Color representation using statistical pattern recognition

Jussi Parkkinen; Timo Jaaskelainen

doi:10.1364/AO.26.004240

Applied Optics
Vol. 26,
Issue 19,
pp. 4240-4245
(1987)
•https://doi.org/10.1364/AO.26.004240

Color representation using statistical pattern recognition

Jussi Parkkinen and Timo Jaaskelainen

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Jussi Parkkinen and Timo Jaaskelainen, "Color representation using statistical pattern recognition," Appl. Opt. 26, 4240-4245 (1987)

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Abstract

A statistical pattern recognition method, the subspace method, closely related to the principal component analysis was used in color recognition. It is shown that color spectra can be accurately reconstructed using a few principal spectra. Further, it is shown that our method is capable of discriminating samples which were inseparable using usual methods.

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WAVE-LENGTH	SAMPLE NUMBER
nm	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
400	7.52	33.90	0.00	0.00	1.20	26.40	0.96	36.50	42.70	24.00	63.95	63.60	0.00	38.00	4.00	3.37	3.84	3.80	1.78	1.30	0.00	41.20	35.30
410	14.42	43.50	0.00	0.00	0.60	40.30	3.16	40.40	46.10	26.00	70.22	68.90	0.00	46.00	8.00	9.46	2.64	3.82	1.12	5.17	0.00	46.70	39.30
420	20.69	53.10	0.00	0.00	0.80	54.50	8.25	43.60	49.40	29.00	73.98	72.60	0.00	50.00	12.00	0.28	0.15	3.30	6.76	2.77	0.00	49.00	43.10
430	27.59	57.50	0.00	1.00	5.98	62.10	15.00	44.10	50.00	31.00	73.35	73.50	0.00	53.00	17.00	0.73	0.55	0.17	0.25	0.12	1.39	53.70	49.40
440	34.48	58.10	4.20	8.81	19.00	63.50	22.60	43.20	49.40	32.20	71.47	72.40	0.00	55.30	22.00	1.23	1.15	0.51	0.59	0.43	0.11	52.20	53.30
450	38.24	56.70	18.20	17.40	30.10	61.80	30.30	40.90	47.40	32.70	67.71	70.20	0.00	55.80	30.00	1.61	1.83	1.15	1.02	0.97	0.32	50.60	53.30
460	38.87	54.20	30.20	20.90	33.80	58.20	33.20	36.70	43.60	31.40	64.58	66.90	0.00	55.40	36.00	1.71	2.56	1.99	1.39	1.44	0.49	52.50	52.50
470	35.74	51.00	35.90	21.60	32.10	53.00	29.60	31.60	38.50	28.80	61.44	62.80	0.22	55.00	40.00	1.57	3.24	2.69	1.51	1.42	0.42	53.70	53.30
480	28.21	47.50	37.20	20.50	27.00	46.40	22.40	26.40	33.10	25.60	56.43	58.00	0.43	53.00	42.00	1.41	3.76	3.11	1.35	0.96	0.19	51.40	52.50
490	17.55	43.80	35.10	18.00	20.20	38.60	14.10	21.70	28.40	22.20	52.66	53.00	0.39	51.50	41.00	0.83	3.78	2.93	0.95	0.44	6.24	45.90	51.40
500	8.15	39.70	28.80	14.40	11.10	29.50	7.30	18.00	24.40	19.30	46.39	47.70	0.15	48.00	36.00	0.42	3.29	2.35	0.52	0.14	0.00	38.80	48.20
510	2.51	35.70	18.80	10.10	4.39	20.30	2.64	14.90	21.10	16.80	40.75	42.50	0.00	44.50	32.00	0.17	2.16	1.32	0.13	0.00	0.00	30.20	43.90
