Underwater image illumination estimation via an evolving extreme learning machine by an improved salp swarm algorithm

Junyi Yang; Mudan Cai; Chao Wang; Minhui Zheng; Sheng Chen

doi:10.1364/JOSAA.471594

Journal of the Optical Society of America A
Vol. 40,
Issue 3,
pp. 560-572
(2023)
•https://doi.org/10.1364/JOSAA.471594

Underwater image illumination estimation via an evolving extreme learning machine by an improved salp swarm algorithm

Junyi Yang, Mudan Cai, Chao Wang, Minhui Zheng, and Sheng Chen

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Junyi Yang, Mudan Cai, Chao Wang, Minhui Zheng, and Sheng Chen, "Underwater image illumination estimation via an evolving extreme learning machine by an improved salp swarm algorithm," J. Opt. Soc. Am. A 40, 560-572 (2023)

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Abstract

Underwater images have chromatic aberrations under different light sources and complex underwater scenes, which can lead to the wrong choice when using an underwater robot. To solve this problem, this paper proposes an underwater image illumination estimation model, which we call the modified salp swarm algorithm (SSA) extreme learning machine (MSSA-ELM). It uses the Harris hawks optimization algorithm to generate a high-quality SSA population, and uses a multiverse optimizer algorithm to improve the follower position that makes an individual salp carry out global and local searches with a different scope. Then, the improved SSA is used to iteratively optimize the input weights and hidden layer bias of ELM to form a stable MSSA-ELM illumination estimation model. The experimental results of our underwater image illumination estimations and predictions show that the average accuracy of the MSSA-ELM model is 0.9209. Compared to similar models, the MSSA-ELM model has the best accuracy for underwater image illumination estimation. The analysis results show that the MSSA-ELM model also has high stability and is significantly different from other models.

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Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

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Activation Functions
Fold	Sigmoid	Tribas	Hardlim	Sign	Sine
1	0.0231	0.0386	0.0315	0.0401	0.0278
2	0.0228	0.0371	0.0322	0.0398	0.0263
3	0.0234	0.0376	0.0319	0.0413	0.0272
4	0.0238	0.0381	0.0328	0.0422	0.0261
5	0.0229	0.0379	0.0334	0.0408	0.0268
6	0.0233	0.0383	0.0314	0.0391	0.0273
7	0.0227	0.0369	0.0323	0.0396	0.0276
8	0.0229	0.0373	0.0325	0.0403	0.0271
9	0.0241	0.0388	0.0318	0.0399	0.0265
10	0.0236	0.0375	0.0321	0.0409	0.0269
Average	0.0233	0.0378	0.0322	0.0404	0.0270

Population Size
Maximum Iterations	10	20	30	40	50
10	0.8916	0.9055	0.8951	0.9063	0.9081
20	0.8934	0.8991	0.9016	0.9088	0.9093
30	0.8973	0.9063	0.9128	0.9035	0.9108
40	0.8961	0.9064	0.9093	0.9057	0.9124
50	0.9059	0.9083	0.9116	0.9127	0.9089
60	0.9098	0.9156	0.9171	0.9155	0.9205
70	0.8993	0.9097	0.9129	0.9117	0.9221
80	0.9138	0.9169	0.9226	0.9221	0.9197
90	0.9174	0.9198	0.9229	0.9232	0.9229
100	0.9145	0.9201	0.9231	0.9228	0.9230

Population Size
Maximum Iterations	10	20	30	40	50
10	0.8497	0.8538	0.8696	0.8675	0.8704
20	0.8523	0.8691	0.8716	0.8684	0.8746
30	0.8597	0.8685	0.8739	0.8745	0.8751
40	0.8641	0.8693	0.8781	0.8718	0.8799
50	0.8699	0.8776	0.8789	0.8753	0.8808
60	0.8782	0.8839	0.8804	0.8817	0.8826
70	0.8838	0.8931	0.8993	0.8934	0.8911
80	0.8781	0.8976	0.9043	0.9036	0.9044
90	0.8931	0.8995	0.9034	0.9041	0.9038
100	0.8965	0.8993	0.9039	0.9041	0.9037

