Color Difference Calculation Method for Three-Dimensional Printed Spheres

Fig. 8. Scatter distributions of the original ΔE and PF_3D optimized ΔE'. (a) CIELAB color difference is 0.0—5.0; (b) CIELAB color difference is greater than 5.0

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Fig. 9. Chromaticity-ellipses plotted in different diagrams from different spaces. (a) a^*b^* plane from CIELAB space; (b) a'b'plane from CAM16-SCD space

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Table 1. Information of the experiments
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Table 1. Information of the experiments
Exp. Colorcenters Samplepairs Glossiness Measuredinstruments Observers Age Total assessments
Ⅰ 5 150 Matte X-Rite eXact 33 19—26 6450
Ⅱ 5 50 Gloss X-Rite Ci64 26 19—24 2500

Table 2. Chromaticity values of the standard sphere

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Table 2. Chromaticity values of the standard sphere

Color	Matte					Gloss
Color	$L_{10}^{*}$	$a_{10}^{*}$	$b_{10}^{*}$	$C_{ab, 10}^{*}$	$h_{ab, 10}^{*}$	$L_{10}^{*}$	$a_{10}^{*}$	$b_{10}^{*}$	$C_{ab, 10}^{*}$	$h_{ab, 10}^{*}$
Gray	62.76	0.17	0.48	0.51	70.58	59.97	0.18	1.37	1.38	82.35
Red	48.38	33.06	19.77	38.52	30.88	50.85	41.82	33.53	53.60	38.72
Yellow	82.37	-8.52	43.52	44.35	101.08	86.96	-9.01	51.69	52.47	99.89
Green	59.04	-29.97	0.22	29.97	179.58	58.10	-34.81	3.53	34.99	174.21
Blue	37.33	5.14	-26.70	27.19	280.89	40.75	5.25	-28.45	28.93	280.45

Table 3. Observer variability in visual experiments
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Table 3. Observer variability in visual experiments
Item Exp. I (matte) Exp. II (gloss)
Intra-observer Inter-observer Intra-observer Inter-observer
Max 37.0 55.4 36.8 45.9
Min 12.4 21.9 10.8 19.5
Mean 21.9 31.2 20.0 30.3

Table 4. Performance of original color difference formulas in terms of STRESS

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Table 4. Performance of original color difference formulas in terms of STRESS

Magnitudes	Formulas
	CIELAB	CIEDE2000	CIECAM02-			CAM16-
	CIELAB	CIEDE2000	LCD	SCD	UCS	LCD	SCD	UCS
0—5 (ΔE_mean=3.01)	41.3	43.1	43.1	42.3	42.5	42.6	41.4	41.8
5—13 (ΔE_mean=7.15)	24.4	26.8	28.4	24.6	26.1	26.8	23.3	24.6
Total	34.3	36.6	37.0	34.7	35.6	36.1	33.9	34.7

Table 5. a, b, and k_L factors of color difference formula with different optimized methods

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Table 5. a, b, and k_L factors of color difference formula with different optimized methods

Formulas	Factor	CIELAB	CIEDE2000	CIECAM02-		CAM16-
Formulas	Factor	CIELAB	CIEDE2000	SCD	UCS	SCD	UCS
PF_2D	a	1.26	1.43	1.45	1.3		1.41
	b	0.55	0.7	0.75	0.75		0.63
Optimized 1 (PF_3D∶a、b)	a	2.10	2.02	1.87	2.05	1.94	2.02
	b	0.55	0.50	0.53	0.52	0.50	0.53
Optimized 2 (k_L)	k_L	1.43	1.22	1.66	1.63	1.60	1.55
	a	2.21	2.27	2.11	2.29	2.12	2.30
Optimized 3 (a、b、k_L)	b	0.57	0.50	0.54	0.56	0.54	0.56
	k_L	1.56	1.77	2.25	2.09	2.24	2.08

Table 6. Performance of original and optimized color difference formulas

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Table 6. Performance of original and optimized color difference formulas

STRESS	CIELAB	CIEDE2000	CIECAM02-		CAM16-
STRESS	CIELAB	CIEDE2000	SCD	UCS	SCD	UCS
Original	34.3	36.6	34.7	35.6	33.9	34.7
PF_2D	29.1	28.9	29.1	30.1		27.6
Optimized 1	29.1	27.0	27.0	27.9	26.2	27.2
Optimized 2	32.9	35.9	33.3	32.0	32.8	31.6
Optimized 3	28.1	25.3	24.9	24.8	24.0	23.9

Table 7. F test results of the modified and the original color difference formula

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Table 7. F test results of the modified and the original color difference formula

F-test	CIELAB	CIEDE2000	CIECAM02-		CAM16-
F-test	CIELAB	CIEDE2000	SCD	UCS	SCD	UCS
Original	1.00	1.00	1.00	1.00	1.00	1.00
PF_2D	0.72	0.63	0.70	0.71		0.63
Optimized 1	0.72	0.55	0.60	0.62	0.60	0.61
Optimized 2	0.92	0.96	0.92	0.81	0.94	0.83
Optimized 3	0.67	0.48	0.52	0.48	0.50	0.47

Table 8. Performance of the original formula and the optimized color difference formula (Exp.Ⅱ)

