The DOI matches its Crossref record.
Marching cubes: A high resolution 3D surface construction algorithm
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.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cited by
Features and development of Coot
Emsley, P., Lohkamp, B., Scott, W. G., & Cowtan, K. (2010) · Acta Crystallographica Section D Biological Crystallography · doi:10.1107/s0907444910007493 · Cited by 29,915
Yushkevich, P. A., Piven, J., Hazlett, H. C., Smith, R. G., Ho, S., Gee, J. C., & Gerig, G. (2006) · NeuroImage · doi:10.1016/j.neuroimage.2006.01.015 · Cited by 8,868
Zwanenburg, A., Vallières, M., Abdalah, M. A., Aerts, H. J. W. L., Andrearczyk, V., Apte, A., Ashrafinia, S., Bakas, S., Beukinga, R. J., Boellaard, R., et al. (2020) · Radiology · doi:10.1148/radiol.2020191145 · Cited by 4,177
A volumetric method for building complex models from range images
Curless, B., & Levoy, M. (1996) · Proceedings of the 23rd annual conference on Computer graphics and interactive techniques · doi:10.1145/237170.237269 · Cited by 3,124
Three-dimensional alpha shapes
Edelsbrunner, H., & Mücke, E. P. (1994) · ACM Transactions on Graphics · doi:10.1145/174462.156635 · Cited by 2,488
Display of surfaces from volume data
Levoy, M. (1988) · IEEE Computer Graphics and Applications · doi:10.1109/38.511 · Cited by 2,446
Reconstruction and representation of 3D objects with radial basis functions
Carr, J. C., Beatson, R. K., Cherrie, J. B., Mitchell, T. J., Fright, W. R., McCallum, B. C., & Evans, T. R. (2001) · Proceedings of the 28th annual conference on Computer graphics and interactive techniques · doi:10.1145/383259.383266 · Cited by 1,852
Evaluation of prostate segmentation algorithms for mri: The promise12 challenge
Litjens, G., Toth, R., van de Ven, W., Hoeks, C., Kerkstra, S., van Ginneken, B., Vincent, G., Guillard, G., Birbeck, N., Zhang, J., et al. (2014) · Medical Image Analysis · doi:10.1016/j.media.2013.12.002 · Cited by 857
Liu, F., Zhou, Z., Jang, H., Samsonov, A., Zhao, G., & Kijowski, R. (2018) · Magnetic Resonance in Medicine · doi:10.1002/mrm.26841 · Cited by 319
Automated graph-based analysis and correction of cortical volume topology
Shattuck, D. W., & Leahy, R. M. (2001) · IEEE Transactions on Medical Imaging · doi:10.1109/42.963819 · Cited by 215
Learning Gradient Fields for Shape Generation
Cai, R., Yang, G., Averbuch-Elor, H., Hao, Z., Belongie, S., Snavely, N., & Hariharan, B. (2020) · Lecture Notes in Computer Science · doi:10.1007/978-3-030-58580-8_22 · Cited by 225
Deep convolutional neural network for segmentation of knee joint anatomy
Zhou, Z., Zhao, G., Kijowski, R., & Liu, F. (2018) · Magnetic Resonance in Medicine · doi:10.1002/mrm.27229 · Cited by 202
Automatic Liver Segmentation Based on Shape Constraints and Deformable Graph Cut in CT Images
Li, G., Chen, X., Shi, F., Zhu, W., Tian, J., & Xiang, D. (2015) · IEEE Transactions on Image Processing · doi:10.1109/tip.2015.2481326 · Cited by 185
Morphological alterations in the thalamus, striatum, and pallidum in autism spectrum disorder
Schuetze, M., Park, M. T. M., Cho, I. Y., MacMaster, F. P., Chakravarty, M. M., & Bray, S. L. (2016) · Neuropsychopharmacology · doi:10.1038/npp.2016.64 · Cited by 186
Klingensmith, M., Dryanovski, I., Srinivasa, S., & Xiao, J. (2015) · Robotics: Science and Systems XI · doi:10.15607/rss.2015.xi.040 · Cited by 163
Synergies Between Affordance and Geometry: 6-DoF Grasp Detection via Implicit Representations
Jiang, Z., Zhu, Y., Svetlik, M., Fang, K., & Zhu, Y. (2021) · arXiv · doi:10.48550/arxiv.2104.01542 · Cited by 122
Dried plum prevents bone loss in a male osteoporosis model via IGF-I and the RANK pathway.
