More Web Proxy on the site http://driver.im/

article

Free access

Marching cubes: A high resolution 3D surface construction algorithm

Authors:

William E. Lorensen,

Harvey E. ClineAuthors Info & Claims

ACM SIGGRAPH Computer Graphics, Volume 21, Issue 4

Pages 163 - 169

https://doi.org/10.1145/37402.37422

Published: 01 August 1987 Publication History

Abstract

We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle topology. The algorithm processes the 3D medical data in scan-line order and calculates triangle vertices using linear interpolation. We find the gradient of the original data, normalize it, and use it as a basis for shading the models. The detail in images produced from the generated surface models is the result of maintaining the inter-slice connectivity, surface data, and gradient information present in the original 3D data. Results from computed tomography (CT), magnetic resonance (MR), and single-photon emission computed tomography (SPECT) illustrate the quality and functionality of marching cubes. We also discuss improvements that decrease processing time and add solid modeling capabilities.

References

[1]

Artzy, E., Frieder, G., and Herman, G.T. The Theory, Design, Implementation and Evaluation of a Three-Dimensional Surface Detection Algorithm. Comptlter Graphics and Ima~,e Processinj, 15, 1 (January 1981), 1-24.

[2]

Barillot, C., Gibaud, B., Scarabin, J., and Coatrieux, J. 3D Reconstruction of Cerebral Blood Vessels. IEEE Comlmwr Graphk's attd Applk'ations 5, 12 (December 1985), 13-19.

[3]

Bates, R. H., Garden, K. L., and Peters, T. M. Overview of Computerized Tomography with Emphasis on Future Developments. Proc. of the IEEE 71, 3 (March 1983), 356-372.

[4]

Bloch, P. and Udupa, J. K. Application of Computerized Tomography to Radiation Therapy and Surgical Planning. Proc. oi' the IEEE 71, 3 (March 1983), 351-355.

[5]

Brewster, L. J., Trivedi, S. S., Tut, H. K., and Udupa, J. K. Interactive Surgical Planning. IEEE Computer Graphics and Applications 4, 3 (March 1984), 31-40.

[6]

Burk, D. L., Mears, D. C., Kennedy, W. H., Cooperstein, L. A., and Herbert, D. L. Three-Dimensional Computed Tomography of Acetabula Fractures. Radiology 155, 1 (1985), 183-186.

[7]

Chen, L., Herman, G. T., Reynolds, R. A., and Udupa, J. K. Surface Shading in the Cuberille Environment. IEEE Computer Graphics and Applications 5, 12 (December 1985), 33-43.

Digital Library

[8]

Christiansen, H. N. and Sederberg, T. W. Conversion of Complex Contour Line Definitions into Polygonal Element Meshes. Computer Graphics 12, 3 (August 1978), 187-192.

Digital Library

[9]

Cline, H. E., Dumoulin, C. L., Lorensen, W. E., Hart, H. R., and Ludke, S. 3D Reconstruction of the Brain from Magnetic Resonance Images. Magnetic Resonance Imaging (1987, to appear).

[10]

Cline, H. E., Lorensen, W. E., Ludke, S, Crawford, C. R., and Teeter, B. C. High-Resolution Three- Dimensional Reconstruction of Tomograms. Medical Physics (1987, to appear).

[11]

Cook, L. T., Dwyer, S. J., Batnitzky, S., and Lee, K. R. A Three-Dimensional Display System for Diagnostic Imaging Applications. IEEE Computer Graphics and Applications 3, 5 (August 1983), 13-19.

[12]

Farrell, E. J. Color Display and Interactive Interpretation of Three-Dimensional Data. IBM J. Res. Develop 27, 4 (July 1983), 356-366.

[13]

Farrell, E. J., Zappulla, R., and Yang, W. C. Color 3D Imaging of Normal and Pathologic Intracranial Structures. IEEE Computer Graphics and Applications 4, 9 (September 1984), 5-17.

Digital Library

[14]

Fuchs, H., Kedem, Z. M., and Uselton, S. P. Optimal Surface Reconstruction from Planar Contours. Comm. o{'the ACM 20, 10 (October 1977), 693-702.

Digital Library

[15]

Gordon, D. and Reynolds, R. A. Image Space Shading of 3-Dimensional Objects. Computer Graphics and Image Processing 29, 3 (March 1985), 361-376.

[16]

Hale, J. D., Valk, P. E., and Watts, J. C. MR Imaging of Blood Vessels Using Three-Dimensional Reconstruction: Methodology. Radiolo,xv 157, 3 (December 1985), 727-733.

[17]

Hemmy, D. C., David, D. J., and Herman, G. T. Three-Dimensional Reconstruction of Craniofacial Deformity Using Computed Tomography. Neurosurgery 13, 5 (November 1983), 534-541.

