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- Publisher
- Wiley
- Copyright
- Copyright © 1996 John Wiley & Sons, Inc.
- ISSN
- 0361-2317
- eISSN
- 1520-6378
- DOI
- 10.1002/col.5080210405
- Publisher site
- See Article on Publisher Site
Abstract
,* * * * * * * * * * * * = 2«( I C 2 -a, a2*-~' b 2{(\, C2/~' a2 +b, b 2) C, C 2 +a, a2 +b l b 2 * * b * )-2 (a,b * , 0 ** *, C,*C * +a, a-. +b,* b 2 2 2-a 2 and, by taking the square root with the appropriate sign for the numerator, * * * *_ Q,b 2 - Q* b, 2 (6) 6.H -[05 ( (,*,* a *a2+ b*l* 'e' . '(2+ l * ')2)] The quantity given by Formula (6) has the same sign as the one given by Formula (3) or by Formula (4). In other words, when the hue difference is positive, sample 2 has the highest hue angle. Formula (6) has some advantages: • No test to evaluate the sign ofthe hue difference, which is obtained directly. • Same quantities are needed for Formula (6) and Formula(4). • Number of operations needed for both formula is very similar. Formula (6) requires one division but no test, contrary to Formula (4). • With both formulas we need to compute a square root. Due to rounding errors, the square root may be applied to a negative quantity. This may happen for Formula (4) when the hue angles are very close, but as a minor advantage, with Formula (6), this is the case only if the two color stimuli have hue angles nearly opposite. This is extremely infrequent. Of course, all these formulas can be written with the CIELUV color space by interchanging the appropriate coordinates. In conclusion the proposed Formula (6) may be considered as a better practical one when computing hue differences. According to the ClE, this color difference may also be expressed differently, thanks to the ClE 1976 lightness difference 6.L *, the ClE 1976 chroma difference 6.C*, and the ClE 1976 hue difference 6.H*: 6.E*=[6.L*2+6.C*2+6.H*2],n. (2) For the CIE, , the hue difference 6.H* is defined in order to satisfy the relation (2). But Seve? has published a new formula for 6.H*: which can be deduced from Eqs. ( I ) and (2). Formula (3) clarifies the hue difference in relation with a geometrical interpretation.? This is the main purpose of that proposal. Moreover, Formula (3) leads to a direct way for computing the hue difference with some computational advantages, as previously explained." Stokes and Brill} observed that Form ula (3) is not appropriate for some computing problems, and suggested an alternative relation: * * / '1* 6.7 - 5'[2«('*C* - a,a2 - b*b*)] '/2 , '2 '2 (4) where s = I I'f a,*b* > a *l ),* , ot herwi s = - I . 2 2 erwise This proposal must test for the sign of s, in order to evaluate the sign ofthe hue difference, which is not very convenient for small computing devices. We are proposing an improved formula. From relations ( I ) and ( 2 ), as well from relation ( 4 ) we have, as a starting point R.SEVE 10, Avenue Gabriel Peri 94100 Saint Maur des Fosses France I. Coloritnctrv. Second Ed.. C1E Publication No. 15.2. Central Bureau ofCIE. Vienna. 1986. 2. R. Seve. New formula for the computation ofClE 1976 hue difference. Color Res. "/1'1'1. 16,217-218 ( 1991 ). 3. M. Stokes and M. H. Brill. Efficient computation of ')'Jl~,,, Color Res ./1'/>1.17,410-411 (1992). (5) By introducing the conjugate quantity, we may write CCC 0361-2317/96/040314-01 COLOR research and application
Journal
Color Research & Application – Wiley
Published: Aug 1, 1996