Low Brightness Image Enhancement Based on Quantum Harmony Search Fuzzy Sets in NSCT Domain

Jie Zhang; Yipeng Liao; Lu Dai; Xueyan Li

doi:10.3788/LOP202158.2415008

Laser & Optoelectronics Progress, Volume. 58, Issue 24, 2415008(2021)

Low Brightness Image Enhancement Based on Quantum Harmony Search Fuzzy Sets in NSCT Domain

Jie Zhang¹, Yipeng Liao^2、*, Lu Dai¹, and Xueyan Li¹

Author Affiliations

¹College of Artificial Intelligence, Yango University, Fuzhou, Fujian 350015, China

²College of Physics and Information Engineering, Fuzhou University, Fuzhou, Fujian 350108, China

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Figures & Tables(13)

Fig. 1. Schematic diagram of HS algorithm

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Fig. 2. Decomposition diagram of NSCT

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Fig. 3. Enhancement and contrast of coin images. (a) Original coin image; (b) image of low frequency sub-band; (c) processing result of low frequency sub-band; (d) image of high frequency scale 1; (e) image of high frequency scale 2; (f) image of high frequency scale 3; (g) processing result of high frequency scale 1; (h) processing result of high frequency scale 2; (i) processing result of high frequency scale 3; (j) enhancement result obtained by proposed method; (k) enhancement result obtained by homomorphic filtering method; (l) enhancement result obtained by wavelet transform; (m) enhancement result obtained by Retinex algorithm; (n) enhancement result obtained by method in Ref. [7]; (o) enhancement result obtained by method in Ref. [8]; (p) enhancement result obtained by method based on original QHS optimize to fuzzy sets

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Fig. 4. Enhancement and contrast of human skeleton images. (a) Human skeleton image; (b) enhancement result obtained by proposed method; (c) enhancement result obtained by homomorphic filtering method; (d) enhancement result obtained by wavelet transform; (e) enhancement result obtained by Retinex algorithm; (f) enhancement result obtained by method in Ref. [7]; (g) enhancement result obtained by method in Ref. [8]; (h) enhancement result obtained by method based on original QHS optimize to fuzzy sets

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Fig. 5. Enhancement and contrast of infrared images. (a) Infrared image; (b) enhancement result obtained by proposed method; (c) enhancement result obtained by homomorphic filtering method; (d) enhancement result obtained by wavelet transform; (e) enhancement result obtained by Retinex algorithm; (f) enhancement result obtained by method in Ref. [7]; (g) enhancement result obtained by method in Ref. [8]; (h) enhancement result obtained by method based on original QHS optimize to fuzzy sets

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Fig. 6. Denoising and edge enhancement effect of coin noise images. (a) Original coin image; (b) noisy image; (c) enhancement result obtained by proposed method; (d) edge detection result of Fig. 6(c); (e) image of low frequency sub-band; (f) image of high frequency scale 1; (g) image of high frequency scale 2; (h) image of high frequency scale 3; (i) processing result of low frequency sub-band; (j) processing result of high frequency scale 1; (k) processing result of high frequency scale 2; (l) processing result of high frequency scale 3; (m) enhancement result obtained by homomorphic filtering method; (n) enhancement result obtained by wavelet transform; (o) enhancement result obtained by Retinex algorithm; (p) enhancement result obtained by method in Ref. [7]; (q) enhancement result obtained by method in Ref. [8]; (r) edge detection result of Fig. 6(a); (s) edge detection result of Fig. 6(m); (t) edge detection result of Fig. 6(n); (u) edge detection result of Fig. 6(o); (v) edge detection result of Fig. 6(p); (w) edge detection result of Fig. 6(q)

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Table 1. Benchmark functions

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Table 1. Benchmark functions

