Spherical sampling methods for the calculation of metamer mismatch volumes

Area of Science:

• Color Science
• Computational Geometry
• Optimization Theory

Background:

• Metamer mismatch volumes are crucial for understanding color perception and material appearance.
• Existing methods often rely on simplifying assumptions about spectral shapes, potentially underestimating mismatch volumes.

Purpose of the Study:

• To propose and validate two novel methods for calculating theoretically maximal metamer mismatch volumes.
• To overcome the limitations of prior art techniques by avoiding assumptions on spectral boundary shapes.

Main Methods:

• Spherical sampling approach combined with linear programming optimization.
• Spherical sampling approach combined with computational geometry via half-space intersection.

Main Results:

• Demonstrated two distinct methods for calculating maximal metamer mismatch volumes.
• Showcased that under specific conditions, the theoretically maximal volume can be substantially larger than previously approximated.

Conclusions:

• The proposed methods offer a more accurate and comprehensive approach to quantifying metamer mismatch volumes.
• These findings have implications for color reproduction, material characterization, and the fundamental understanding of visual perception.