Franklin, M., Bu, S. Y., Lerner, M. R., Lancaster, E. A., Bellmer, D., Marlow, D., Lightfoot, S. A., Arjmandi, B. H., Brackett, D. J., Lucas, E. A., et al. (2006) · Bone · doi:10.1016/j.bone.2006.05.024 · Cited by 120
Synergies Between Affordance and Geometry: 6-DoF Grasp Detection via Implicit Representations
Jiang, Z., Zhu, Y., Svetlik, M., Fang, K., & Zhu, Y. (2021) · Robotics: Science and Systems XVII · doi:10.15607/rss.2021.xvii.024 · Cited by 122
Martin, A., David, V., Malaval, L., Lafage-Proust, M.-H., Vico, L., & Thomas, T. (2007) · Endocrinology · doi:10.1210/en.2006-1541 · Cited by 111
Lenardon, M. D., Sood, P., Dorfmueller, H. C., Brown, A. J. P., & Gow, N. A. R. (2020) · The Cell Surface · doi:10.1016/j.tcsw.2020.100047 · Cited by 110
Morales-Navarrete, H., Segovia-Miranda, F., Klukowski, P., Meyer, K., Nonaka, H., Marsico, G., Chernykh, M., Kalaidzidis, A., Zerial, M., & Kalaidzidis, Y. (2015) · eLife · doi:10.7554/elife.11214 · Cited by 98
Revishvili, A. S., Wissner, E., Lebedev, D. S., Lemes, C., Deiss, S., Metzner, A., Kalinin, V. V., Sopov, O. V., Labartkava, E. Z., Kalinin, A. V., et al. (2015) · Europace · doi:10.1093/europace/euu339 · Cited by 89
Ditto: Building Digital Twins of Articulated Objects from Interaction
Jiang, Z., Hsu, C.-C., & Zhu, Y. (2022) · 2022 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr52688.2022.00553 · Cited by 92
Zauli, G., Rimondi, E., Stea, S., Baruffaldi, F., Stebel, M., Zerbinati, C., Corallini, F., & Secchiero, P. (2008) · Journal of Cellular Physiology · doi:10.1002/jcp.21165 · Cited by 63
Learning Semantic Deformation Flows with 3D Convolutional Networks
Yumer, M. E., & Mitra, N. J. (2016) · Lecture Notes in Computer Science · doi:10.1007/978-3-319-46466-4_18 · Cited by 60
Computer Aided Orthopaedic Surgery: Incremental Shift or Paradigm Change?
Joskowicz, L., & Hazan, E. J. (2016) · Medical Image Analysis · doi:10.1016/j.media.2016.06.036 · Cited by 58
Petascale neural circuit reconstruction: automated methods
Macrina, T., Lee, K., Lu, R., Turner, N. L., Wu, J., Popovych, S., Silversmith, W., Kemnitz, N., Bae, J. A., Castro, M. A., et al. (2021) · doi:10.1101/2021.08.04.455162 · Cited by 55
Dickson, J., Drury, H., & Van Essen, D. C. (2001) · Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences · doi:10.1098/rstb.2001.0913 · Cited by 54
Morphological Changes in Femoral Tunnels after Anatomic Anterior Cruciate Ligament Reconstruction
Tachibana, Y., Mae, T., Shino, K., Kanamoto, T., Sugamoto, K., Yoshikawa, H., & Nakata, K. (2015) · Knee Surgery Sports Traumatology Arthroscopy · doi:10.1007/s00167-014-3252-6 · Cited by 49
Akiyama, K., Sakai, T., Koyanagi, J., Yoshikawa, H., & Sugamoto, K. (2011) · Osteoarthritis and Cartilage · doi:10.1016/j.joca.2011.01.017 · Cited by 48
Mercan, E., Hopper, R. A., & Maga, A. M. (2020) · Journal of Anatomy · doi:10.1111/joa.13085 · Cited by 34
Jaroš, M., Strakoš, P., Karásek, T., Říha, L., Vašatová, A., Jarošová, M., & Kozubek, T. (2017) · Advances in Engineering Software · doi:10.1016/j.advengsoft.2016.05.008 · Cited by 34
Claes, P., Reijniers, J., Shriver, M. D., Snyders, J., Suetens, P., Nielandt, J., De Tré, G., & Vandermeulen, D. (2015) · Journal of Anatomy · doi:10.1111/joa.12252 · Cited by 32
3D reconstruction of medical images from slices automatically landmarked with growing neural models
Angelopoulou, A., Psarrou, A., Garcia-Rodriguez, J., Orts-Escolano, S., Azorin-Lopez, J., & Revett, K. (2015) · Neurocomputing · doi:10.1016/j.neucom.2014.03.078 · Cited by 31
Accurate and precise 2D–3D registration based on X-ray intensity
Aouadi, S., & Sarry, L. (2008) · Computer Vision and Image Understanding · doi:10.1016/j.cviu.2007.05.006 · Cited by 30
Predicting Alzheimer’s Disease Using Combined Imaging-Whole Genome SNP Data
Kong, D., Initiative, A. F. T. A. D. N., Giovanello, K. S., Wang, Y., Lin, W., Lee, E., Fan, Y., Murali Doraiswamy, P., & Zhu, H. (2015) · Journal of Alzheimer's Disease · doi:10.3233/jad-150164 · Cited by 26
Breast MRI and X-ray mammography registration using gradient values
García, E., Diez, Y., Diaz, O., Lladó, X., Gubern-Mérida, A., Martí, R., Martí, J., & Oliver, A. (2019) · Medical Image Analysis · doi:10.1016/j.media.2019.02.013 · Cited by 26
A Virtual Training System Using a Force Feedback Haptic Device for Oral Implantology
Chen, X., Lin, Y., Wang, C., Shen, G., & Wang, X. (2012) · Lecture Notes in Computer Science · doi:10.1007/978-3-642-31439-1_21 · Cited by 23
Kim, N., Kim, H. J., Hwang, J., Yoon, S. J., Cho, H. B., Renshaw, P. F., Lyoo, I. K., & Kim, J. E. (2011) · Neuroscience Letters · doi:10.1016/j.neulet.2010.11.005 · Cited by 11
Yuan (2020) · doi:10.1111/cgf.14121 · Cited by 2
Metadata
- Authors
- Lorensen, W. E., & Cline, H. E.
- Venue
- ACM SIGGRAPH Computer Graphics
- Published
- 1987-08
- Volume
- 21
- Issue
- 4
- Pages
- 163-169
- ISSN
- 0097-8930 (ISSN-L)
- OpenAlex
- W4233857083
- Cited by
- 8,647
- References
- 0
- FWCI
- 35.10
- Type
- journal article
- Language
- en
- Open access
- closed
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.