Function	Function formula	Parameter range of a_s	Optimal value
Rosenbrock	$f_{1} a = \overset{S - 1}{\sum_{s = 1}} [100 (a_{s + 1} - a_{s}^{2})^{2} + (a_{s} {- 1)}^{2}]$	[-10, 10]	0
Rastrigrin	$f_{2} a = \overset{S}{\sum_{s = 1}} [a_{s}^{2} - 10 \cos (2 π a_{s}^{2}) + 10]$	[-100, 100]	0
Schewefel	$f_{3} a = 418.9829 S + \overset{S}{\sum_{s = 1}} (- a_{s} \sin \sqrt[]{a_{s}})$	[-500, 500]	0
Shubert	$f_{4} a = 0.5 - \frac{si n^{2} \sqrt[]{a_{1}^{2} + a_{2}^{2}} - 0.5}{[1 + 0.001 (a_{1}^{2} + a_{2}^{2} {)]}^{2}}$	[-100, 100]	1

Table 2. Parameter testing of λ and Δθ
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Table 2. Parameter testing of λ and Δθ
Function Optimal value of λ Optimal value of Δθ
Rosenbrock 1.5 0.4π
Rastrigrin 1.7 0.4π
Schewefel 1.7 0.5π
Shubert 1.7 0.2π

Table 3. Performance testing of different algorithms

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Table 3. Performance testing of different algorithms

Algorithm	Average value	Optimal value	Worst value
HS	2.04×10^-1	1.82×10^-2	5.60×10^-1
QGA	1.56×10^-3	2.99×10^-5	1.40×10^-2
QHS	3.22×10^-5	2.15×10^-9	2.10×10^-4
QBFA	1.37×10^-5	5.89×10^-10	3.92×10^-4
Improved QHS	5.44×10^-6	7.21×10^-11	1.18×10^-4

Table 4. Quantitative comparison of enhancement effects of coin images

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Table 4. Quantitative comparison of enhancement effects of coin images

Method	Information entropy	Contrast ratio	Definition
Original image	6.3153	18.4254	10.5878
Homomorphic filtering	6.2122	52.6358	21.1163
Wavelet transform	6.0037	21.1810	11.0198
Retinex algorithm	5.7908	41.0980	16.8536
Method in Ref. [7]	7.7662	17.1940	11.6188
Method in Ref. [8]	6.0610	37.2307	16.6904
Method based on original QHS optimize to fuzzy sets	6.4412	38.5640	18.5762
Proposed method	6.8128	43.0273	18.6284

Table 5. Quantitative comparison of enhancement effects of human skeleton images

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Table 5. Quantitative comparison of enhancement effects of human skeleton images

Method	Information entropy	Contrast ratio	Definition
Original image	7.5286	7.0157	7.5282
Homomorphic filtering	6.9013	24.4868	16.5464
Wavelet transform	6.4962	9.4826	8.9901
Retinex algorithm	6.8555	15.4502	11.4918
Method in Ref. [7]	7.9618	7.1577	8.4743
Method in Ref. [8]	6.8649	16.1318	12.3101
Method based on original QHS optimize to fuzzy sets	6.6320	38.6521	11.5873
Proposed method	6.8128	43.0273	18.6284

Table 6. Quantitative comparison of enhancement effects of infrared images

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Table 6. Quantitative comparison of enhancement effects of infrared images

Method	Information entropy	Contrast ratio	Definition
Original image	5.9898	14.1011	8.8670
Homomorphic filtering	5.4445	45.2402	20.9698
Wavelet transform	6.2000	20.2866	11.6263
Retinex algorithm	5.5698	61.2892	25.0389
Method in Ref. [7]	7.0972	13.3551	9.2217
Method in Ref. [8]	4.1476	21.0801	10.6735
Method based on original QHS optimize to fuzzy sets	6.8268	40.0512	19.0563
Proposed method	6.9312	41.2877	19.9500

Table 7. PSNR and texture correlation of coin noisy images enhanced by different methods

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Table 7. PSNR and texture correlation of coin noisy images enhanced by different methods

Method	PSNR /dB	Texture correlation
Homomorphic filtering	7.1061	0.7746
Wavelet transform	10.1543	0.8655
Retinex algorithm	8.4954	0.7717
Method in Ref. [7]	10.4281	0.9254
Method in Ref. [8]	7.1022	0.9597
Proposed method	10.8431	0.9701

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Jie Zhang, Yipeng Liao, Lu Dai, Xueyan Li. Low Brightness Image Enhancement Based on Quantum Harmony Search Fuzzy Sets in NSCT Domain[J]. Laser & Optoelectronics Progress, 2021, 58(24): 2415008

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