Underwater image quality assessment

Xieliu Yang; Jianping Li; Wenfeng Liang; Dan Wang; Jinbao Zhao; Xiaohua Xia

doi:10.1364/JOSAA.485307

Journal of the Optical Society of America A
Vol. 40,
Issue 7,
pp. 1276-1288
(2023)
•https://doi.org/10.1364/JOSAA.485307

Underwater image quality assessment

Xieliu Yang, Jianping Li, Wenfeng Liang, Dan Wang, Jinbao Zhao, and Xiaohua Xia

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Xieliu Yang, Jianping Li, Wenfeng Liang, Dan Wang, Jinbao Zhao, and Xiaohua Xia, "Underwater image quality assessment," J. Opt. Soc. Am. A 40, 1276-1288 (2023)

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Abstract

To obtain high-visual-quality underwater images by image post-processing, many underwater image restoration and enhancement methods have been proposed. Underwater image quality assessment (UIQA) methods have been developed to compare these restoration and enhancement methods. This paper comprehensively summarizes the subjective and objective UIQA methods, metrics, and datasets. Experiments are conducted on two underwater image datasets to analyze the performance of several typical UIQA metrics. Suggestions for further research directions are put forward as well.

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Data availability

Data underlying the results presented in this paper are available in [14,40].

14. C. Li, C. Guo, W. Ren, R. Cong, J. Hou, S. Kwong, and D. Tao, “An underwater image enhancement benchmark dataset and beyond,” IEEE Trans. Image Process. 29, 4376–4389 (2019). [CrossRef]

40. C. Sanchez-Ferreira, L. S. Coelho, H. V. H. Ayala, M. C. Q. Farias, and C. H. Llanos, “Bio-inspired optimization algorithms for real underwater image restoration,” Signal Process. Image Commun. 77, 49–65 (2019). [CrossRef]

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Metric	Formula	Notes
MAE	$M A E = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} \| f (i, j) - \hat{f} (i, j) \|$	$M$ and $N$ represent the number in rows and columns of the image. $f (i, j)$ and $\hat{f} (i, j)$ represent the pixel intensity values at coordinates $(i, j)$ in the reference and test images. $L$ is the dynamic range of the intensity values of the pixels. For example, $L = 255$ for 8-bit grayscale images. $K_{1}$ and $K_{2}$ are small constants much smaller than 1. $α$ , $β$ , and $γ$ are constants and could be set to one.
MSE	$M S E = \frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} {[f (i, j) - \hat{f} (i, j)]}^{2}$
RMSE	$R M S E = \sqrt{M S E}$
SNR	$S N R = 10 \log_{10} \frac{\frac{1}{M \times N} \sum_{i = 1}^{M} \sum_{j = 1}^{N} [f (i, j)]^{2}}{M S E}$
PSNR	$P S N R = 10 {l o g}_{10} \frac{L^{2}}{M S E}$
SSIM	$S S I M (x, y) = l (x, y)^{α} \cdot c (x, y)^{β} \cdot s (x, y)^{γ}$ , $l (x, y) = \frac{2 μ_{x} μ_{y} + C_{1}}{μ_{x}^{2} + μ_{y}^{2} + C_{1}}, c (x, y) = \frac{2 σ_{x} σ_{y} + C_{2}}{σ_{x}^{2} + σ_{y}^{2} + C_{2}}, s (x, y) = \frac{σ_{xy} + C_{3}}{σ_{x} σ_{y} + C_{3}}$ , $μ_{x} = \frac{1}{N} \sum_{i = 1}^{N} x_{i}$ , $σ_{x}^{2} = \frac{1}{N - 1} \sum_{i = 1}^{N} {(x_{i} - μ_{x})}^{2}$ , $σ_{xy} = \frac{1}{N - 1} \sum_{i = 1}^{N} (x_{i} - μ_{x}) (y_{i} - μ_{y})$ , $C_{1} = (K_{1} L)^{2}, C_{2} = (K_{2} L)^{2}, C_{3} = C_{2} / 2$

Feature ID	Description	Computation Procedure
$f_{1} - f_{2}$	Shape and variance	Fit generalized Gaussian distribution to mean subtracted contrast normalized (MSCN) coefficients.
$f_{3} - f_{6}$	Shape, mean, left variance, right variance	Fit asymmetric generalized Gaussian distribution (AGGD) to the horizontal pairwise product of neighboring MSCN coefficients.
$f_{7} - f_{10}$	Shape, mean, left variance, right variance	Fit AGGD to the vertical pairwise product of neighboring MSCN coefficients.
$f_{11} - f_{14}$	Shape, mean, left variance, right variance	Fit AGGD to the main diagonal pairwise product of neighboring MSCN coefficients.
$f_{15} - f_{18}$	Shape, mean, left variance, right variance	Fit AGGD to the secondary diagonal pairwise product of neighboring MSCN coefficients.

