Quantify uniformity in hierarchical color maps

Develop a quantifiable metric for uniformity in hierarchical color maps that captures their adherence to the represented hierarchical structure, including inconsistencies arising when unrelated nodes receive similar colors at different hierarchy levels.

Background

The paper compares Dynamic Tree Colors with Cuttlefish using global and local discriminative-power metrics based on color distances. The authors observe that color-distance metrics do not capture whether a color map preserves hierarchical structure: Cuttlefish can achieve higher global discriminative power on imbalanced datasets while assigning similar hues to unrelated parts of the hierarchy at different levels.

The authors explicitly identify uniformity—understood as adherence to hierarchical structure—as a relevant quality dimension for which no quantifiable metric is currently available. Such a metric would complement discriminative-power and instability measures when evaluating hierarchical color maps.