","key":"9175_CR28","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1023\/A:1023705401078","volume":"54","author":"A.B. Lee","year":"2003","unstructured":"Lee, A.B., Pederson, K.S., Mumford, D.: The nonlinear statistics of high-contrast patches in natural images. Int. J. Comput. Vis. 54(1\u20133), 83\u2013103 (2003)","journal-title":"Int. J. Comput. Vis."},{"issue":"1","key":"9175_CR29","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."},{"issue":"1\u20133","key":"9175_CR30","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\u20133), 419\u2013441 (2008)","journal-title":"Discrete Comput. Geom."},{"issue":"5500","key":"9175_CR31","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(5500), 2323\u20132326 (2000)","journal-title":"Science"},{"key":"9175_CR32","unstructured":"Seow, M.-J., Tompkins, R.C., Asari, V.K.: A new nonlinear dimensionality reduction technique for pose and lighting invariant face recognition. In: Proc. IEEE Conf. on Computer Vision and Pattern Recognition\u2014Workshops, p. 160 (2005)"},{"issue":"5500","key":"9175_CR33","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(5500), 2319\u20132323 (2000)","journal-title":"Science"},{"key":"9175_CR34","doi-asserted-by":"crossref","unstructured":"Vlachos, M., Domeniconi, C., Gunopulos, D., Kollios, G., Koudas, N.: Non-linear dimensionality reduction techniques for classification and visualization. In: Proc. 8th ACM SIGKDD Internat. Conf. on Knowledge Discovery and Data Mining, pp. 645\u2013651 (2002)","DOI":"10.1145\/775047.775143"},{"issue":"2","key":"9175_CR35","doi-asserted-by":"crossref","first-page":"249","DOI":"10.1007\/s00454-004-1146-y","volume":"33","author":"A. Zomorodian","year":"2005","unstructured":"Zomorodian, A., Carlsson, G.: Computing persistent homology. Discrete Comput. Geom. 33(2), 249\u2013274 (2005)","journal-title":"Discrete Comput. Geom."}],"container-title":["Discrete &amp; Computational Geometry"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9175-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00454-009-9175-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00454-009-9175-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,5,28]],"date-time":"2019-05-28T19:47:37Z","timestamp":1559072857000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00454-009-9175-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,4,28]]},"references-count":35,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2009,7]]}},"alternative-id":["9175"],"URL":"https:\/\/doi.org\/10.1007\/s00454-009-9175-1","relation":{},"ISSN":["0179-5376","1432-0444"],"issn-type":[{"value":"0179-5376","type":"print"},{"value":"1432-0444","type":"electronic"}],"subject":[],"published":{"date-parts":[[2009,4,28]]}}}