Metric	Formula	Note
UCIQE [69]	$U C I Q E = c_{1} \times σ_{c} + c_{2} \times c o n_{l} + c_{3} \times μ_{s}$	$σ_{c}$ is the standard deviation of chroma, $c o n_{l}$ is the contrast of luminance, and $μ_{s}$ is the average of saturation. Usually, $c_{1} = 0.4859$ , $c_{2} = 0.2745$ , and $c_{3} = 0.2576$ .
UIQM [10]	$U I Q M = c_{1} \times U I C M + c_{2} \times U I S M + c_{3} \times U I C o n M$	UICM is the image colorfulness measure, UISM is the sharpness measure, and UIConM is the contrast measure. Usually, $c_{1} = 0.0282$ , $c_{2} = 0.2953$ , and $c_{3} = 3.5753$ .
CCF [39]	$C C F = ω_{1} X_{1} + ω_{2} X_{2} + ω_{3} X_{3}$	$X_{1}$ is the color index, $X_{2}$ is the contrast index, and $X_{3}$ is the fog density index. Usually, $ω_{1} = 0.17593$ , $ω_{2} = 0.61759$ , and $ω_{3} = 0.33988$ .
FDUM [1]	$F D U M = ω_{1} X_{1} + ω_{2} X_{2} + ω_{3} X_{3}$	$X_{1}$ is the colorfulness index, $X_{2}$ is the contrast index, and $X_{3}$ is the sharpness index. Usually, $ω_{1} = 0.2982$ , $ω_{2} = 0.04439$ , and $ω_{3} = 0.028$ .
UEIQM [38]	$U E I Q M = w^{T} ϕ (U I F) + b$	UIF = [UICM; UISM; UIConM]. $ϕ (\cdot)$ is the radial basis function. $w$ and $b$ are the model parameters.
NUIQ [34]	$N U I Q = R a n k ([F_{c h r;} F_{l u m}])$	[ $F_{c h r}$ ; $F_{l u m}$ ] is the feature vector, and Rank ( $\cdot$ ) is the ranking model learned by applying SVMrank.
UWEQM [70]	$U W E Q M = \frac{1}{M} \sum_{m = 1}^{M} ψ_{L, {\hat{Θ}}_{m}} (U W I Q F)$	UWIQF is the feature vector, and $U W I Q F = {[H}_{T M} \| H_{M L C} {\| H}_{S L B P} \| H_{{R G B - C A C}_{S}} \| H_{{H S V - C A C}_{S}}]$ . $ψ_{L, {\hat{Θ}}_{m}}$ is the random regression tree model.
NR-UWIQA [71]	$N R - U W I Q A = \frac{1}{M} \sum_{m = 1}^{M} ψ_{L, {\hat{Θ}}_{m}} (H)$	$H$ represents the multiscale salient local binary pattern feature vector.

Index	Formula	Note
NIPQ [76]	$C_{R} = \| C_{d} (R O I) \| \times C_{f} (R O I)$	$\| \cdot \|$ represents normalization, $C_{R}$ represents the color quality of region of interest (ROI) block, $C_{R} \in (0, 1)$ . $C_{d} (\cdot)$ is the color richness index, and $C_{f} (\cdot)$ is the color fidelity index.
$K$ [77]	$K = \frac{{‖ u ‖}_{2}}{{‖ m ‖}_{2}}$	$u = (u_{a}, u_{b})$ , $σ = (σ_{a}, σ_{b})$ , and $m = (m_{a}, m_{b})$ are the mean, standard deviation, and mean absolute deviation vectors in the CIELab color space, respectively. $σ_{g r a y}$ is the gray standard deviation. $A$ and $ε$ are thresholds. $I_{a v g}^{c} = max ({a v g}_{x} I^{c} (x), 0.1)$ and $D_{σ} = ({‖ u ‖}_{2} - {‖ σ ‖}_{2}) / {‖ σ ‖}_{2}$ .
$K^{'}$ [77]	$K^{'} = \frac{{‖ u ‖}_{2}}{{‖ m ‖}_{2} \cdot max (\| min (σ_{g r a y}^{2} - A, 1) \| 1)}$
$φ^{c}$ [78]	$φ^{c} = {\frac{{max}_{k \in {r, g, b}} I_{avg}^{k}}{I_{avg}^{c}}}^{\frac{1}{\sqrt{max (ξ (D_{σ}), 1)}}}$ , $ξ (z) = {\begin{matrix} z, & z > ε \\ \infty, & z \leq ε \end{matrix}$

