The components of our images: luminance and chrominance

There is nothing natural about the concept of color. The objects around us absorb certain wavelengths of light and reflect others; our eyes detect their frequencies, which are then interpreted by our brains (see "Different color systems"). Colors as we perceive them therefore have no independent physical existence; they depend entirely on our human reality. Nevertheless, color has always been part of our daily lives. In recent decades, it has also taken over our cinema and television screens.

Grassmann's laws and luminance ------------------------------

The world of color is modeled by Grassmann's laws, named after a Prussian mathematician and physicist (see box) who was also one of the unsung pioneers of tensor calculus and vector spaces. These laws confirm that color space is three-dimensional and postulate that colors combine linearly. This assumption of linear color mixing implies that the color perceived by our eyes must be independent of its spectral components.

box

Günther Grassmann, an unsung mathematical genius ------------------------------------------------

Hermann Günther Grassmann (1809–1877) was known to his contemporaries chiefly as a linguist. But his exceptional gifts in that field should not overshadow his remarkable mathematical discoveries. As early as 1840, he modeled the phenomenon of tides, unknowingly laying the very foundations of vector-space theory and linear algebra. Unfortunately, no one noticed. His results and ideas then formed the subject of a seminal book, Die lineale Ausdehnungslehre, ein neuer Zweig der Mathematik ("The Theory of Linear Extension, a New Branch of Mathematics"), published in 1844, which failed to receive the recognition it deserved. In it, however, Grassmann introduced the concepts of the dot product and the exterior product, a generalization of the cross product that, among other things, allows parallelepipeds in any dimension to be viewed as the product of the vectors representing their edges (see Vecteurs et Espaces vectoriels, Bibliothèque Tangente 65, 2018). It was not until 1877 that the book was finally rediscovered and republished, most copies of the first edition having been pulped…

In linguistics, Grassmann studied Sanskrit, among other pursuits, and published one of the first dictionaries of the language (Worterbuch zum Rig-Veda, Wiesbaden, 1873), enabling the Rigveda—a collection of sacred hymns from ancient India dating from the second millennium BCE—to be translated.

The components of our images: luminance and chrominance

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