520	0.63	31.80	8.90	5.60	1.66	11.90	0.50	12.60	18.20	14.20	36.36	38.20	0.00	39.50	23.00	0.00	0.85	0.35	0.00	0.00	0.00	26.30	40.00
530	0.00	27.70	2.35	2.52	0.35	5.44	0.00	11.00	16.20	12.70	32.60	34.60	0.00	33.00	13.00	0.00	0.00	0.00	0.00	0.00	0.00	19.60	32.50
540	0.00	22.80	0.33	0.64	0.00	1.95	0.00	10.00	15.10	11.80	29.47	31.30	0.00	25.00	6.00	0.00	0.00	0.00	0.00	0.00	0.00	16.50	27.50
550	0.00	18.20	0.00	0.10	0.00	0.58	0.00	9.10	13.80	11.00	26.33	28.40	0.00	18.00	2.00	0.00	0.00	0.00	0.00	0.00	0.00	13.70	18.40
560	0.00	13.70	0.00	0.00	0.00	0.18	0.00	8.10	12.60	9.76	25.08	26.50	0.00	12.00	0.50	0.00	0.00	0.00	0.00	0.00	0.00	13.30	15.30
570	0.00	9.60	0.00	0.00	0.00	0.00	0.00	7.40	11.60	8.81	23.82	25.20	0.00	8.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.40	9.80
580	0.00	6.30	0.00	0.00	0.00	0.00	0.00	7.20	11.10	8.50	22.57	23.70	0.00	5.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.00	8.20
590	0.00	3.90	0.00	0.00	0.00	0.00	0.00	6.90	10.80	8.29	21.32	22.20	0.00	4.50	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.80	6.30
600	0.00	2.60	0.00	0.00	0.00	0.00	0.00	6.20	10.00	7.56	20.06	20.80	0.00	3.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	14.90	5.90
610	0.00	1.60	0.00	0.00	0.00	0.00	0.00	5.20	8.80	6.45	19.44	20.10	0.00	3.60	0.00	0.00	0.00	0.00	0.00	0.00	0.00	16.90	4.70
620	0.00	1.00	0.00	0.00	0.00	0.00	0.00	4.20	7.40	5.13	18.81	19.30	0.00	3.60	0.00	0.00	0.00	0.00	0.00	0.00	0.00	16.90	5.50
630	0.00	0.50	0.00	0.00	0.00	0.00	0.00	3.40	6.00	4.17	17.55	18.50	0.00	3.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	19.20	5.10
640	0.00	0.20	0.00	0.00	0.00	0.00	0.00	2.90	5.10	3.47	17.55	17.90	0.00	4.20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	21.20	5.50
650	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.60	4.80	3.16	17.55	17.90	0.00	4.30	0.75	0.00	0.00	0.00	0.00	0.00	0.00	31.00	6.70
660	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.60	4.90	3.09	18.18	18.30	0.00	3.90	1.00	0.00	0.00	0.00	0.00	0.00	0.00	46.30	7.10
670	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.70	5.00	3.16	18.18	18.60	0.00	3.50	1.50	0.00	0.00	0.00	0.00	0.00	0.00	48.20	5.90
680	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.70	4.90	3.16	17.55	18.20	0.44	3.70	1.50	8.50	0.00	0.00	0.00	0.00	0.00	51.40	6.70
690	0.00	0.00	0.00	0.20	0.25	0.00	0.00	2.60	4.80	3.16	16.93	17.50	5.02	5.50	1.00	3.33	0.00	0.00	0.00	0.00	0.00	53.30	8.60
700	0.63	0.00	0.49	2.24	0.85	0.00	0.00	2.80	5.00	3.3	18.18	17.70	18.70	11.50	1.00	7.30	0.00	0.00	0.00	0.00	0.00	55.70	17.30

Number of eigenvector	Percent	Percent
1	79.5	79.5
2	10.2	89.7
3	4.4	94.1
4	3.9	98.0
5	1.0	99.0
6	0.5	99.5
7	0.3	99.8
8	0.1	99.9
9	0.1	100.0
10	0.0	100.0

