{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,5,2]],"date-time":"2025-05-02T04:12:48Z","timestamp":1746159168950,"version":"3.40.4"},"publisher-location":"Berlin, Heidelberg","reference-count":18,"publisher":"Springer Berlin Heidelberg","isbn-type":[{"type":"print","value":"9783642539251"},{"type":"electronic","value":"9783642539268"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2014]]},"DOI":"10.1007\/978-3-642-53926-8_4","type":"book-chapter","created":{"date-parts":[[2014,1,21]],"date-time":"2014-01-21T12:30:46Z","timestamp":1390307446000},"page":"33-46","source":"Crossref","is-referenced-by-count":3,"title":["Length Estimation for Exponential Parameterization and \u03b5-Uniform Samplings"],"prefix":"10.1007","author":[{"given":"Ryszard","family":"Kozera","sequence":"first","affiliation":[]},{"given":"Lyle","family":"Noakes","sequence":"additional","affiliation":[]},{"given":"Piotr","family":"Szmielew","sequence":"additional","affiliation":[]}],"member":"297","reference":[{"issue":"18","key":"4_CR1","first-page":"28","volume":"7","author":"M. Janik","year":"2013","unstructured":"Janik, M., Kozera, R., Kozio\u0142, P.: Reduced data for curve modeling - applications in graphics, computer vision and physics. Advances in Science and Technology\u00a07(18), 28\u201335 (2013)","journal-title":"Advances in Science and Technology"},{"key":"4_CR2","doi-asserted-by":"publisher","DOI":"10.1142\/4172","volume-title":"Methods of Shape-Preserving Spline Approximation","author":"B.I. Kvasov","year":"2000","unstructured":"Kvasov, B.I.: Methods of Shape-Preserving Spline Approximation. World Scientific Publishing Company, Singapore (2000)"},{"key":"4_CR3","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"518","DOI":"10.1007\/3-540-44692-3_63","volume-title":"Computer Analysis of Images and Patterns","author":"L. Noakes","year":"2001","unstructured":"Noakes, L., Kozera, R., Klette, R.: Length estimation for curves with \u03b5-uniform samplings. In: Skarbek, W. (ed.) CAIP 2001. LNCS, vol.\u00a02124, pp. 518\u2013526. Springer, Heidelberg (2001)"},{"key":"4_CR4","series-title":"Computational Imaging and Vision","doi-asserted-by":"publisher","first-page":"59","DOI":"10.1007\/1-4020-3858-8_4","volume-title":"Geometric Properties of Incomplete Data","author":"L. Noakes","year":"2006","unstructured":"Noakes, L., Kozera, R.: Cumulative chords piecewise-quadratics and piecewise-cubics. In: Klette, R., Kozera, R., Noakes, L., Weickert, J. (eds.) Geometric Properties of Incomplete Data. Computational Imaging and Vision, vol.\u00a031, pp. 59\u201375. Kluver Academic Publishers, The Netherlands (2006)"},{"key":"4_CR5","unstructured":"Kozera, R., Noakes, L.: Asymptotics in length estimation for exponential parameterization and \u03b5-uniformly sampled reduced data (to be submitted)"},{"key":"4_CR6","volume-title":"A Practical Guide to Splines","author":"C. Boor de","year":"2001","unstructured":"de Boor, C.: A Practical Guide to Splines. Springer, Heidelberg (2001)"},{"issue":"4B-61","key":"4_CR7","first-page":"1","volume":"25","author":"R. Kozera","year":"2004","unstructured":"Kozera, R.: Curve modeling via interpolation based on multidimensional reduced data. Studia Informatica\u00a025(4B-61), 1\u2013140 (2004)","journal-title":"Studia Informatica"},{"issue":"3","key":"4_CR8","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1090\/qam\/1999832","volume":"61","author":"L. Noakes","year":"2003","unstructured":"Noakes, L., Kozera, R.: More-or-less uniform samplings and lengths of curves. Quarterly of Applied Mathematics\u00a061(3), 475\u2013484 (2003)","journal-title":"Quarterly of Applied Mathematics"},{"key":"4_CR9","doi-asserted-by":"crossref","unstructured":"Kozera, R., Noakes, L., Klette, R.: External versus internal parameterization for lengths of curves with nonuniform samplings. In: Asano, T., Klette, R., Ronse, C. (eds.) Geometry, Morphology, and Computational Imaging 2002. LNCS, vol.