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Abstract Two ideas, proposed by Thomas Young and James Clerk Maxwell, form the foundations of color science: (1) Three types of retinal receptors encode light under daytime conditions, and (2) color matching experiments establish the critical spectral properties of this encoding. Experimental quantification of these ideas are used in international color standards. But, for many years the field did not reach consensus on the spectral properties of the biological substrate of color matching: the sensitivity of the in situ cones (cone fundamentals). By combining auxiliary data (thresholds, inert pigment analyses), complex calculations, and color matching from genetically analyzed dichromats, the human cone fundamentals have now been standardized.
Here we describe a new computational method to estimate the cone fundamentals using only color matching from dichromatic observers. We show that it is not necessary to include data from trichromatic observers in the analysis or to know the primary lights used in the matching experiments. Remarkably, it is even possible to estimate the fundamentals by combining data from experiments using different, unknown primaries. We then suggest how the new method may be applied to color management in modern image systems.
Maxwell experiments by Koh Terai
Koh did a very nice project at Stanford (Psych 221, Image Systems Engineering, Wandell-Farrell-Cardinal, 2023) laying out the ideas of Maxwell's experimental apparatus and his measurements. The beauty of Maxwell's work is very clearly explained in Koh's excellent page.
This repository depends on ISETCam. To run this code, please download that repository and this one and place both on your path. If you are interested in modeling the human visual system, you might try ISETBio, as well.
Click on the link to see the code for the figure.
Figure 1 The color matching data reported by Maxwell [1]. The solid curves are the CIE (1931) tristimulus color matching functions. The dashed curves are the current CIE cone fundamentals [11, 12] linearly transformed to match the CIE 1931 functions. The points are color matching functions measured by Maxwell in two observers (J,squares; K,circles), also linearly transformed to match the CIE 1931 functions. The general agreement between Maxwell’s data and the CIE curves was pointed out by Judd, who provided a conversion of Maxwell’s wavelength units (Paris inches) to nanometers [6]. Here we include a small (10 nm shift) correction to Judd’s estimate of the Maxwell’s wavelengths, as well as show the comparison with the current CIE cone fundamentals.
Figure 3. The Wright dichromatic color matching functions (solid) compared with a linear transformation of the CIE cone fundamentals (dotted). The protan and deutan functions were converted to digital form from figures in Wright’s book [37]. The tritanopic data were provided as tables [38]; notice that the wavelength range for the tritanopes is narrower. The original deutan data have an implausible short-wavelength color matching function (gray dashed curves). The estimates in Figure 4 were made substituting the protan blue primary for the deutan (corrected). For both of these dichromats the short-wavelength primary should be dominated by the common S-cone.
Figure 4 Cone fundamentals derived from the Wright and Pitt dichromatic color matching functions. The top row compares the better of the two estimated fundamentals (dark, x𝑝 solution) with the CIE cone fundamentals (gray) [12]. The estimates are calculated from the modified Wright data (Figure 3). The bottom row shows the log10 difference between the curves for CIE values greater than 0.05 (peak = 1).
Figure 2
Figure 5
In addition to the computational methods, the repository includes historical data from James Clerk Maxwell's and W.D. Wright (references below). These are in the 'data' directory. We have put the data both in spreadsheet format, mat-files, and CSV files. At the Referees' request we placed these files on the Stanford Digital Repository as well.
The repository also has additional scripts that we used as we explored the ideas. We particularly draw your attention to the calculation of the Maxwell CMFs directly from the matching data to white. This calculation was interesting to us because it uses modern methods that could be used even if we do not have special experimental considerations that Maxwell applied for selecting wavelengths.
The analysis scripts contain many details and specific calculations. In the fullness of time, we expect to write more detail in this wiki page and to incorporate the ideas and historical data in the next edition of Wandell's book, Foundations of Vision. Which will be online as a WordPress site in addition to a PDF book.
@ARTICLE{Maxwell1860-xg, title = "{IV}. On the theory of compound colours, and the relations of the colours of the spectrum", author = "Maxwell, J C", journal = "Philos. Trans. R. Soc. Lond.", publisher = "The Royal Society", volume = 150, number = 0, pages = "57--84", month = dec, year = 1860, url = "https://doi.org/10.1098/rstl.1860.0005", language = "en" }
@ARTICLE{Wright1952-du, title = "The characteristics of tritanopia", author = "Wright, W D", journal = "J. Opt. Soc. Am.", volume = 42, number = 8, pages = "509--521", month = aug, year = 1952, url = "http://dx.doi.org/10.1364/josa.42.000509", keywords = "COLOR VISION", language = "en" }
@BOOK{Wright1938-ya, title = "Colour Vision. Research on Normal and Defective Colour Vision", author = "Wright, W D", year = 1938, url = "https://play.google.com/store/books/details?id=UTxjXwAACAAJ", language = "en" }