[18]

Hemmy, D. C. and Tessier, P. L. CT of Dry Skulls with Craniofacial Deformities: Accuracy of Three- Dimensional Reconstruction. Radiology 157, 1 (October 1985), 113-116.

[19]

Herman, G. T. and Udupa, J. K. Display of 3D Digital Images: Computational Foundations and Medical Applications. IEEE Computer Graphics and Applications 3, 5 (August 1983), 39-46.

Digital Library

[20]

Hinshaw, W. S. and Lent, A. H. An Introduction to NMR Imaging: From the Bloch Equation to the Imaging Equation. Proc. of the IEEE 71, 3 (March 1983), 338-350.

[21]

Hoffman, E. A. and Ritman, E. L. Shape and Dimensions of Cardiac Chambers: Importance of CT Section Thickness and Orientation. Radiology 155, 3 (June 1985), 73%744.

[22]

Hohne, K. H. and Bernstein, R. Shading 3D-Images from CT Using Gray-Level Gradients. IEEE Trans. on Medical Imaging MI-5, 1 (March 1986), 45-47.

[23]

Keppel, E. Approximating Complex Surfaces by Triangulation of Contour Lines. IBM J. Res. Develop 19, 1 (January 1975), 2-11.

Digital Library

[24]

Knoll, G. F. Single-Photon Emission Computed Tomography. Proc. of the IEEE 71, 3 (March 1983), 320-329.

[25]

Meagher, D. J. Geometric Modeling Using Octree Encoding. Computer Graphics and Image Processing 19, 2 (June 1982), 129-147.

[26]

Robb, R. A., Hoffman, E. A., Sinak, L. J., Harris, L. D., and Ritman, E. L. High-Speed Three-Dimensional X-Ray Computed Tomography: The Dynamic Spatial Reconstructor. Proc. of the IEEE 71, 3 (March 1983), 308-319.

[27]

Sunguroff, A. and Greenberg, D. Computer Generated Images for Medical Application. Computer Graphics 12, 3 (August 1978), 196-202.

Digital Library

[28]

Sutherland, I. E. and Hodgman, G. W. Reentrant Polygon Clipping. Comm. of the ACM 17, 1 (January 1974), 32-42.

Digital Library

[29]

Trivedi, S, S., Herman, G. T., and Udupa, J. K. Segmentation Into Three Classes Using Gradients. 1EEE Trans. on Medical Imaging MI-5, 2 (June 1986), 116-119.

[30]

Udupa, J. K. Interactive Segmentation and Boundary Surface Formation for 3-D Digital Images. Computer Graphics and Image Processing 18, 3 (March 1982), 213-235.

[31]

Vannier, M. W., Marsh, J. L., and Warren, J. O. Three Dimensional CT Reconstruction Images for Craniofacial Surgical Planning and Evaluation. Radiology 150, 1 (January 1984), 179-184.

[32]

Zucker, S. W. and Hummel, R. A. A Three- Dimensional Edge Operator. IEEE Trans. on Pattern Analysis and Machine Intelligence PAMI-3, 3 (May 1981), 324-331.

Digital Library

Cited By

Nie ZZhao Y(2025)High-Accuracy and Efficient Simulation of Numerical Control Machining Using Tri-Level Grid and Envelope TheoryMachines10.3390/machines1301006913:1(69)Online publication date: 18-Jan-2025
https://doi.org/10.3390/machines13010069
Ikumi AAsai REda YUchida TKohyama SOgawa TYoshii Y(2025)A Novel Method to Represent the Three-Dimensional Inclination of the Distal Radius Joint SurfaceDiagnostics10.3390/diagnostics1503034515:3(345)Online publication date: 1-Feb-2025
https://doi.org/10.3390/diagnostics15030345
N’Guyen FKanit TImad A(2025)Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 2: Labeled ImagesComputation10.3390/computation1302005713:2(57)Online publication date: 19-Feb-2025
https://doi.org/10.3390/computation13020057
Show More Cited By

Index Terms

Marching cubes: A high resolution 3D surface construction algorithm

Recommendations

Marching cubes: A high resolution 3D surface construction algorithm
SIGGRAPH '87: Proceedings of the 14th annual conference on Computer graphics and interactive techniques

We present a new algorithm, called marching cubes, that creates triangle models of constant density surfaces from 3D medical data. Using a divide-and-conquer approach to generate inter-slice connectivity, we create a case table that defines triangle ...
On marching cubes

A characterization and classification of the isosurfaces of trilinear functions is presented. Based upon these results, a new algorithm for computing a triangular mesh approximation to isosurfaces for data given on a 3D rectilinear grid is presented. ...
Quality isosurface mesh generation using an extended marching cubes lookup table
EuroVis'08: Proceedings of the 10th Joint Eurographics / IEEE - VGTC conference on Visualization

The Marching Cubes Algorithm may return degenerate, zero area isosurface triangles, and often returns isosurface triangles with small areas, edges or angles. We show how to avoid both problems using an extended Marching Cubes lookup table. As opposed to ...