\u00a02616, pp. 403\u2013418. Springer, Heidelberg (2003)","DOI":"10.1007\/3-540-36586-9_26"},{"key":"4_CR10","first-page":"95","volume":"5","author":"L.M. Koci\u0107","year":"1990","unstructured":"Koci\u0107, L.M., Simoncelli, A.C., Della Vecchia, B.: Blending parameterization of polynomial and spline interpolants, Facta Universitatis (NI\u0160). Series Mathematics and Informatics\u00a05, 95\u2013107 (1990)","journal-title":"Series Mathematics and Informatics"},{"key":"4_CR11","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-59223-2","volume-title":"The NURBS Book","author":"L. Piegl","year":"1997","unstructured":"Piegl, L., Tiller, W.: The NURBS Book. Springer, Heidelberg (1997)"},{"issue":"6","key":"4_CR12","doi-asserted-by":"publisher","first-page":"363","DOI":"10.1016\/0010-4485(89)90003-1","volume":"21","author":"E.T.Y. Lee","year":"1987","unstructured":"Lee, E.T.Y.: Choosing nodes in parametric curve interpolation. Computer-Aided Design\u00a021(6), 363\u2013370 (1987)","journal-title":"Computer-Aided Design"},{"key":"4_CR13","series-title":"Lecture Notes in Computer Science","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1007\/978-3-642-40925-7_40","volume-title":"Computer Information Systems and Industrial Management","author":"R. Kozera","year":"2013","unstructured":"Kozera, R., Noakes, L., Szmielew, P.: Trajectory estimation for exponential parameterization and different samplings. In: Saeed, K., Chaki, R., Cortesi, A., Wierzcho\u0144, S. (eds.) CISIM 2013. LNCS, vol.\u00a08104, pp. 430\u2013441. Springer, Heidelberg (2013)"},{"key":"4_CR14","unstructured":"Kozera, R., Noakes, L.: Exponential parameterization and \u03b5-uniformly sampled reduced data (submitted)"},{"key":"4_CR15","doi-asserted-by":"publisher","first-page":"620","DOI":"10.1016\/j.amc.2013.06.060","volume":"221","author":"R. Kozera","year":"2013","unstructured":"Kozera, R., Noakes, L.: Piecewise-quadratics and exponential parameterization for reduced data. Applied Mathematics and Computation\u00a0221, 620\u2013638 (2013)","journal-title":"Applied Mathematics and Computation"},{"key":"4_CR16","unstructured":"Wolfram Mathematica 9, Documentation Center, http:\/\/reference.wolfram.com\/mathematica\/guide\/Mathematica.html"},{"key":"4_CR17","doi-asserted-by":"publisher","first-page":"25","DOI":"10.1093\/imanum\/dri022","volume":"26","author":"M.S. Floater","year":"2006","unstructured":"Floater, M.S.: Chordal cubic spline interpolation is fourth order accurate. IMA Journal of Numerical Analysis\u00a026, 25\u201333 (2006)","journal-title":"IMA Journal of Numerical Analysis"},{"issue":"3-4","key":"4_CR18","doi-asserted-by":"crossref","first-page":"285","DOI":"10.3233\/FUN-2004-613-406","volume":"61","author":"R. Kozera","year":"2004","unstructured":"Kozera, R., Noakes, L.: C 1 interpolation with cumulative chord cubics. Fundamenta Informaticae\u00a061(3-4), 285\u2013301 (2004)","journal-title":"Fundamenta Informaticae"}],"container-title":["Lecture Notes in Computer Science","Image and Video Technology \u2013 PSIVT 2013 Workshops"],"original-title":[],"link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/978-3-642-53926-8_4","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,5,1]],"date-time":"2025-05-01T16:23:34Z","timestamp":1746116614000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/978-3-642-53926-8_4"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2014]]},"ISBN":["9783642539251","9783642539268"],"references-count":18,"URL":"https:\/\/doi.org\/10.1007\/978-3-642-53926-8_4","relation":{},"ISSN":["0302-9743","1611-3349"],"issn-type":[{"type":"print","value":"0302-9743"},{"type":"electronic","value":"1611-3349"}],"subject":[],"published":{"date-parts":[[2014]]}}}