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Electrical and Computer Engineering ECE Technical Reports Purdue Libraries Year A New Color Representation for Non-White Illumination Conditions Jae Byung Park Avinash C. Kak This paper is posted at Purdue e-Pubs. http://docs.lib.purdue.edu/ecetr/8

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Electrical and Computer Engineering

ECE Technical Reports

Purdue Libraries Year

A New Color Representation for

Non-White Illumination Conditions

Jae Byung Park Avinash C. Kak

This paper is posted at Purdue e-Pubs.

http://docs.lib.purdue.edu/ecetr/8

A NEW COLOR REPRESENTATION FOR NON-WHITE ILLUMINATION CONDITIONS

JAE BYUNG PARK AVINASH C. KAK

TR-ECE – 05-06 JUNE 2005

SCHOOL OF ELECTRICAL AND COMPUTER ENGINEERING PURDUE UNIVERSITY WEST LAFAYETTE, IN 47907-2035

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0 50 100 150 200 2500

100

200

0

50

100

150

200

250

R

Illumination axis and gray axis

G

B

B

G

R

Gray AxisIllumination Axis

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Normalized R

Nor

mal

ized

G

Mean = (0.4866, 0.3927)

Mean = (0.0915, 0.6099)

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¥NQPjDFKZI�PRI�;>GJI�[SX>=�9�EF;FNVGoLCI�?�GJACK�m�GJWHI�PRI7XvI�NQ;FU/GJWFI7DFKRAlaZI�?�GRNQAC;HP|A<_�GRWFIdN�TQT�EFBqN�;�9�GRNQAC;�9��sNQP|A<;�GJWHI/ �mf¡}mv9<;F[S¢ð â�ã&ämñxè«ðÑðÑè�ë£ìí÷&ø�ç¥ã+é¥ä�ê`ã&è!ðÑû+ê�ã+å�ý«äWë�è!é°�!ä�û¾ë�ä�ðíð£ñxè!éÁæ+ê²ñxè«é©û&ä�ç¥ä�ï(çÈìí÷&ø�êÈå�çÈæ&é�å�ç¥ìÑè«÷Éå�÷+û§ðÆå«ï���è«ñLå!ûcädì�æ+å�ç¥äWìíðÑðíæ+õ²ìÑ÷+å�ç¥ìÑè«÷~�YæJèè�ý«ä�é��×êÈå�ç¥æ+éÈå�ç¥ìÑè«÷�ç¥ã+é¥ä�ê`ã&è!ðÑû~� max (µR, µG, µB) ≥ 252 ëcå�÷�û+é�è�ìí÷+å!ûcädì�æ+å�ç¥äLìÑðíðÑæ&õ�ìí÷�å�ç¥ìÑè«÷WçÈã&é¥ä�ê`ã+è«ðÆû>� min (µR, µG, µB) ≤ 2 �

9��sI�P�g}�zWFI7T�9<PcG�?�ACTQEHBq;1A<_-GJWFIbG�9<XHTQI#9<TQPZA)PRWFA�koP�GRWFI#KRA<GJ9�GJN�AC;39��sNQPoX>=:9)EF;FNVGoLCI�?�GJACKo_�ACKj9q?�I�KcG�9<N�;�KZA<G�9�GRNQAC;A<_`GJWFI1 #¡`¢ ?�EFX'IqGJWF9�GbkoNQTQT�X'I/I��sDFT�9�NQ;FI�[�N�;\GRWFIq;HI��OG�PZI�?�GRNQAC;�g�«pI/PRWHACEFTQ[p9<TQPZA�PcG�9�GRI/GRW�9�G7NQ;�9<TQTnA<_}GJWHII��sD'I�KZNQB/I�;>GJPoEFPZI�[1_�ACKfGJWHI^?�AC;FPcGJKZEF?�GRNQAC;3A<_6GJWFN�P}G�9<XHTQI<mOkoWFN�GRI^X�9<TQ9<;F?�N�;FUY9<;H[�9�EHGJACBq9�GRNQ?|UC9<NQ;�?�AC;>GJKRA<TtNQ;�GJWHI?h9�BqI�KJ9<P}k`I�KZI7Bq9<[FI^N�;�9<?�GRN�L<I<g

