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Split-quaternions for perceptual white balance

Michel Berthier, Nicoletta Prencipe, Edoardo Provenzi

TL;DR

The paper introduces a perceptual white balance method, split-CAT, grounded in a quantum-like color perception model and implemented via the sub-algebra S0 of split-quaternions. Color measurements are encoded as sandwich operations in S0, effectively modeling perceptual transformations as Lorentz boosts, with the practical CAT given by q'(x) = p_e^{-1/2} q(x) p_e^{-1/2} for each pixel. The approach is evaluated against the von Kries CAT on color checker rendering, with results showing competitive or superior performance, and improvements obtained by modifying hue representations to encode Hering-like opponency (H1CV, H2CV). The work suggests that a rigorous algebraic and geometric framing of color perception can yield effective perceptual color processing tools and highlights avenues for broader color-space deployment and psychophysical integration.

Abstract

We propose a perceptual chromatic adaptation transform for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantum-like model of color perception, consists at stressing the link between the algebraic structures appearing in this model and a certain sub-algebra of the split-quaternions. We show the potentiality of this approach for color image processing applications by proposing a chromatic adaptation transform, implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries chromatic adaptation transform are provided.

Split-quaternions for perceptual white balance

TL;DR

The paper introduces a perceptual white balance method, split-CAT, grounded in a quantum-like color perception model and implemented via the sub-algebra S0 of split-quaternions. Color measurements are encoded as sandwich operations in S0, effectively modeling perceptual transformations as Lorentz boosts, with the practical CAT given by q'(x) = p_e^{-1/2} q(x) p_e^{-1/2} for each pixel. The approach is evaluated against the von Kries CAT on color checker rendering, with results showing competitive or superior performance, and improvements obtained by modifying hue representations to encode Hering-like opponency (H1CV, H2CV). The work suggests that a rigorous algebraic and geometric framing of color perception can yield effective perceptual color processing tools and highlights avenues for broader color-space deployment and psychophysical integration.

Abstract

We propose a perceptual chromatic adaptation transform for white balance that makes use of split-quaternions. The novelty of the present work, which is motivated by a recently developed quantum-like model of color perception, consists at stressing the link between the algebraic structures appearing in this model and a certain sub-algebra of the split-quaternions. We show the potentiality of this approach for color image processing applications by proposing a chromatic adaptation transform, implemented via an appropriate use of the split-quaternion multiplication. Moreover, quantitative comparisons with the widely used state-of-the art von Kries chromatic adaptation transform are provided.

Paper Structure

This paper contains 13 sections, 36 equations, 3 figures, 1 table.

Table of Contents

  1. Introduction
  2. Color perception and color measurements
  3. Color measurements and quantum information
  4. Color measurements and Lorentz boosts
  5. Color measurements and split-quaternions
  6. The algebra of split-quaternions
  7. The sub-algebra $\mathbb S_0$ of the split-quaternion algebra
  8. The sandwich formula for color measurements
  9. A sandwich without conjugate
  10. Application to white balance
  11. Modification of HCV to encode Hering's opponency
  12. Quantitative evaluation of the color checker rendering
  13. Conclusions and future perspectives

Figures (3)

  • Figure 1: Left: input images. Center: output images after white balance using the von Kries CAT. Right: output images after white balance using the split-CAT. The white balanced images have been obtained using the same illuminant estimation. The illuminant vector is extracted automatically from the white patch of the color checker present in each image.
  • Figure 2: Red, yellow, green and blue hue positions in the hue-chroma planes of the HCV, H$_1$CV and H$_2$CV color spaces.
  • Figure 3: Left: output of the split-CAT in HCV. Center: output of the split-CAT in H$_1$CV. Right: output of the split-CAT in H$_2$CV.