{ "abstract": "Since the 1970's B-splines have evolved to become the {\\em de facto} \r\nstandard for curve and surface representation due to many\r\nof their salient properties. Conventional least-squares \r\nscattered data fitting techniques for B-splines require the inversion \r\nof potentially large matrices. This is time-consuming as well \r\nas susceptible to ill-conditioning which leads to undesired\r\nresults. Lee {\\em et al.} proposed a novel B-spline \r\nalgorithm for fitting a 2-D cubic B-spline surface to scattered \r\ndata in \\cite{Lee}. The proposed algorithm utilizes an \r\noptional multilevel approach for better fitting results. \r\nWe generalize this technique to support N-dimensional \r\ndata fitting as well as arbitrary degree of B-spline. In addition, \r\nwe generalize the B-spline kernel function class to accommodate \r\nthis new image filter.", "authors": [ { "author_fullname": "Tustison, Nicholas J.", "author_place": 1, "persona_email": "ntustison@gmail.com", "persona_firstname": "Nicholas J.", "persona_id": 8833, "persona_lastname": "Tustison" }, { "author_fullname": "Gee, James C.", "author_place": 2, "persona_email": "gee@mail.med.upenn.edu", "persona_firstname": "James", "persona_id": 236, "persona_lastname": "Gee" } ], "categories": [], "comments": [ { "content": "Thanks for this. I just added a test for the ITK repository here:\r\n\r\nhttp://review.source.kitware.com/#/c/20010/", "date": "2015-07-20T13:10:33.000Z", "persona_email": "ntustison@gmail.com", "persona_firstname": "Nicholas J.", "persona_id": 8833, "persona_lastname": "Tustison" }, { "content": "Thanks for this. I just added a test for the ITK repository here:\r\n\r\nhttp://review.source.kitware.com/#/c/20010/", "date": "2015-07-20T13:10:35.000Z", "persona_email": "ntustison@gmail.com", "persona_firstname": "Nicholas J.", "persona_id": 8833, "persona_lastname": "Tustison" }, { "content": "Has the code been tested for the case where the N-D contour (to be interpolated) is a \"closed\" contour? The documentation talks about this - but there are no examples provided. The closed-contour use case is not as well documented (from a quick read through) as the open-contour case.", "date": "2015-07-20T04:25:54.000Z", "persona_email": "k.patwardhan@samsung.com", "persona_firstname": "Kedar", "persona_id": 9594, "persona_lastname": "Patwardhan" } ], "date_submitted": "2005-11-15T20:39:45Z", "journals": [ { "journal_id": 3, "journal_name": "The Insight Journal" } ], "license": "You are licensing your work to Kitware Inc. under the\nCreative Commons Attribution License Version 3.0.\n\nKitware Inc. agrees to the following:\n\nKitware is free\n * to copy, distribute, display, and perform the work\n * to make derivative works\n * to make commercial use of the work\n\nUnder the following conditions:\n\\\"by Attribution\\\" - Kitware must attribute the work in the manner specified by the author or licensor.\n\n * For any reuse or distribution, they must make clear to others the license terms of this work.\n * Any of these conditions can be waived if they get permission from the copyright holder.\n\nYour fair use and other rights are in no way affected by the above.\n\nThis is a human-readable summary of the Legal Code (the full license) available at\nhttp://creativecommons.org/licenses/by/3.0/legalcode", "publication_id": 57, "reviews": [], "revisions": [ { "article": "bafkreieqxsym7xsdm4vvmoze2m44wvwnzefowpbzer7bwy7ktflfq72o4e", "citation_list": [ { "key": "ref1", "score": 48.537983, "unstructured": "The numerical evaluation of B-splines+Jour. Inst. Math. Applic.+2+1+149+1972+M. G. Cox." }, { "key": "ref2", "score": 56.852184, "unstructured": "On calculating with B-splines+Jour. Approx. Theory+2+1+62+1972+C. de Boor" }, { "key": "ref3", "score": 49.420082, "unstructured": "Fundamental Developments of Computer-Aided Geometric Modeling , chapter B-spline basics+27+49+1993" }, { "key": "ref4", "score": 41.948067, "unstructured": "Approximation of scattered data with multilevel B-splines+Technical report+2001+3+4+Oyvind Hjelle" }, { "doi": "10.1109/2945.620490", "key": "ref5", "score": 100.609795, "unstructured": "Scattered data interpolation with multilevel B-splines+IEEE Transactions on Visualization and Computer Graphics+1+3+4+244+1997+Seungyong Lee+George Wolberg" }, { "doi": "10.1016/0010-4485(94)00018-9", "key": "ref6", "score": 110.883286, "unstructured": "Parameterization of randomly measured points for least squares fitting of B-spline curves and surfaces+2+2+675+1995+Weiyin Ma+J. P. Kruth" }, { "key": "ref7", "score": 57.182716, "unstructured": "The NURBS Book+1997+Les Piegl+Wayne Tiller" }, { "key": "ref8", "score": 41.713196, "unstructured": "Applications of B-Spline Approximation to Geometric Problems of ComputerAided Design+PhD thesis+1975+R. F. Riesenfeld" }, { "key": "ref9", "score": 57.24843, "unstructured": "Spline functions and the problem of graduation+Proc. Nat. Acad. Sci.+3+2+950+1964+I. J. Schoenberg" }, { "doi": "10.1109/tmi.2005.861015", "key": "ref10", "score": 115.91271, "unstructured": "Biventricular myocardial strains via nonrigid registration of anatomical NURBS model [corrected]+IEEE Trans Med Imaging+1+3+2+112+Jan 2006+J. Nicholas+Amir A. Tustison+Amini" }, { "doi": "10.1109/tbme.2003.814530", "key": "ref11", "score": 116.86429, "unstructured": "Myocardial kinematics from tagged MRI based on a 4-D B-spline model+IEEE Trans Biomed Eng+3+8+2+1040+Aug 2003+J. Nicholas+Tustison+Davila-Roman+A. Amir+Amini" } ], "dapp": null, "dataset": null, "doi": "10.54294/0d55to", "handle": "1926/140", "source_code": "bafybeid2tppv5b54jc3ytx6mvzpkvocva57kngdsspriry4ujxclycxokm", "source_code_git_ref": null } ], "source_code_git_repo": null, "submitted_by_author": { "author_email": "ntustison@gmail.com", "author_firstname": "Nicholas J.", "author_fullname": "Tustison, Nicholas J.", "author_id": 8833, "author_institution": "", "author_lastname": "Tustison" }, "tags": [ "B-splines", "data approximation" ], "title": "N-D $C^k$ B-Spline Scattered Data Approximation" }