Gauss-Seidel Retinex

Afsaneh Karami; Graham D. Finlayson

Gauss-Seidel Retinex

Research output: Contribution to conference › Paper › peer-review

Abstract

Retinex has many algorithmic variants, differing in the method used to decouple illumination from reflectance, including path-based methods, center-surround
operators, and lightness processing. The center-surround approach is putatively the most compatible with the human visual mechanism, as it mimics the operation in receptive fields to detect lightness ratios between a central region and its annular surround.
In our previous work [8], we reformulated the path-based McCann99 Retinex into an iterative convolutional center-surround framework, introducing the Jacobi Retinex algorithm. In this paper, we propose a modified version of the Jacobi approach by replacing the Jacobi iteration with Gauss-Seidel, resulting in faster convergence. The Gauss-Seidel method can also be considered a convolutional center-surround algorithm, but it uses an immediate as opposed to a delayed replacement strategy in Jacobi convolution. This immediate replacement strategy allows Retinex to use the most recently computed values within the current iteration—unlike Jacobi, which relies on values from the previous
iteration—thereby accelerating convergence. Both the Jacobi and Gauss-Seidel variants, compared to McCann99, return images of equal or better quality with fewer artefacts such as halos.

Original language	English
Publication status	Published - Oct 2025

Cite this

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title = "Gauss-Seidel Retinex",

abstract = "Retinex has many algorithmic variants, differing in the method used to decouple illumination from reflectance, including path-based methods, center-surround operators, and lightness processing. The center-surround approach is putatively the most compatible with the human visual mechanism, as it mimics the operation in receptive fields to detect lightness ratios between a central region and its annular surround. In our previous work [8], we reformulated the path-based McCann99 Retinex into an iterative convolutional center-surround framework, introducing the Jacobi Retinex algorithm. In this paper, we propose a modified version of the Jacobi approach by replacing the Jacobi iteration with Gauss-Seidel, resulting in faster convergence. The Gauss-Seidel method can also be considered a convolutional center-surround algorithm, but it uses an immediate as opposed to a delayed replacement strategy in Jacobi convolution. This immediate replacement strategy allows Retinex to use the most recently computed values within the current iteration—unlike Jacobi, which relies on values from the previous iteration—thereby accelerating convergence. Both the Jacobi and Gauss-Seidel variants, compared to McCann99, return images of equal or better quality with fewer artefacts such as halos.",

author = "Afsaneh Karami and Finlayson, \{Graham D.\}",

year = "2025",

month = oct,

language = "English",

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TY - CONF

T1 - Gauss-Seidel Retinex

AU - Karami, Afsaneh

AU - Finlayson, Graham D.

PY - 2025/10

Y1 - 2025/10

N2 - Retinex has many algorithmic variants, differing in the method used to decouple illumination from reflectance, including path-based methods, center-surround operators, and lightness processing. The center-surround approach is putatively the most compatible with the human visual mechanism, as it mimics the operation in receptive fields to detect lightness ratios between a central region and its annular surround. In our previous work [8], we reformulated the path-based McCann99 Retinex into an iterative convolutional center-surround framework, introducing the Jacobi Retinex algorithm. In this paper, we propose a modified version of the Jacobi approach by replacing the Jacobi iteration with Gauss-Seidel, resulting in faster convergence. The Gauss-Seidel method can also be considered a convolutional center-surround algorithm, but it uses an immediate as opposed to a delayed replacement strategy in Jacobi convolution. This immediate replacement strategy allows Retinex to use the most recently computed values within the current iteration—unlike Jacobi, which relies on values from the previous iteration—thereby accelerating convergence. Both the Jacobi and Gauss-Seidel variants, compared to McCann99, return images of equal or better quality with fewer artefacts such as halos.

AB - Retinex has many algorithmic variants, differing in the method used to decouple illumination from reflectance, including path-based methods, center-surround operators, and lightness processing. The center-surround approach is putatively the most compatible with the human visual mechanism, as it mimics the operation in receptive fields to detect lightness ratios between a central region and its annular surround. In our previous work [8], we reformulated the path-based McCann99 Retinex into an iterative convolutional center-surround framework, introducing the Jacobi Retinex algorithm. In this paper, we propose a modified version of the Jacobi approach by replacing the Jacobi iteration with Gauss-Seidel, resulting in faster convergence. The Gauss-Seidel method can also be considered a convolutional center-surround algorithm, but it uses an immediate as opposed to a delayed replacement strategy in Jacobi convolution. This immediate replacement strategy allows Retinex to use the most recently computed values within the current iteration—unlike Jacobi, which relies on values from the previous iteration—thereby accelerating convergence. Both the Jacobi and Gauss-Seidel variants, compared to McCann99, return images of equal or better quality with fewer artefacts such as halos.

M3 - Paper

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