The DOI matches its Crossref record; 31 of the 32 references it cites were found in a registry or an index.
Snakes, shapes, and gradient vector flow
Abstract
Snakes, or active contours, are used extensively in computer vision and image processing applications, particularly to locate object boundaries. Problems associated with initialization and poor convergence to boundary concavities, however, have limited their utility. This paper presents a new external force for active contours, largely solving both problems. This external force, which we call gradient vector flow (GVF), is computed as a diffusion of the gradient vectors of a gray-level or binary edge map derived from the image. It differs fundamentally from traditional snake external forces in that it cannot be written as the negative gradient of a potential function, and the corresponding snake is formulated directly from a force balance condition rather than a variational formulation. Using several two-dimensional (2-D) examples and one three-dimensional (3-D) example, we show that GVF has a large capture range and is able to move snakes into boundary concavities.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
Citations
Cites
Kass, M., Witkin, A., & Terzopoulos, D. (1988) · International Journal of Computer Vision · doi:10.1007/bf00133570 · Cited by 17,330
Methods of Theoretical Physics
Morse, P. M., Feshbach, H., & Hill, E. L. (1954) · American Journal of Physics · doi:10.1119/1.1933765 · Cited by 13,197
Horn, B. K. P., & Schunck, B. G. (1981) · Artificial Intelligence · doi:10.1016/0004-3702(81)90024-2 · Cited by 10,312
Methods of Mathematical Physics
Courant, R., & Hilbert, D. R. (1989) · Wiley eBooks · doi:10.1002/9783527617210 · Cited by 8,151
Horn, B. K. P., & Schunck, B. G. (1981) · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · doi:10.1117/12.965761 · Cited by 7,443
Fundamentals of digital image processing
Jain, A. K. (1988) · Cited by 7,000
Caselles, V., Kimmel, R., & Sapiro, G. (1997) · International Journal of Computer Vision · doi:10.1023/a:1007979827043 · Cited by 5,285
Methods of theoretical physics
Domenicali, C. A. (1954) · Journal of the Franklin Institute · doi:10.1016/0016-0032(54)90634-1 · Cited by 4,893
Fundamentals of digital image processing
(1989) · Computer Vision Graphics and Image Processing · doi:10.1016/0734-189x(89)90041-8 · Cited by 4,703
Shape modeling with front propagation: a level set approach
Malladi, R., Sethian, J. A., & Vemuri, B. C. (1995) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.368173 · Cited by 3,166
On active contour models and balloons
Cohen, L. D. (1991) · CVGIP Image Understanding · doi:10.1016/1049-9660(91)90028-n · Cited by 2,164
A geometric model for active contours in image processing
Caselles, V., Catt�, F., Coll, T., & Dibos, F. (1993) · Numerische Mathematik · doi:10.1007/bf01385685 · Cited by 1,744
Finite-element methods for active contour models and balloons for 2-D and 3-D images
Cohen, L. D., & Cohen, I. (1993) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.244675 · Cited by 1,379
Caselles, V., Kimmel, R., & Sapiro, G. (2002) · IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.1995.466871 · Cited by 1,170
Gradient vector flow: a new external force for snakes
Xu, C., & Prince, J. L. (2002) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.1997.609299 · Cited by 756
Self-citationMethods of mathematical physics, Vol. 2, Partial differential equations
Courant, R., & Hilbert, D. (1989) · Wiley eBooks · doi:10.1002/9783527617234 · Cited by 738
Tracking deformable objects in the plane using an active contour model
Leymarie, F. F., & Levine, M. D. (1993) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.216733 · Cited by 555
Numerical Methods for Partial Differential Equations
Ying, L.-A., & Guo, B. (1992) · Numerical Methods for Partial Differential Equations · doi:10.1142/9789814537735 · Cited by 532
Terzopoulos, D., & Fleischer, K. (1988) · The Visual Computer · doi:10.1007/bf01908877 · Cited by 477
A discrete dynamic contour model
