We have described a number of transformations by mapping the cone signal vector 𝐶, formed by 𝐿𝑀𝑆, to opponent space 𝑂, formed by achromatic signal 𝑂 𝐴 , red-green signal 𝑂 𝑟𝑔 , and yellow-blue signal 𝑂 𝑦𝑏 . Two new transformations, Γ 𝑜𝑝1 and Γ 𝑜𝑝2 , are proposed, based on the CIE 2006 spectral luminous efficiency function, 𝑉 𝐹 (𝜆) , and Hurvich's opponent spectral red-green and yellow-blue responses, 𝐻 𝑟𝑔 (𝜆) and 𝐻 𝑦𝑏 (𝜆), without and with constraints, respectively. Γ 𝑜𝑝1 is better than Γ 𝑜𝑝2 in terms of best fit of 𝐻 𝑟𝑔 (𝜆) and 𝐻 𝑦𝑏 (𝜆), and both transformations improved previously proposed ones. Finally, we discuss the neutral conditions in cone space using each of the new and some of the extant transformations, as well as choosing scaling factors so that the neutral conditions in cone space are satisfied.

Currently the fixed-point iteration method with initial guess 0 0.5 m = is officially recommended by the CIE MES2 system [CIE 191:2010] in order to compute the adaptation coefficient m and the mesopic luminance . mes L However, recently, Gao et al. [Opt. Express 25, 18365 (2017)] and Shpak et al. [Lighting Res. Technol. 49, 111 ( 2017)] have numerically found that the fixed-point iteration method could be not convergent for large values of / S P . Shpak et al. suspected that, to achieve convergence, the / S P ratio cannot be greater than 17. In this paper, a theoretical consideration for the CIE MES2 system is given. Namely, it is shown that the ratio / S P be smaller than a constant 2 ( 18.1834) C ≈ is a sufficient condition for the convergence of the fixed-point iteration method. In addition, a new initial guess strategy, achieving faster convergence, is proposed.

We studied skin color in participants before and after a 100‐m sprint using a Konica Minolta CM‐2600d spectrophotometer. Four body positions (forehead, cheek, neck, and inner forearm) were measured for the approximately 30 students (non‐professional runners) who participated in the experiment. Skin reflectance was measured three times at each position before running and again soon afterward. Analysis of the data showed that average measurement repeatability (mean color difference from the mean [MCDM]) was 0.5, 0.4, 0.3, and 0.2 CIELAB units for forehead, cheek, neck, and inner forearm, respectively. However, average skin color differences produced by running were 1.8, 2.2, 2.0, and 1.7 CIELAB units for forehead, cheek, neck, and inner forearm positions, respectively, which are considerably higher than repeatability before or after running. Furthermore, appearance variation was analyzed in the CIELAB space, and it was found that sprinting for 100 m considerably changes the values of the red‐green a* coordinate, while the lightness L* and yellow‐blue b* coordinates remain almost constant. More specifically, on average, a* decreases after running for the forehead, cheek, and neck positions, while the opposite is true for the inner forearm position. The findings in this article may be useful to test previous physical models, achieve more realistic images of human skin after sprinting, and contribute to work of CIE TC 1‐92 on skin spectra database.

No abstract