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Optimal surface reconstruction from planar contours

Authors:

H. Fuchs,

Z. M. Kedem, and

S. P. UseltonAuthors Info & Claims

Communications of the ACM, Volume 20, Issue 10

Pages 693 - 702

https://doi.org/10.1145/359842.359846

Published: 01 October 1977 Publication History

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Abstract

In many scientific and technical endeavors, a three-dimensional solid must be reconstructed from serial sections, either to aid in the comprehension of the object's structure or to facilitate its automatic manipulation and analysis. This paper presents a general solution to the problem of constructing a surface over a set of cross-sectional contours. This surface, to be composed of triangular tiles, is constructed by separately determining an optimal surface between each pair of consecutive contours. Determining such a surface is reduced to the problem of finding certain minimum cost cycles in a directed toroidal graph. A new fast algorithm for finding such cycles is utilized. Also developed is a closed-form expression, in terms of the number of contour points, for an upper bound on the number of operations required to execute the algorithm. An illustrated example which involves the construction of a minimum area surface describing a human head is included.

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Park YLee THahn JKang MOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)p-Poisson surface reconstruction in curl-free flow from point cloudsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668748(60077-60098)Online publication date: 10-Dec-2023
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Published In

Communications of the ACM Volume 20, Issue 10

Oct. 1977

93 pages

ISSN:0001-0782

EISSN:1557-7317

DOI:10.1145/359842

Editor:
Robert L. Ashenhurst
Univ. of Chicago, Chicago, IL

Issue’s Table of Contents

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 October 1977

Published in CACM Volume 20, Issue 10

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Cited By

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Park YLee THahn JKang MOh ANaumann TGloberson ASaenko KHardt MLevine S(2023)p-Poisson surface reconstruction in curl-free flow from point cloudsProceedings of the 37th International Conference on Neural Information Processing Systems10.5555/3666122.3668748(60077-60098)Online publication date: 10-Dec-2023
https://dl.acm.org/doi/10.5555/3666122.3668748
Legland DLe TAlvarado CGirousse CChateigner-Boutin A(2023)New Growth-Related Features of Wheat Grain Pericarp Revealed by Synchrotron-Based X-ray Micro-Tomography and 3D ReconstructionPlants10.3390/plants1205103812:5(1038)Online publication date: 24-Feb-2023
https://doi.org/10.3390/plants12051038
Monteiro MVale FFerreira NMarques FRibeiro MSantos MOliveira CMcEvoy MTravassos RNunes CPaula AFrancisco ICaramelo F(2023)Realistic Facial Three-Dimensional Reconstruction from CT Images and 2D Photographic Images for Surgical-Orthognathic PlanningApplied Sciences10.3390/app1302122613:2(1226)Online publication date: 16-Jan-2023
https://doi.org/10.3390/app13021226
Huang QZhang LLiu LCao YMa HWang LZhou C(2023)3D Visualization of Pulmonary Vessel Based on Low-Cost Segmentation and Fast ReconstructionIEEE Access10.1109/ACCESS.2023.327332711(44866-44878)Online publication date: 2023
https://doi.org/10.1109/ACCESS.2023.3273327
Liu J(2023)On the Mating Between a Polygonal Curve and a Convex PolygonCombinatorial Optimization and Applications10.1007/978-3-031-49614-1_18(240-252)Online publication date: 15-Dec-2023
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Wu ZBi LZhong DZhang JTang QJia M(2022)Orebody Modeling Method Based on the Coons Surface InterpolationMinerals10.3390/min1208099712:8(997)Online publication date: 6-Aug-2022
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Li ZZhong DWang LTang QWu Z(2022)Mesh Processing for Snapping Feature Points and Polylines in Orebody ModelingMathematics10.3390/math1015259310:15(2593)Online publication date: 25-Jul-2022
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Lechelek LHorna SZrour RNaudin MGuillevin C(2022)A Hybrid Method for 3D Reconstruction of MR ImagesJournal of Imaging10.3390/jimaging80401038:4(103)Online publication date: 7-Apr-2022
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