The DOI matches its Crossref record; 17 of the 17 references it cites were found in a registry or an index.
Algorithms for Finding Global Minimizers of Image Segmentation and Denoising Models
Abstract
We show how certain nonconvex optimization problems that arise in image processing and computer vision can be restated as convex minimization problems. This allows, in particular, the finding of global minimizers via standard convex minimization schemes.
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Cites
Kass, M., Witkin, A., & Terzopoulos, D. (1988) · International Journal of Computer Vision · doi:10.1007/bf00133570 · Cited by 17,070
Nonlinear total variation based noise removal algorithms
Rudin, L. I., Osher, S., & Fatemi, E. (1992) · Physica D: Nonlinear Phenomena · doi:10.1016/0167-2789(92)90242-f · Cited by 15,704
Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
Osher, S., & Sethian, J. A. (1988) · Journal of Computational Physics · doi:10.1016/0021-9991(88)90002-2 · Cited by 14,062
Chan, T. F., & Vese, L. A. (2001) · IEEE Transactions on Image Processing · doi:10.1109/83.902291 · Cited by 10,304
Self-citationOptimal approximations by piecewise smooth functions and associated variational problems
Mumford, D., & Shah, J. (1989) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160420503 · Cited by 5,208
Level Set Methods and Dynamic Implicit Surfaces
Osher, S., & Fedkiw, R. (2003) · Applied Mathematical Sciences · doi:10.1007/b98879 · Cited by 4,951
A Multiphase Level Set Framework for Image Segmentation Using the Mumford and Shah Model
Vese, L. A., & Chan, T. F. (2002) · International Journal of Computer Vision · doi:10.1023/a:1020874308076 · Cited by 2,384
Self-citationConvex Analysis and Minimization Algorithms I
Hiriart-Urruty, J.-B., & Lemaréchal, C. (1993) · Grundlehren der mathematischen Wissenschaften · doi:10.1007/978-3-662-02796-7 · Cited by 2,378
Minimal Surfaces and Functions of Bounded Variation
Giusti, E. (1984) · Birkhäuser Boston eBooks · doi:10.1007/978-1-4684-9486-0 · Cited by 2,261
Approximation of functional depending on jumps by elliptic functional via t‐convergence
Ambrosio, L., & Tortorelli, V. M. (1990) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.3160430805 · Cited by 1,471
Cited by
A study on continuous max-flow and min-cut approaches
Yuan, J., Bae, E., & Tai, X.-C. (2010) · 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2010.5539903 · Cited by 237
Vyas, N., Sammons, R. L., Addison, O., Dehghani, H., & Walmsley, A. D. (2016) · Scientific Reports · doi:10.1038/srep32694 · Cited by 98
Incorporating prior knowledge in medical image segmentation: a survey
Nosrati, M. S., & Hamarneh, G. (2016) · arXiv · doi:10.48550/arxiv.1607.01092 · Cited by 55
Local‐ and Global‐Statistics‐Based Active Contour Model for Image Segmentation
Wu, B., & Yang, Y. (2012) · Mathematical Problems in Engineering · doi:10.1155/2012/791958 · Cited by 30
Yang, J., Li, X., Xu, J., Cao, Y., Zhang, Y., Wang, L., & Jiang, S. (2018) · Applied Optics · doi:10.1364/ao.57.002490 · Cited by 29
Metadata
- Authors
- Chan, T. F., Esedoglu, S., & Nikolova, M.
- Venue
- SIAM Journal on Applied Mathematics
- Published
- 2006-01
- Volume
- 66
- Issue
- 5
- Pages
- 1632-1648
- ISSN
- 0036-1399 (ISSN-L)
- 1095-712X
- OpenAlex
- W2038495454
- Cited by
- 1,049
- References
- 17
- FWCI
- 33.72
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