Metrics	Consistent	Opposite	Accuracy (Consistent/Total)	Time (fps)
BRISQUE	32	88	26.7%	7.1
NIQE	78	42	65%	4.7
UCIQE	115	5	95.8%	14.3
UIQM	117	3	97.5%	3.5
CCF	110	10	91.7%	1.4
FDUM	118	2	98.3%	0.5
NUIQ	69	51	57.5%	0.8

Metrics	SSIM	PSNR	PCQI	BRISQUE	NIQE	UCIQE	UIQM	CCF	NUIQ	FDUM
SROCC	0.9833	0.9262	0.9976	−0.5667	0.4059	0.9810	0.9441	0.9905	0.1429	0.9810
KROCC	0.9746	0.9111	0.9937	−0.6127	0.3073	0.9556	0.9048	0.9810	0.0762	0.9556
Time (fps)	27.6	18.8	1442.5	10.4	256.6	308.6	188. 0	89.1	4.2	58.7

	Images
Metrics	(a)	(b)	(c)	(d)	(e)	(f)	(g)
Ranking score ( $↓$ )	1	2	3	4	5	6	7
BRISQUE ( $↓$ )	68.4639	66.8536	55.6371	48.8604	48.6388	48.9981	48.3609
NIQE ( $↓$ )	39.7994	39.8014	39.8010	39.8001	39.8001	39.7985	39.7988
PCQI ( $↑$ )	1.0000	0.6692	0.5977	0.4694	0.4071	0.3203	0.2756
UCIQE ( $↑$ )	0.3527	0.3625	0.3535	0.3323	0.3205	0.3174	0.3095
UIQM ( $↑$ )	4.0451	3.7374	3.5247	3.3856	3.1969	3.3362	3.2807
CCF ( $↑$ )	7.3222	7.3918	6.4747	5.7039	5.3622	5.2191	5.1924
NUIQ ( $↑$ )	4.9565	5.2001	4.9207	1.0851	2.3851	−0.5962	−3.8807
SSIM ( $↑$ )	1.0000	0.9457	0.9412	0.9170	0.9012	0.8785	0.8650
PSNR ( $↑$ )	Inf	33.9504	31.5103	28.5326	27.3663	24.7831	23.2409
FDUM ( $↑$ )	0.1258	0.1419	0.0978	0.0849	0.0628	0.0599	0.0609

Acronym	Full Names	Acronym	Full Names
AMEE	Agaian Measure of Enhancement by Engropy	RGBD	Red green blue depth
BRISQUE	Blind/Referenceless Image Spatial Quality Evaluator	RMS	Root mean square
CCF	Color correction factor	RMSE	Root mean squared error
CIEDE2000	Commission Internationale de l’Eclairage (CIE) 2000 Delta E	RR-IQA	Reduced-reference image quality assessment
FDUM	Full-Reference Underwater Image Quality Assessment Metric	RUIE	Real-World Underwater Image Enhancement
FR-IQA	Full-reference image quality assessment	SAUD	Subjectively Annotated UIE Benchmark Dataset
IQA	Image quality assessment	SNR	Signal-to-noise ratio
KROCC	Kendall’s rank correlation coefficient	SQUID	Single-Image Quantitative Underwater Dataset
MAE	Mean absolute error	SSIM	Structural similarity
MAV	Mean annoyance value	SVM	Support vector machine
MOS	Mean opinion score	SVR	Support vector regression
MSE	Mean squared error	SROCC	Spearman’s rank correlation coefficient
MVG	Multivariate Gaussian	UCIQE	Underwater Color Image Quality Evaluation
NIQE	Natural Image Quality Evaluator	UEIQM	Underwater Enhancement Image Quality Metric
NR-IQA	No-reference image quality assessment	UEIQA	Underwater Enhanced Image Quality Assessment
NR-UWIQA	No-Reference Underwater Image Quality Assessment	UID-LEIA	Underwater Image Database of Laboratory of Embedded Systems and Integrated circuits Applications
NSS	Natural scene statistic	UIEB	Underwater Image Enhancement Benchmark
NUIQ	No-Reference Underwater Image Quality metric	UIQA	Underwater Image Quality Assessment
NIPQ	No-Reference Image Quality Predictor	UIQM	Underwater Image Quality Measure
PCQI	Patch-based contrast quality index	UWEQM	Underwater image Enhancement Quality Metric
PKU-EAQA	Peking University Enhancement Algorithm Quality Assessment	UWIQA	Underwater Image Quality Assessment
PSNR	Peak signal-to-noise ratio	Water-GAN	Water Generative Adversarial Networks

Abstract

Data availability

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Tables (8)

Equations (2)

Journal of the Optical Society of America A