Number of Hidden Layer Nodes
Fold	15	30	45	60	75
1	0.0319	0.0298	0.0261	0.0271	0.0241
2	0.0303	0.0304	0.0275	0.0251	0.0265
3	0.0289	0.0283	0.0291	0.0267	0.0257
4	0.0293	0.0279	0.0283	0.0281	0.0246
5	0.0316	0.0297	0.0267	0.0258	0.0231
6	0.0291	0.0301	0.0289	0.0264	0.0253
7	0.0299	0.0288	0.0276	0.0274	0.0229
8	0.0318	0.0293	0.0278	0.0261	0.0232
9	0.0291	0.0292	0.0268	0.0263	0.0255
10	0.0301	0.0287	0.0281	0.0259	0.0261
Average	0.0302	0.0292	0.0277	0.0265	0.0247

Number of Hidden Layer Nodes
Fold	100	125	150	175	200
1	0.0218	0.0226	0.0254	0.0269	0.0298
2	0.0226	0.0259	0.0239	0.0273	0.0271
3	0.0241	0.0234	0.0251	0.0251	0.0254
4	0.0247	0.0251	0.0235	0.0239	0.0263
5	0.0239	0.0238	0.0262	0.0256	0.0245
6	0.0229	0.0253	0.0229	0.0243	0.0251
7	0.0242	0.0221	0.0268	0.0259	0.0269
8	0.0238	0.0246	0.0239	0.0267	0.0256
9	0.0245	0.0235	0.0261	0.0243	0.0274
10	0.0223	0.0251	0.0245	0.0271	0.0283
Average	0.0235	0.0241	0.0248	0.0257	0.0266

Algorithm	Parameter	Value
MPA-ELM	Population number	30
	Maximum iterations	80
	FADs	0.2
	P	0.5
SSA-ELM	Population number	30
SSA-ELM	Maximum iterations	80
DE-ELM	Population number	30
	Maximum iterations	80
	F	0.5
	CR	0.9
HHO-ELM	Population number	30
HHO-ELM	Maximum iterations	80
MVO-ELM	Population number	30
	Maximum iterations	80
	WEP Maximum	1
	WEP Minimum	0.2
WOA-ELM	Population number	30
WOA-ELM	Maximum iterations	80
GWO-ELM	Population number	30
GWO-ELM	Maximum iterations	80

Model	Average	Best	Worst	RMSE
MSSA-ELM	0.9209	0.9258	0.9136	0.0239
MPA-ELM	0.8913	0.9092	0.8807	0.0268
SSA-ELM	0.9042	0.9163	0.8898	0.0257
DE-ELM	0.8506	0.8714	0.8336	0.0288
HHO-ELM	0.8957	0.9103	0.8814	0.0263
MVO-ELM	0.9005	0.9195	0.8816	0.0261
WOA-ELM	0.8829	0.9037	0.8601	0.0276
GWO-ELM	0.8654	0.8905	0.8412	0.0279
ELM	0.8319	0.8403	0.8093	0.0295

Algorithm	Mean	Med	Best 25%	Worst 25%
Gray World [23]	7.33	6.28	1.36	11.24
Shades of Gray [24]	4.23	3.61	0.91	8.31
Interactive WB Method [25]	3.83	3.32	0.36	5.43
Data-Driven WB Method [26]	3.06	3.25	0.29	6.86
Second-Order Gray-Edge [27]	4.22	3.56	0.97	7.35
MSSA-ELM(ours)	3.49	3.18	0.83	5.16

Proposed Algorithm	Comparison Algorithm	$p$ Value
MSSA-ELM	MPA-ELM	0.2834
	SSA-ELM	0.7158
	DE-ELM	0.0095
	HHO-ELM	0.2178
	MVO-ELM	0.5124
	WOA-ELM	0.0336
	GWO-ELM	0.8376
	ELM	0.0406

Proposed Algorithm	Comparison Algorithm	$p$ Value
MSSA-ELM	MPA-ELM	8.13E-11
	SSA-ELM	3.81E-14
	HHO-ELM	5.67E-09
	MVO-ELM	2.94E-15
	GWO-ELM	4.11E-16

Abstract

Data availability

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Figures (14)

Tables (13)

Equations (30)

Journal of the Optical Society of America A