Stripe Binary Encoding Method Using Genetic Algorithms to Optimize Kernel Parameters of Error Diffusion

Changhui Zhu; Pei Zhou; Jiangping Zhu; Di You; Shiyong An

doi:10.3788/AOS202141.2110002

Acta Optica Sinica, Volume. 41, Issue 21, 2110002(2021)

Stripe Binary Encoding Method Using Genetic Algorithms to Optimize Kernel Parameters of Error Diffusion

Changhui Zhu¹, Pei Zhou^1,2, Jiangping Zhu^1,2、*, Di You², and Shiyong An²

Author Affiliations

¹College of Computer Science(software), Sichuan University, Chengdu, Sichuan 610065, China

²National Key Laboratory of Fundamental Science on Synthetic Vision, Sichuan University, Chengdu, Sichuan 610065, China

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Abstract Get PDF(in Chinese)

Figures & Tables(15)

Fig. 1. Mechanism of error diffusion. (a) Original image; (b) image after error diffusion; (c) image after Gaussian filter; (d) gray values of line 128 in Fig.1 (a) and Fig.1 (c)

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Fig. 2. Phase error distributions of periodic binary codes with different fringe sizes under different Gaussian windows. (a) 5 pixel×5 pixel; (b) 9 pixel×9 pixel; (c) 13 pixel×13 pixel

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Fig. 3. Error comparison of different fringe patterns in diffused kernel coding. (a) Diffusion nuclei optimized under different size windows; (b) encoded images at 36 pixel periods; (c) encoded images with 12-120 pixel cycles; (d) phase errors under different periodicity

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Fig. 4. Optimal convergence results of error diffusion kernel under different conditions. (a) T=36 pixel, k=5,9,13 pixel, respectively; (b) k=5 pixel, T=36,72,108 pixel, respectively

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Fig. 5. Fringe pattern graphs generated by different algorithms and their local enlargements. (a) Ideal sinusoidal fringe pattern at T=36 pixel; (b) H algorithm; (c) F algorithm; (d) proposed algorithm

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Fig. 6. Phase errors and local magnification of different algorithms in Gaussian windows of different sizes. (a) 5 pixel×5 pixel; (b) 9 pixel×9 pixel; (c) 13 pixel×13 pixel

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Fig. 7. Layout of experimental system

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Fig. 8. Effect of defocusing square wave stripes. (a) Square wave fringe image at 72 pixel period before defocusing; (b) square wave fringe image captured after defocusing; (c) effect of defocus degree on gray value of square wave fringe boundary

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Fig. 9. Results of different algorithms. (a) Proposed algorithm; (b) F algorithm; (c) H algorithm

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Fig. 10. Phase errors and local magnification at different defocusing degrees. (a) Small defocus, σ≈5/3; (b) medium defocus, σ≈9/3; (c) large defocus, σ≈13/3

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Fig. 11. Average modulation of fringe images with different periods under different defocusing degrees. (a) Small defocus, σ≈5/3; (b) medium defocus, σ≈9/3; (c) large defocus, σ≈13/3

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Fig. 12. Phase error changes with the image blur degree under different blur degree. (a) k=5 pixel; (b) k=9 pixel; (c) k=13 pixel

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Table 1. Influence of number of phase shift steps on optimization error

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Table 1. Influence of number of phase shift steps on optimization error

