Number of colors generated by smooth nonfluorescent reflectance spectra

Abstract

In this study, we have analyzed statistical properties of the values of the first- and second-order derivatives of spectral reflectance curves. We show that values of all four tested spectral data sets have very similar statistical properties. We set outer limits that bound the clear majority of the values of the first- and second-order derivatives. These limits define smoothness of all nonfluorescent reflectance curves, and they can be used to form a new object color solid inside classical MacAdam limits, including all possible colors generated by smooth nonfluorescent reflectance spectra. We have used the CIELAB color space and filled the new object color solid with a hexagonal closest packing-point lattice to estimate that there exist about 2.5 million different colors, when viewed under the D65 standard illumination.

Non-spectroscopic sensing enabled by electro-optical reservoir computer

“…It is inspired by the biomimetic design which previously has been demonstrated successfully for chemical [18][19][20] and biological sample [21] detection. The biomimetic sensor mimics the operation of the human eyes, which are capable of discriminating over 100,000 shades of (visible) colour over an environmental background despite being equipped with only three main types of cone cells [22,23]. Key to this ability is the spectral sensitivity of these cone cell types which are sprectrally broad and overlapping [24].…”

How many object colors can we distinguish? A comment on prof. Kuehni

“…was based on the use of unit cubes (or unit squares on the planes of constant lightness) filling OOCS in the CIELAB color space at a CCT of 6500 K. A sphere with the diameter of one CIELAB color difference unit fits the outlines of a unit cube and the number of spheres packed according to the SC lattice matches the number of unit cubes and further, the number of unit cubes filling the OOCS corresponds its volume. With the same assumptions, spheres packed according to the HCP lattice provide about 3.24 million discernible colors . The result can be easily converted to concern SC lattice by dividing it by , when it becomes consistent with the estimate given by Pointer and Attridge.…”

Numerical methods for smoothest reflectance reconstruction

“…Many investigators have observed that measured reflectance distributions of natural colors tend to be smooth . The goal of seeking the smoothest reflectance function was advanced by van Trigt, who minimized the integral of slope squared over the visible portion of the spectrum, sometimes adding explicit constraints on reflectance to prevent the values from exceeding the range 0 to 1 .…”

“…40 Many investigators have observed that measured reflectance distributions of natural colors tend to be smooth. 6,9,[41][42][43][44][45][46][47][48][49][50][51] The goal of seeking the smoothest reflectance function was advanced by van Trigt, who minimized the integral of slope squared over the visible portion of the spectrum, sometimes adding explicit constraints on reflectance to prevent the values from exceeding the range 0 to 1. 11,12 Li and Luo later implemented van Trigt's approach, using a numerical optimization treatment of van Trigt's functional analysis approach.…”