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Mathematical definition and analysis of the Retinex algorithm
Abstract
We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am. 61, 1 (1071)]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.
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Cited by
Structure-Revealing Low-Light Image Enhancement Via Robust Retinex Model
Li, M., Liu, J., Yang, W., Sun, X., & Guo, Z. (2018) · IEEE Transactions on Image Processing · doi:10.1109/tip.2018.2810539 · Cited by 1,245
A Weighted Variational Model for Simultaneous Reflectance and Illumination Estimation
Fu, X., Zeng, D., Huang, Y., Zhang, X.-P., & Ding, X. (2016) · 2016 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2016.304 · Cited by 1,081
A neural field model for color perception unifying assimilation and contrast
Song, A., Faugeras, O., & Veltz, R. (2019) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1007050 · Cited by 18
Metadata
- Authors
- Provenzi, E., Marini, D., De Carli, L., & Rizzi, A.
- Venue
- Journal of the Optical Society of America A
- Publisher
- Optica Publishing Group
- Published
- 2005-12-01
- Volume
- 22
- Issue
- 12
- Pages
- 2613
- ISSN
- 1084-7529 (ISSN-L)
- 1520-8532
- OpenAlex
- W1986462898
- Cited by
- 207
- References
- 0
- FWCI
- 3.99
- Type
- journal article
- Language
- en
- Open access
- closed
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- CoChat. (2026). Citation check: Mathematical definition and analysis of the Retinex algorithm. https://app.cochat.ai/papers/10.1364/josaa.22.002613
- The paper
- Provenzi, E., Marini, D., De Carli, L., & Rizzi, A. (2005). Mathematical definition and analysis of the Retinex algorithm. Journal of the Optical Society of America A. https://doi.org/10.1364/josaa.22.002613
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