Measurement no.	Plate no. 4		Plate no. 5
Measurement no.	x	y	x	y
1	0.309	0.317	0.309	0.316
2	0.319	0.317	0.310	0.318
3	0.310	0.318	0.311	0.318
4	0.315	0.322	0.312	0.317
5	0.310	0.317	0.308	0.316
6	0.310	0.313	0.312	0.315
7	0.310	0.317	0.311	0.316
8	0.311	0.318	0.310	0.316
9	0.310	0.317	0.310	0.317
10	0.311	0.318	0.312	0.318
11	0.311	0.319	0.308	0.313
12	0.308	0.313	0.307	0.311
13	0.309	0.314	0.311	0.317
14	0.312	0.318	0.308	0.314
15	0.311	0.318	0.311	0.318
16	0.311	0.317	0.315	0.323
17	0.310	0.317	0.309	0.315
18	0.309	0.319	0.308	0.316
19	0.313	0.320	0.313	0.315

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

WAVE-LENGTH	SAMPLE NUMBER
nm	1	2	3	4	5	6	7	8	9	10	11	12	13	14	15	16	17	18	19	20	21	22	23
400	7.52	33.90	0.00	0.00	1.20	26.40	0.96	36.50	42.70	24.00	63.95	63.60	0.00	38.00	4.00	3.37	3.84	3.80	1.78	1.30	0.00	41.20	35.30
410	14.42	43.50	0.00	0.00	0.60	40.30	3.16	40.40	46.10	26.00	70.22	68.90	0.00	46.00	8.00	9.46	2.64	3.82	1.12	5.17	0.00	46.70	39.30
420	20.69	53.10	0.00	0.00	0.80	54.50	8.25	43.60	49.40	29.00	73.98	72.60	0.00	50.00	12.00	0.28	0.15	3.30	6.76	2.77	0.00	49.00	43.10
430	27.59	57.50	0.00	1.00	5.98	62.10	15.00	44.10	50.00	31.00	73.35	73.50	0.00	53.00	17.00	0.73	0.55	0.17	0.25	0.12	1.39	53.70	49.40
440	34.48	58.10	4.20	8.81	19.00	63.50	22.60	43.20	49.40	32.20	71.47	72.40	0.00	55.30	22.00	1.23	1.15	0.51	0.59	0.43	0.11	52.20	53.30
450	38.24	56.70	18.20	17.40	30.10	61.80	30.30	40.90	47.40	32.70	67.71	70.20	0.00	55.80	30.00	1.61	1.83	1.15	1.02	0.97	0.32	50.60	53.30
460	38.87	54.20	30.20	20.90	33.80	58.20	33.20	36.70	43.60	31.40	64.58	66.90	0.00	55.40	36.00	1.71	2.56	1.99	1.39	1.44	0.49	52.50	52.50
470	35.74	51.00	35.90	21.60	32.10	53.00	29.60	31.60	38.50	28.80	61.44	62.80	0.22	55.00	40.00	1.57	3.24	2.69	1.51	1.42	0.42	53.70	53.30
480	28.21	47.50	37.20	20.50	27.00	46.40	22.40	26.40	33.10	25.60	56.43	58.00	0.43	53.00	42.00	1.41	3.76	3.11	1.35	0.96	0.19	51.40	52.50
490	17.55	43.80	35.10	18.00	20.20	38.60	14.10	21.70	28.40	22.20	52.66	53.00	0.39	51.50	41.00	0.83	3.78	2.93	0.95	0.44	6.24	45.90	51.40
500	8.15	39.70	28.80	14.40	11.10	29.50	7.30	18.00	24.40	19.30	46.39	47.70	0.15	48.00	36.00	0.42	3.29	2.35	0.52	0.14	0.00	38.80	48.20
510	2.51	35.70	18.80	10.10	4.39	20.30	2.64	14.90	21.10	16.80	40.75	42.50	0.00	44.50	32.00	0.17	2.16	1.32	0.13	0.00	0.00	30.20	43.90
520	0.63	31.80	8.90	5.60	1.66	11.90	0.50	12.60	18.20	14.20	36.36	38.20	0.00	39.50	23.00	0.00	0.85	0.35	0.00	0.00	0.00	26.30	40.00
530	0.00	27.70	2.35	2.52	0.35	5.44	0.00	11.00	16.20	12.70	32.60	34.60	0.00	33.00	13.00	0.00	0.00	0.00	0.00	0.00	0.00	19.60	32.50
