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Alexander D Logvinenko1,2, Brian Funt3,4, Pouya Bastani3,5

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A new algorithm accurately calculates the true object-color solid, surpassing previous approximations. This advancement resolves a century-old problem by determining optimal reflectances for any given color direction.

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Area of Science:

  • Color Science
  • Computer Vision
  • Computational Imaging

Background:

  • Previous methods approximated the object-color solid using Schrödinger's assumption of two-transition optimal reflectances.
  • Schrödinger's assumption was partially incorrect, as optimal reflectances can have three or four transitions.

Purpose of the Study:

  • To accurately compute the true object-color solid.
  • To quantify the differences between approximate and true object-color solids.
  • To present a method for determining optimal reflectances for any given color direction.

Main Methods:

  • Developed a novel algorithm for accurate computation of the object-color solid.
  • Quantified the discrepancies arising from simplified reflectance models.
  • Parametrized the object-color solid using two variables, despite complex reflectances.

Main Results:

  • The true object-color solid is larger than previously approximated solids.
  • Differences between approximate and true object-color solids have been quantified.
  • The algorithm successfully determines optimal reflectances for any color direction.

Conclusions:

  • The developed algorithm provides the first accurate computation of the true object-color solid.
  • The study corrects and expands upon Schrödinger's foundational work in object-color solid computation.
  • This research offers a complete solution to a long-standing problem in color science.