Parameter	1	2	3	4	5
Kernel-3	$\frac{1}{95} [\begin{array}{l} \begin{array}{l} 0 \\ 36 \end{array} & \begin{array}{l} 0 \\ 4 \end{array} & \begin{array}{l} 55 \\ 0 \end{array} \end{array}]$	$\frac{1}{101} [\begin{array}{l} \begin{array}{l} 0 \\ 12 \end{array} & \begin{array}{l} 0 \\ 43 \end{array} & \begin{array}{l} 43 \\ 3 \end{array} \end{array}]$	$\frac{1}{101} [\begin{array}{l} \begin{array}{l} 0 \\ 23 \end{array} & \begin{array}{l} 0 \\ 43 \end{array} & \begin{array}{l} 33 \\ 2 \end{array} \end{array}]$	$\frac{1}{63} [\begin{array}{l} \begin{array}{l} 0 \\ 7 \end{array} & \begin{array}{l} 0 \\ 29 \end{array} & \begin{array}{l} 26 \\ 1 \end{array} \end{array}]$	$\frac{1}{130} [\begin{array}{l} \begin{array}{l} 0 \\ 16 \end{array} & \begin{array}{l} 0 \\ 60 \end{array} & \begin{array}{l} 53 \\ 1 \end{array} \end{array}]$
E_total-3	0.0051	0.0054	0.0053	0.0053	0.0053
Kernel-4	$\frac{1}{135} [\begin{array}{l} \begin{array}{l} 0 \\ 28 \end{array} & \begin{array}{l} 0 \\ 61 \end{array} & \begin{array}{l} 45 \\ 1 \end{array} \end{array}]$	$\frac{1}{172} [\begin{array}{l} \begin{array}{l} 0 \\ 50 \end{array} & \begin{array}{l} 0 \\ 54 \end{array} & \begin{array}{l} 63 \\ 5 \end{array} \end{array}]$	$\frac{1}{149} [\begin{array}{l} \begin{array}{l} 0 \\ 35 \end{array} & \begin{array}{l} 0 \\ 61 \end{array} & \begin{array}{l} 53 \\ 0 \end{array} \end{array}]$	$\frac{1}{93} [\begin{array}{l} \begin{array}{l} 0 \\ 24 \end{array} & \begin{array}{l} 0 \\ 36 \end{array} & \begin{array}{l} 32 \\ 1 \end{array} \end{array}]$	$\frac{1}{176} [\begin{array}{l} \begin{array}{l} 0 \\ 54 \end{array} & \begin{array}{l} 0 \\ 58 \end{array} & \begin{array}{l} 63 \\ 1 \end{array} \end{array}]$
E_total-4	0.0050	0.0051	0.0050	0.0048	0.0049
Kernel-6	$\frac{1}{56} [\begin{array}{l} \begin{array}{l} 0 \\ 18 \end{array} & \begin{array}{l} 0 \\ 10 \end{array} & \begin{array}{l} 27 \\ 1 \end{array} \end{array}]$	$\frac{1}{145} [\begin{array}{l} \begin{array}{l} 0 \\ 40 \end{array} & \begin{array}{l} 0 \\ 60 \end{array} & \begin{array}{l} 44 \\ 1 \end{array} \end{array}]$	$\frac{1}{109} [\begin{array}{l} \begin{array}{l} 0 \\ 22 \end{array} & \begin{array}{l} 0 \\ 53 \end{array} & \begin{array}{l} 33 \\ 1 \end{array} \end{array}]$	$\frac{1}{130} [\begin{array}{l} \begin{array}{l} 0 \\ 28 \end{array} & \begin{array}{l} 0 \\ 62 \end{array} & \begin{array}{l} 40 \\ 0 \end{array} \end{array}]$	$\frac{1}{117} [\begin{array}{l} \begin{array}{l} 0 \\ 15 \end{array} & \begin{array}{l} 0 \\ 47 \end{array} & \begin{array}{l} 54 \\ 1 \end{array} \end{array}]$
E_total-6	0.0049	0.0047	0.0046	0.0045	0.0049

Table 2. Phase errors of coded binary graphs with different algorithms

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Table 2. Phase errors of coded binary graphs with different algorithms

Pitch-width /pixel	Small defocus(σ≈5/3)		Medium defocus(σ≈9/3)		Large defocus(σ≈13/3)
Pitch-width /pixel	F /%	H /%	F /%	H /%	F /%	H /%
12	40.82			-14.61			50.16	8.75	20.62	3.53
24	50.10			17.65			54.66	9.01	35.38	8.81
36	38.78			5.12			64.37	18.48	43.86	3.34
48	32.32			3.78			58.60	15.18	27.41	6.46
60	23.92			-0.69			52.79	12.13	20.26	4.48
72	20.80			2.72			42.53	10.37	31.07	0.13
84	10.12			1.45			37.51	15.88	31.11	2.95
96	10.68			1.44			26.76	6.41	18.02	13.51
108	6.04			2.54			26.76	4.15	21.39	2.46
120	13.08			1.38			23.47	7.56	16.77	10.41

Table 3. [in Chinese]
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Table 3. [in Chinese]
Pitch-width /pixel Proposed algorithm Ref. [20] Ref. [24] Ref. [25]
36 68.22 100.69 0.02 23064.00
72 71.77 232.74 25.43 23736.00
120 72.97 380.43 18420.00 26526.00

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Changhui Zhu, Pei Zhou, Jiangping Zhu, Di You, Shiyong An. Stripe Binary Encoding Method Using Genetic Algorithms to Optimize Kernel Parameters of Error Diffusion[J]. Acta Optica Sinica, 2021, 41(21): 2110002

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