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ûfü ý û~ü üYý ûfü ü üYý ûfü þvý û~þdý û�þ·üYý û�þ·ü üYýÿ ü �������������� �� ÿ ü �����}ü���� ���dü �� ��� ����Rü���������� ��� ����Rü������}ü ��� ��� � ���ü������}ü ��� ���������}ü ��� �"!dü �

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ûWmax

ý ûLRGB=(LR,LG,LB

ý ûLXY Z=(LX ,LY ,LZ)

ý(UXY X=(u,v,w))

û�:jýÿ �);=<*>�� ��?�@�� ����A'ü��� ÿ ü �����

ÿ �);=<*>�� ��?�@�� ����A'ü��� ÿ ü �����B �� C��û�:�D#D��+��������EGF#DFý

LR = 0.7930

LG = 0.5679

LB = 0.2205

LX = 0.3418

LY = 0.2579

LZ = 0.9037

u = 0.6023

v = −0.7983

w = 0

ûHFFýI ü ���#<>�� )�?�@�� ����A'ü��� ÿ ü �����

I ü ���#<�>�� ������� ����A'ü��� ÿ ü �����B �� C��û�:�D#D��+��������EJ:)K·ý

LR = 0.8992

LG = 0.4270

LB = 0.0956

LX = 0.5415

LY = 0.2436

LZ = 0.8046

u = 0.4103

v = −0.9128

w = 0

ûHLFý�H���%����A� ����% ����ÿ ü ������û*� �A=ý

��&�� þ����dü �M � ����AN ��@L#OP�� )ARQPeak 625nmû�:�D#D��+��������EGSFý

LR = 0.9834

LG = 0.0810

LB = 0.1624

LX = 0.7240

LY = −0.0592

LZ = 0.6872

u = −0.0815

v = −0.9967

w = 0

û�K·ý�H���%����A� ����% ����ÿ ü ������û*�#� � ��vý

��&�� þ����dü �M � ����AN ��@L#OUTV� ) ��WQPeak 535nmû�:�D#D��+��������EGSFý

LR = 0.4351

LG = 0.6888

LB = 0.5799

LX = −0.1722

LY = 0.0815

LZ = 0.9817

u = 0.4278

v = 0.9039

w = 0

ûHSFý�H���%����A� ����% ����ÿ ü ������û�C�� � ný

��&�� þ����dü �M � ����AN ��@L#O B � � �QPeak 425nmû�:�D#D��+��������EGSFý

LR = 0.2278

LG = 0.5112

LB = 0.8287

LX = −0.3787

LY = −0.2355

LZ = 0.8951

u = −0.5281

v = 0.8492

w = 0

ûHXFý�H���%����A� ����% ����ÿ ü �����

13Y M � ����AN ��@L#O9Z[ )� � �);\QPeak 570nmûHF#D#D��+��������EGLFý

LR = 0.7556

LG = 0.5914

LB = 0.2816

LX = 0.2744

LY = 0.2307

LZ = 0.9335

u = 0.6435

v = −0.7654

w = 0

û?]Xý^ ����#�H�� ��ÿ ü ����� B �� C��ûH>dü���_dý

T.`ba=������# �QPeak 600nmû�:�D#D��+��������EGXFý

LR = 0.8606

LG = 0.4455

LB = 0.2467

LX = 0.4402

LY = 0.1473

LZ = 0.8857

u = 0.3173

v = −0.9483

w = 0

ûHOFýI �#� �#�# ��ÿ ü ����� B �� C��

I �#� �#�# �� ÿ ü �����B �� C��@QûHS#D#D�J���?����EJ:jý

LR = 0.5180

LG = 0.6283

LB = 0.5804

LX = −0.0747

LY = 0.0360

LZ = 0.996

u = 0.4341

v = 0.9008

w = 0

ûHcFýM � �#� )�?�% ����ÿ ü �����

T.`b�#���?edf�#���^ O�QûHL#F��+��������EJ:�FFý

LR = 0.5975

LG = 0.5834

LB = 0.5501

LX = 0.0266

LY = 0.0249

LZ = 0.0993

u = 0.6834

v = −0.7301

w = 0

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Cluster #1 Detected (HSI) Cluster #2 Detected (HSI) Cluster #3 Detected (HSI)

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