Comments

Please enable JavaScript to view thecomments powered by Disqus.

Information & Contributors

Information

Published In

cover image ACM SIGGRAPH Computer Graphics

ACM SIGGRAPH Computer Graphics Volume 21, Issue 4

July 1987

299 pages

ISSN:0097-8930

DOI:10.1145/37402

Editor:
Maureen C. Stone

Issue’s Table of Contents

SIGGRAPH '87: Proceedings of the 14th annual conference on Computer graphics and interactive techniques
August 1987
352 pages
ISBN:0897912276
DOI:10.1145/37401
Editor:
Maureen C. Stone

Copyright © 1987 ACM.

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 August 1987

Published in SIGGRAPH Volume 21, Issue 4

Check for updates

Badges

Seminal Paper

Qualifiers

Article

Contributors

Other Metrics

View Article Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

8,527
Total Citations
View Citations
54,461
Total Downloads

Downloads (Last 12 months)7,205
Downloads (Last 6 weeks)939

Reflects downloads up to 03 Mar 2025

Other Metrics

View Author Metrics

Citations

Cited By

Nie ZZhao Y(2025)High-Accuracy and Efficient Simulation of Numerical Control Machining Using Tri-Level Grid and Envelope TheoryMachines10.3390/machines1301006913:1(69)Online publication date: 18-Jan-2025
https://doi.org/10.3390/machines13010069
Ikumi AAsai REda YUchida TKohyama SOgawa TYoshii Y(2025)A Novel Method to Represent the Three-Dimensional Inclination of the Distal Radius Joint SurfaceDiagnostics10.3390/diagnostics1503034515:3(345)Online publication date: 1-Feb-2025
https://doi.org/10.3390/diagnostics15030345
N’Guyen FKanit TImad A(2025)Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 2: Labeled ImagesComputation10.3390/computation1302005713:2(57)Online publication date: 19-Feb-2025
https://doi.org/10.3390/computation13020057
N’Guyen FKanit TImad A(2025)Unbiased Finite Element Mesh Delaunay Constrained Triangulation Applied to 2D Images with High Morphological Complexity Using Mathematical Morphology Tools Part 1: Binary ImagesComputation10.3390/computation1302005213:2(52)Online publication date: 13-Feb-2025
https://doi.org/10.3390/computation13020052
Cai ZDeng YZhu XLi BXu CLi D(2025)High-Throughput 3D Rice Chalkiness Detection Based on Micro-CT and VSE-UNetAgronomy10.3390/agronomy1502045015:2(450)Online publication date: 12-Feb-2025
https://doi.org/10.3390/agronomy15020450
Nispel KLerchl TGruber GMoeller HGraf RSenner VKirschke J(2025)From MRI to FEM: an automated pipeline for biomechanical simulations of vertebrae and intervertebral discsFrontiers in Bioengineering and Biotechnology10.3389/fbioe.2024.148511512Online publication date: 3-Jan-2025
https://doi.org/10.3389/fbioe.2024.1485115
Палехова ЕДолгополов ДМелкий В(2025)Реализация математического алгоритма определения объема объекта, не имеющего «нависания», по данным лазерного сканированияVestnik SSUGT10.33764/2411-1759-2025-30-1-66-7630:1(66-76)Online publication date: 28-Feb-2025
https://doi.org/10.33764/2411-1759-2025-30-1-66-76
Li BLiu NBai JXu JTang YLiu Y(2025)MTMU: Multi-domain Transformation based Mamba-UNet designed for unruptured intracranial aneurysm segmentationBMC Medical Imaging10.1186/s12880-025-01611-625:1Online publication date: 6-Mar-2025
https://doi.org/10.1186/s12880-025-01611-6
Brugali DMuratore LDe Luca A(2025)Mobile robots exploration strategies and requirements: A systematic mapping studyThe International Journal of Robotics Research10.1177/02783649241313471Online publication date: 17-Feb-2025
https://doi.org/10.1177/02783649241313471
Augoyard MZanolli CProfico AThibeault ACazenave MOettlé AL′Abbé EHoffman JBayle P(2025)Exploration of the covariation signal between cortical bone and dentine volumes across the upper limb bones and anterior teeth in modern humans and relevance to evolutionary anthropologyJournal of Anatomy10.1111/joa.14227Online publication date: 6-Feb-2025
https://doi.org/10.1111/joa.14227
Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

eReader

View online with eReader.

Login options

Check if you have access through your login credentials or your institution to get full access on this article.

Full Access

Get this Publication

Figures

Tables

Media

View Issue’s Table of Contents