Applications of vectorial color

Abstract

A companion article introduced a set of orthonormal opponent color matching functions. That "orthonormal basis" is an expedient for plotting lights in Jozef Cohen's logical color space. Indeed, graphing the new color matching functions (CMFs) together (as a parametric plot) gives Cohen's invariant "locus of unit monochromats," or LUM. In this article, the functions and related vector methods are applied to fundamental problems. In signal transmission and propagation-of-errors work, it is desirable to describe stimuli by decorrelated components. The orthonormal CMFs inherently do this, and an example is worked out using a large set of color chips. Starting with the orthonormal functions, related functions, such as cone sensitivities, are graphed as directions in color space, showing their intrinsic relationships. Building on work of Tominaga and co-authors, vectorial plots are related to the problem of guessing the illuminant, a step towards a constancy method. The issue of color rendering is clarified when the vectorial compositions of test and reference lights are graphed. A single graph shows the constraint that the total vectors are the same, but also shows the differences in colorimetric terms. Since the LUM summarizes a trichromatic system by a 3-dimensional graph, dichromatic observers can be represented by 2-D graphs, revealing details in a consistent way. The "fit first method" compares camera to human, applying the Maxwell-Ives criterion in graphical detail.

Vectorial color

“…† Clarity is gained when we see that the camera has its own invariant LUM, which should match or resemble that of the eye. The “fit first method” uses projection matrix R in a short algorithm to compare the two LUMs 23. Cohen's algebra and logic are used explicitly.…”

“…(9). One can then discover the benefit of the orthonormal and vectorial methods by working with them 23…”

“…The companion article 23 works out other key applications. One would like a camera to see colors as a person does.…”

“…The ''fit first method'' uses projection matrix R in a short algorithm to compare the two LUMs. 23 Cohen's algebra and logic are used explicitly. Dichromatic observers have flat LUMs, giving an invariant graphical picture for each type.…”

Two Applications of Vectorial Color: Camera Design and Lighting of Colored Objects

“…The Fit First Method, based on a few matrix operations, allows a detailed comparison of camera and eye, directly using Cohen's discovery of the invariant LUM. [16] …”