# Spherical sampling methods for the calculation of metamer mismatch volumes

## TL;DR

This paper introduces two novel spherical sampling methods for calculating maximal metamer mismatch volumes without shape assumptions, revealing larger mismatch volumes than previous approximation techniques.

## Contribution

It presents two new methods—linear programming and computational geometry—for more accurate calculation of metamer mismatch volumes without boundary shape assumptions.

## Key findings

- Maximal mismatch volumes are significantly larger with the new methods.
- The methods outperform prior art in accuracy.
- Spherical sampling enables flexible mismatch volume estimation.

## Abstract

In this paper, we propose two methods of calculating theoretically maximal metamer mismatch volumes. Unlike prior art techniques, our methods do not make any assumptions on the shape of spectra on the boundary of the mismatch volumes. Both methods utilize a spherical sampling approach, but they calculate mismatch volumes in two different ways. The first method uses a linear programming optimization, while the second is a computational geometry approach based on half-space intersection. We show that under certain conditions the theoretically maximal metamer mismatch volume is significantly larger than the one approximated using a prior art method.