Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
skip to main content
article
Open access

Surface reconstruction from unorganized points

Published: 01 July 1992 Publication History

Abstract

We describe and demonstrate an algorithm that takes as input an unorganized set of points {xl, . . . . xn} ⊂ R3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance - all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.

References

[1]
E.L. Allgower and P. H. Schmidt. An algorithm for piecewise linear approximation of an implicitly defined manifold. SlAM Journal of Numerical Analysis, 22:322-346, April 1985.
[2]
J.L. Bentley. Multidimensional divide and conquer. Comm. ACM, 23(4):214--229, 1980.
[3]
Y. Breseler, J. A. Fessler, and A. Macovski. A Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain. IEEE Trans. Pat. Anal. Mach. InteU., 11 (8):840-858, August 1989.
[4]
James F. Brinkley. Knowledge-driven ultrasonic threedimensional organ modeling. IEEE Trans. Pat. Anal. Mach. lntell., 7(4):431-441, July 1985.
[5]
David P. Dobkin, Silvio V. E Levy, William P. Thurston, and Allan R. Wilks. Contour tracing by piecewise linear approximations. ACM TOG, 9(4):389-423, October 1990.
[6]
John A. Eisenman. Graphical editing of composite bezier curves. Master's thesis, Department of Electrical Engineering and Computer Science, M.I.T., 1988.
[7]
T.A. Foley. interpolation to scattered data on a spherical domain. In M. Cox and J. Mason, editors, Algorithms for Approximation l}, pages 303-310. Chapman and Hall, London, 1990.
[8]
Michael R. Garey and David S. Johnson. Computers and Intractability. W. H. Freeman and Company, 1979.
[9]
T. Hastie and W. Stuetzle. Principal curves. JASA, 84:502- 516, 1989.
[10]
Averill M. Law and W. David Kelton. Simulation Modeling and Analysis. McGraw-Hill, Inc., second edition, 1991.
[11]
Marshal L. Merriam. Experience with the cyberware 3D digitizer. In NCGA Proceedings, pages 125-133, March 1992.
[12]
David Meyers, Shelly Skinner, and Kenneth Sloan. Surfaces from contours: The correspondence and branching problems. In Proceedings of Graphics Interface '91, pages 246-254, June 1991.
[13]
Doug Moore and Joe Warren. Approximation of dense scattered data using algebraic surfaces. TR 90-135, Rice University, October 1990.
[14]
Doug Moore and Joe Warren. Adaptive mesh generation ii: Packing solids. TR 90-139, Rice University, March 1991.
[15]
Shigeru Muraki. Volumetric shape description of range data using "blobby model". Computer Graphics (SIGGRAPH '91 Proceedings), 25(4):227-235, July 1991.
[16]
Gregory M. Nielson, Thomas A. Foley, Bernd Hamann, and David Lane. Visualizing and modeling scattered multivariate data. IEEECG&A, 11(3):47-55, May 1991.
[17]
Barrett O'Neill. Elementary Differential Geometry. Academic Press, Orlando, Florida, 1966.
[18]
Vaughan Pratt. Direct least-squares fitting of algebraic surfaces. Computer Graphics (SIGGRAPH '87 Proceedings), 21(4): 145-152, July 1987.
[19]
Emanuel Sachs, Andrew Roberts, and David Stoops. 3-Draw: A tool for designing 3 D shapes. {EEE Computer Graphics and Applications, 11(6):18-26, November 1991.
[20]
Hanan Samet. Applications of Spatial Data Structures. Addison-Wesley, 1990.
[21]
Philip J. Schneider. Phoenix: An interactive curve design system based on the automatic fitting of hand-sketched curves. Master's thesis, Department of Computer Science, U. of Washington, 1988.
[22]
R. B. Schudy and D. H. Ballard. Model detection of cardiac chambers in ultrasound images. Technical Report 12, Computer Science Department, University of Rochester, 1978.
[23]
R.B. Schudy and D. H, Ballard. Towards an anatomical model of heart motion as seen in 4-d cardiac ultrasound data. In Proceedings of the 6th Conference on Computer Applications in Radiology and Computer.Aided Analysis of Radiological Images, 1979.
[24]
Stan Sclaroff and Alex Pentland. Generalized implicit functions for computer graphics. Computer Graphics (SIGGRAPH '91 Proceedings), 25(4):247-250, July 1991.
[25]
G. Taubin. Estimation of planar curves, surfaces and nonplanat space curves defined by implicit equations, with applications to edge and range image segmentation. Technical Report LEMS-66, Division of Engineering, Brown University, 1990.
[26]
B. C. Vemuri. Representation and Recognition of Objects From Dense Range Maps. PhD thesis, Department of Electrical and Computer Engineering, University of Texas at Austin, 1987.
[27]
B. C. Vemuri, A. Mitiche, and J. K. Aggarwal. Curvaturebased representation of objects from range data. Image and Vision Computing, 4(2): 107-114,1986.
[28]
13. Wyvill, C. McPheeters, and B. Wyvill. Data structures for soft objects. The Visual Computer, 2(4):227-234, August 1986.