540	0.00	22.80	0.33	0.64	0.00	1.95	0.00	10.00	15.10	11.80	29.47	31.30	0.00	25.00	6.00	0.00	0.00	0.00	0.00	0.00	0.00	16.50	27.50
550	0.00	18.20	0.00	0.10	0.00	0.58	0.00	9.10	13.80	11.00	26.33	28.40	0.00	18.00	2.00	0.00	0.00	0.00	0.00	0.00	0.00	13.70	18.40
560	0.00	13.70	0.00	0.00	0.00	0.18	0.00	8.10	12.60	9.76	25.08	26.50	0.00	12.00	0.50	0.00	0.00	0.00	0.00	0.00	0.00	13.30	15.30
570	0.00	9.60	0.00	0.00	0.00	0.00	0.00	7.40	11.60	8.81	23.82	25.20	0.00	8.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.40	9.80
580	0.00	6.30	0.00	0.00	0.00	0.00	0.00	7.20	11.10	8.50	22.57	23.70	0.00	5.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.00	8.20
590	0.00	3.90	0.00	0.00	0.00	0.00	0.00	6.90	10.80	8.29	21.32	22.20	0.00	4.50	0.00	0.00	0.00	0.00	0.00	0.00	0.00	11.80	6.30
600	0.00	2.60	0.00	0.00	0.00	0.00	0.00	6.20	10.00	7.56	20.06	20.80	0.00	3.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	14.90	5.90
610	0.00	1.60	0.00	0.00	0.00	0.00	0.00	5.20	8.80	6.45	19.44	20.10	0.00	3.60	0.00	0.00	0.00	0.00	0.00	0.00	0.00	16.90	4.70
620	0.00	1.00	0.00	0.00	0.00	0.00	0.00	4.20	7.40	5.13	18.81	19.30	0.00	3.60	0.00	0.00	0.00	0.00	0.00	0.00	0.00	16.90	5.50
630	0.00	0.50	0.00	0.00	0.00	0.00	0.00	3.40	6.00	4.17	17.55	18.50	0.00	3.80	0.00	0.00	0.00	0.00	0.00	0.00	0.00	19.20	5.10
640	0.00	0.20	0.00	0.00	0.00	0.00	0.00	2.90	5.10	3.47	17.55	17.90	0.00	4.20	0.00	0.00	0.00	0.00	0.00	0.00	0.00	21.20	5.50
650	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.60	4.80	3.16	17.55	17.90	0.00	4.30	0.75	0.00	0.00	0.00	0.00	0.00	0.00	31.00	6.70
660	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.60	4.90	3.09	18.18	18.30	0.00	3.90	1.00	0.00	0.00	0.00	0.00	0.00	0.00	46.30	7.10
670	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.70	5.00	3.16	18.18	18.60	0.00	3.50	1.50	0.00	0.00	0.00	0.00	0.00	0.00	48.20	5.90
680	0.00	0.00	0.00	0.00	0.00	0.00	0.00	2.70	4.90	3.16	17.55	18.20	0.44	3.70	1.50	8.50	0.00	0.00	0.00	0.00	0.00	51.40	6.70
690	0.00	0.00	0.00	0.20	0.25	0.00	0.00	2.60	4.80	3.16	16.93	17.50	5.02	5.50	1.00	3.33	0.00	0.00	0.00	0.00	0.00	53.30	8.60
700	0.63	0.00	0.49	2.24	0.85	0.00	0.00	2.80	5.00	3.3	18.18	17.70	18.70	11.50	1.00	7.30	0.00	0.00	0.00	0.00	0.00	55.70	17.30

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

Abstract

Cited By

Figures (5)

Tables (4)

Equations (11)

Applied Optics

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—

Number of eigenvectors	Data set I rotation		Data set II rotation
	no	yes	no	yes
1	6	4	1	1
2	3	0	2	1
3	1	0	1	0
4	2	—	2	—
5	2	—	2	—
6	0	—	2	—
7	—	—	2	—