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Table 8. Performance of the original formula and the optimized color difference formula (Exp.Ⅱ)

Formulas	CIELAB	CIEDE2000	CIECAM02-		CAM16-
Formulas	CIELAB	CIEDE2000	SCD	UCS	SCD	UCS
Original	25.8	25.4	25.5	25.7	25.9	26.0
PF_2D	18.6	17.1	18.3	19.1		17.6
Optimized 1	18.6	16.8	16.9	17.9	17.1	17.7
Optimized 2	27.8	24.3	23.3	21.3	24.1	22.3
Optimized 3	19.7	14.2	13.9	13.8	13.8	13.9

Table 9. F test results of the modified and the original color difference formula for glossy sphere samples
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Table 9. F test results of the modified and the original color difference formula for glossy sphere samples
F-test CIELAB CIEDE2000 CIECAM02- CAM16-
SCD UCS SCD UCS
PF_2D 0.52 0.45 0.52 0.55 0.46
Optimized 1 0.52 0.44 0.44 0.48 0.43 0.47
Optimized 2 1.17 0.92 0.83 0.69 0.87 0.73
Optimized 3 0.58 0.31 0.30 0.29 0.28 0.29

Table 10. Performance of the original formula and the optimized color difference formula

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Table 10. Performance of the original formula and the optimized color difference formula

Formulas		CIELAB	CIEDE2000	CIECAM02-		CAM16-
Formulas		CIELAB	CIEDE2000	SCD	UCS	SCD	UCS
Original	STRESS	32.8	34.7	33.1	33.9	32.5	33.2
PF_2D	STRESS	27.3	26.9	27.2	28.1		25.8
	F-test	0.69	0.60	0.67	0.69		0.60
PF_3D	STRESS	27.3	25.1	25.1	26.1	24.5	25.4
	F-test	0.69	0.53	0.58	0.59	0.57	0.59

Table 11. Sizes of each chromaticity ellipses

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Table 11. Sizes of each chromaticity ellipses

CIELAB	Gray	Red	Yellow	Green	Blue	Mean	STDEV
Matte	1.88	1.78	2.05	1.82	2.28	1.96	0.21
Gloss	2.09	1.87	1.77	1.82	2.31	1.97	0.22
CAM16-SCD	Gray	Red	Yellow	Green	Blue	Mean	STDEV
Matte	1.90	1.77	1.94	1.83	2.10	1.91	0.13
Gloss	2.20	1.79	1.89	1.79	1.92	1.92	0.17

Table 12. STRESS values for simulated chromaticity ellipses of matte and glossy spheres samples
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Table 12. STRESS values for simulated chromaticity ellipses of matte and glossy spheres samples
Color space Gray Red Yellow Green Blue Mean
CIELAB 10.74 11.55 23.20 1.80 6.46 10.75
CAM16-SCD 17.18 4.69 16.49 6.85 8.95 10.83

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Jie Pan, Min Huang, Yu Li, Yu Wang, Shuyi Zhao, Xiu Li, Yu Liu. Color Difference Calculation Method for Three-Dimensional Printed Spheres[J]. Acta Optica Sinica, 2021, 41(23): 2333001

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Paper Information

Category: Vision, Color, and Visual Optics

Received: May. 26, 2021

Accepted: Jun. 17, 2021

Published Online: Dec. 10, 2021

The Author Email: Huang Min (huangmin@bigc.edu.cn)

DOI:10.3788/AOS202141.2333001

Topics

laser devices and laser physics

Lasers and Laser Optics

Laser physics

laser manufacturing

Instrumentation, Measurement and Metrology

Table 1. Information of the experiments

Table 1. Information of the experiments

Table 2. Chromaticity values of the standard sphere

Table 2. Chromaticity values of the standard sphere

Table 3. Observer variability in visual experiments

Table 3. Observer variability in visual experiments

Table 4. Performance of original color difference formulas in terms of STRESS

Table 4. Performance of original color difference formulas in terms of STRESS

Table 5. a, b, and kL factors of color difference formula with different optimized methods

Table 5. a, b, and kL factors of color difference formula with different optimized methods

Table 6. Performance of original and optimized color difference formulas

Table 6. Performance of original and optimized color difference formulas

Table 7. F test results of the modified and the original color difference formula

Table 7. F test results of the modified and the original color difference formula

Table 8. Performance of the original formula and the optimized color difference formula (Exp.Ⅱ)

Table 8. Performance of the original formula and the optimized color difference formula (Exp.Ⅱ)

Table 9. F test results of the modified and the original color difference formula for glossy sphere samples

Table 9. F test results of the modified and the original color difference formula for glossy sphere samples

Table 10. Performance of the original formula and the optimized color difference formula

Table 10. Performance of the original formula and the optimized color difference formula

Table 11. Sizes of each chromaticity ellipses

Table 11. Sizes of each chromaticity ellipses

Table 12. STRESS values for simulated chromaticity ellipses of matte and glossy spheres samples

Table 12. STRESS values for simulated chromaticity ellipses of matte and glossy spheres samples

Table 5. a, b, and k_L factors of color difference formula with different optimized methods

Table 5. a, b, and k_L factors of color difference formula with different optimized methods