Cited By

View all
  • (2025)Point Cloud Normal Estimation Algorithm Based on Local Structure ConstraintsAdvances in Applied Mathematics10.12677/aam.2025.14102314:01(203-210)Online publication date: 2025
  • (2025)GeoCode: Interpretable Shape ProgramsComputer Graphics Forum10.1111/cgf.15276Online publication date: 12-Feb-2025
  • (2025)Points2Model: a neural-guided 3D building wireframe reconstruction from airborne LiDAR point cloudsInternational Journal of Digital Earth10.1080/17538947.2025.245868218:1Online publication date: 11-Feb-2025
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM SIGGRAPH Computer Graphics
ACM SIGGRAPH Computer Graphics  Volume 26, Issue 2
July 1992
366 pages
ISSN:0097-8930
DOI:10.1145/142920
Issue’s Table of Contents
  • cover image ACM Conferences
    SIGGRAPH '92: Proceedings of the 19th annual conference on Computer graphics and interactive techniques
    July 1992
    420 pages
    ISBN:0897914791
    DOI:10.1145/133994
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]

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 01 July 1992
Published in SIGGRAPH Volume 26, Issue 2

Check for updates

Badges

  • Seminal Paper

Author Tags

  1. geometric modeling
  2. range data analysis
  3. surface fitting
  4. three-dimensional shape recovery

Qualifiers

  • Article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)1,417
  • Downloads (Last 6 weeks)171
Reflects downloads up to 25 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2025)Point Cloud Normal Estimation Algorithm Based on Local Structure ConstraintsAdvances in Applied Mathematics10.12677/aam.2025.14102314:01(203-210)Online publication date: 2025
  • (2025)GeoCode: Interpretable Shape ProgramsComputer Graphics Forum10.1111/cgf.15276Online publication date: 12-Feb-2025
  • (2025)Points2Model: a neural-guided 3D building wireframe reconstruction from airborne LiDAR point cloudsInternational Journal of Digital Earth10.1080/17538947.2025.245868218:1Online publication date: 11-Feb-2025
  • (2025)Pre-training meets iteration: Learning for robust 3D point cloud denoisingPattern Recognition Letters10.1016/j.patrec.2025.02.012190(105-110)Online publication date: Apr-2025
  • (2025)Full reference point cloud quality assessment using support vector regressionImage Communication10.1016/j.image.2024.117239131:COnline publication date: 1-Feb-2025
  • (2024)Integration and evaluation of the high-precision MotionCam-3D into a 3D thermography systemJournal of Sensors and Sensor Systems10.5194/jsss-13-123-202413:1(123-133)Online publication date: 4-Jun-2024
  • (2024)Low‐complexity patch projection method for efficient and lightweight point‐cloud compressionETRI Journal10.4218/etrij.2023-024246:4(683-696)Online publication date: 15-May-2024
  • (2024)三维点云数据的精确快速面图元检测方法Laser & Optoelectronics Progress10.3788/LOP23054961:4(0415006)Online publication date: 2024
  • (2024)Artificial intelligence-assisted restoration and visualization of knapped stone toolsPrehistoric Archaeology10.3724/2097-3063.202400161:2(207-223)Online publication date: 23-Jul-2024
  • (2024)Techniques for Canopy to Organ Level Plant Feature Extraction via Remote and Proximal Sensing: A Survey and ExperimentsRemote Sensing10.3390/rs1623437016:23(4370)Online publication date: 22-Nov-2024
  • Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Login options

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media