Lobregt, S., & Viergever, M. A. (1995) · IEEE Transactions on Medical Imaging · doi:10.1109/42.370398 · Cited by 426
McInerney, T., & Terzopoulos, D. (1995) · Computerized Medical Imaging and Graphics · doi:10.1016/0895-6111(94)00040-9 · Cited by 358
Terzopoulos, D., & Szeliski, R. (1993) · The MIT Press eBooks · Cited by 320
An active contour model for mapping the cortex
Davatzikos, C. A., & Prince, J. L. (1995) · IEEE Transactions on Medical Imaging · doi:10.1109/42.370403 · Cited by 245
Self-citationNumerical analysis of partial differential equations
(2012) · Choice Reviews Online · doi:10.5860/choice.49-5115 · Cited by 127
Image segmentation by reaction-diffusion bubbles
Tek, H., & Kimia, B. B. (2002) · IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.1995.466792 · Cited by 113
Multi-resolution algorithms for active contour models
Leroy, B., Herlin, I., & Cohen, L. D. (1996) · Lecture notes in control and information sciences · doi:10.1007/3-540-76076-8_117 · Cited by 110
A class of constrained clustering algorithms for object boundary extraction
Abrantes, A. J., & Marques, J. S. (1996) · IEEE Transactions on Image Processing · doi:10.1109/83.541421 · Cited by 105
Dynamic contour: A texture approach and contour operations
Ďurikovič, R., Kaneda, K., & Yamashita, H. (1995) · The Visual Computer · doi:10.1007/bf01898405 · Cited by 68
Stochastic models for DIV-CURL optical flow methods
Gupta, S. N., & Prince, J. L. (1996) · IEEE Signal Processing Letters · doi:10.1109/97.484208 · Cited by 41
Self-citationNumerical Analysis of Partial Differential Equations
Lions, J. L. (2010) · Springer eBooks · doi:10.1007/978-3-642-11057-3 · Cited by 33
A New External Force Model For Snakes
Prince, J. L., & Xu, C. (1996) · Cited by 18
Self-citation
Research works printed but not linked: 2
- davatzikos, 1994, Convexity analysis of active contour models, Proc Conf Information Science and Systems, 581
- terzopoulos, 1992, Active Vision, 3
Cited by
Sorted by citations
Chan, T. F.-C., & Vese, L. A. (2001) · IEEE Transactions on Image Processing · doi:10.1109/83.902291 · Cited by 10,279
Current Methods in Medical Image Segmentation
Pham, D. L., Xu, C., & Prince, J. L. (2000) · Annual Review of Biomedical Engineering · doi:10.1146/annurev.bioeng.2.1.315 · Cited by 2,352
Self-citationDistance Regularized Level Set Evolution and Its Application to Image Segmentation
Li, C., Xu, C., Gui, C., & Fox, M. D. (2010) · IEEE Transactions on Image Processing · doi:10.1109/tip.2010.2069690 · Cited by 2,106
Self-citationLevel Set Evolution without Re-Initialization: A New Variational Formulation
Li, C., Xu, C., Gui, C., & Fox, M. D. (2005) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.2005.213 · Cited by 1,809
Self-citationMinimization of Region-Scalable Fitting Energy for Image Segmentation
Li, C., Kao, C., Gore, J. C., & Ding, Z. (2008) · IEEE Transactions on Image Processing · doi:10.1109/tip.2008.2002304 · Cited by 1,723
Metadata
- Authors
- Xu, C., & Prince, J. L.
- Affiliations
- Johns Hopkins University (US)
- Venue
- IEEE Transactions on Image Processing
- Published
- 1998-03
- Volume
- 7
- Issue
- 3
- Pages
- 359-369
- ISSN
- 1057-7149 (ISSN-L)
- OpenAlex
- W2145803225
- Cited by
- 4,001
- References
- 32
- Citations by year
- 2026: 26 · 2025: 30 · 2024: 38 · 2023: 48 · 2022: 62 · 2021: 85 · 2020: 78 · 2019: 110 · 2018: 99 · 2017: 135 · 2016: 165 · 2015: 221 · 2014: 236 · 2013: 243 · 2012: 274
- FWCI
- 35.98
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- IEEE Transactions on Image Processing (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- Topics
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Medical Image Segmentation Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Object Detection Techniques
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Image and Signal Denoising Methods
- Keywords
- snakes, gradient vector flow, external forces, edge maps, gradient diffusion, force balance, object boundary detection
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
