Geometry of color perception. Part 1: structures and metrics of a homogeneous color space

Edoardo Provenzi

doi:10.1186/s13408-020-00084-x

Abstract

This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian metrics on the perceived color space mathcal{P} compatible with the set of Schrödinger’s axioms completed with the hypothesis of homogeneity. We recast Resnikoff’s model into a more modern colorimetric setting, provide a much simpler proof of the main result of the original paper, and motivate the need of psychophysical experiments to confute or confirm the linearity of background transformations, which act transitively on mathcal{P} . Finally, we show that the Riemannian metrics singled out by Resnikoff through an axiom on invariance under background transformations are not compatible with the crispening effect, thus motivating the need of further research about perceptual color metrics.

Highlights

Introduction and state of the artThis first half of a two-part paper provides a thorough review and a critical analysis of the pioneering work of H.L
Resnikoff on color perception developed within the papers [1,2,3] and the book [4]
These works are amongst the major inspirations for a modern program of re-foundation of colorimetry that will be discussed in the second part, in which it will be shown how to recast Resnikoff ’s model in a quantum-like theory via the framework of Jordan algebras

Summary

Introduction

Introduction and state of the artThis first half of a two-part paper provides a thorough review and a critical analysis of the pioneering work of H.L. Resnikoff on color perception developed within the papers [1,2,3] and the book [4] These works are amongst the major inspirations for a modern program of re-foundation of colorimetry that will be discussed in the second part, in which it will be shown how to recast Resnikoff ’s model in a quantum-like theory via the framework of Jordan algebras. [5] for a modern translation of Schrödinger’s work on color) It is the research about the mathematical analogies between optics and color on one side and the oscillating behavior of quantum particles on the other that led Schrödinger to propose the famous equation which bears his name in quantum mechanics [6].

Objectives

Conclusion