Vinogradov's theorem: Difference between revisions
en>YFdyh-bot m r2.7.3) (Robot: Adding ar:مبرهنة فينوغرادوف |
en>K9re11 mNo edit summary |
||
| Line 1: | Line 1: | ||
The '''Neugebauer equations''' are a set of equations used to model [[color printing]] systems, developed by [[Hans E. J. Neugebauer]].<ref>{{cite book|title=Color technology for electronic imaging devices|first=Henry R.|last=Kang|publisher=SPIE Press|year=1997}}</ref> They were intended to predict the color produced by a combination of [[halftone]]s printed in cyan, magenta, and yellow inks. | |||
The equations estimate the [[reflectance]] (in [[CIE XYZ]] coordinates or as a function of wavelength) as a function of the reflectance of the 8 possible combinations of CMY inks (or the 16 combinations of CMYK inks), weighted by the area they take up on the paper. In wavelength form: | |||
:<math>R(\lambda) = \sum_{i=1}^{16} w_i R_i(\lambda)</math> | |||
where <math>R_i(\lambda)</math> is the reflectance of ink combination ''i'', and <math>w_i</math> is the relative proportions of the 16 colors in a uniformly colored patch. The weights are dependent on the halftone pattern and possibly subject to various forms of [[dot gain]]. <ref>Raja Balasubramanian, A spectral Neugebauer model for dot-on-dot printers, Proc. SPIE vol. 2413, (1995) [http://chester.xerox.com/~raja/papers/EI95.pdf]</ref> | |||
Light can interact with the paper and ink in more complex ways. The Yule-Neilsen correction takes into account light entering through blank regions and re-emerging through ink:<ref>J. A. C. Yule and W. J. Neilsen, "The Penetration of light into Paper and its Effect on Halftone Reproduction," 1951 TAGA Proceedings, pp. 65-76</ref> | |||
:<math>R(\lambda) = \left [ \sum_{i=1}^{16} w_i R_i(\lambda)^{1/n} \right ]^n</math> | |||
The factor ''n'' would be 2 for a perfectly diffusing [[Lambertian reflectance|Lambertian]] paper substrate, but can be adjusted based on empirical measurements. Further considerations of the optics, such as multiple internal reflections, can be added at the price of additional complexity. | |||
In order to achieve a desired reflectance these equations have to be inverted to produce the actual dot areas or digital values sent to the printer, a nontrivial operation that may have multiple solutions.<ref>Marc F. Mahy, Insight into the solutions of the Neugebauer equations. Electronic Imaging: SPIE/IS&T International Technical Group Newsletter January 1999, p. 7,11. [http://www.inventoland.net/pdf/Reports/ei_newsletter99ocr.pdf]</ref> | |||
==See also== | |||
* [[CMYK color model]] | |||
==Original paper== | |||
H. E. J. Neugebauer, "Die theoretischen Grundlagen des Mehrfarbenbuchdrucks," ''Zeitschrift für wissenschaftliche Photographie Photophysik und Photochemie,'' 36:4, 1937. p 73-89. | |||
==References== | |||
<references/> | |||
[[Category:Equations]] | |||
[[Category:Color]] | |||
[[Category:Printing]] | |||
{{mathapplied-stub}} | |||
Revision as of 20:14, 24 January 2014
The Neugebauer equations are a set of equations used to model color printing systems, developed by Hans E. J. Neugebauer.[1] They were intended to predict the color produced by a combination of halftones printed in cyan, magenta, and yellow inks.
The equations estimate the reflectance (in CIE XYZ coordinates or as a function of wavelength) as a function of the reflectance of the 8 possible combinations of CMY inks (or the 16 combinations of CMYK inks), weighted by the area they take up on the paper. In wavelength form:
where is the reflectance of ink combination i, and is the relative proportions of the 16 colors in a uniformly colored patch. The weights are dependent on the halftone pattern and possibly subject to various forms of dot gain. [2]
Light can interact with the paper and ink in more complex ways. The Yule-Neilsen correction takes into account light entering through blank regions and re-emerging through ink:[3]
The factor n would be 2 for a perfectly diffusing Lambertian paper substrate, but can be adjusted based on empirical measurements. Further considerations of the optics, such as multiple internal reflections, can be added at the price of additional complexity.
In order to achieve a desired reflectance these equations have to be inverted to produce the actual dot areas or digital values sent to the printer, a nontrivial operation that may have multiple solutions.[4]
See also
Original paper
H. E. J. Neugebauer, "Die theoretischen Grundlagen des Mehrfarbenbuchdrucks," Zeitschrift für wissenschaftliche Photographie Photophysik und Photochemie, 36:4, 1937. p 73-89.
References
- ↑ 20 year-old Real Estate Agent Rusty from Saint-Paul, has hobbies and interests which includes monopoly, property developers in singapore and poker. Will soon undertake a contiki trip that may include going to the Lower Valley of the Omo.
My blog: http://www.primaboinca.com/view_profile.php?userid=5889534 - ↑ Raja Balasubramanian, A spectral Neugebauer model for dot-on-dot printers, Proc. SPIE vol. 2413, (1995) [1]
- ↑ J. A. C. Yule and W. J. Neilsen, "The Penetration of light into Paper and its Effect on Halftone Reproduction," 1951 TAGA Proceedings, pp. 65-76
- ↑ Marc F. Mahy, Insight into the solutions of the Neugebauer equations. Electronic Imaging: SPIE/IS&T International Technical Group Newsletter January 1999, p. 7,11. [2]