A physically grounded model for predicting subtractive colour mixing: towards a perception-independent framework

This work develops a physically grounded model for predicting pigment mixture colours that operates independently of visual perception. The central objective is to identify intrinsic, measurable parameters that enable accurate and linear predictions of colour outcomes, validated through a dataset of 8421 manually prepared samples, including 43 base pigments and their binary mixtures, both inter-pigment and pigment-white.

To achieve this, three interconnected goals are pursued. First, the construction of a high-resolution reflectance database, $\rho \left(\lambda \right)$, and the generation of a corresponding set of colour coordinates using newly defined physical parameters. Second, the formulation of a novel, perception-independent colour space, termed the General Sample Plane (GSP), in which each pigment sample G is uniquely represented by the triplet $\left(G,M_x\left(G\right),M_y\left(G\right)\right)$. This framework is further extended into three dimensions as the General Sample Volume (GSV). Unlike conventional perceptual models, the GSP and GSV are constructed from optical properties alone, with no reliance on observer-based colour metrics. Third, the predictive validity of this coordinate system is evaluated by analysing the linearity of trajectories traced by pigment mixtures and their respective whitening stages in the GSP. The results confirm that mixtures of two components, both pigment-pigment and pigment-white, describe highly linear paths in this space (reaching R² > 0.99), with minimal chromatic distortion even across broad spectral domains. Additionally, quantitative evaluation of interpolation accuracy, based on excluded intermediate mixtures, showed low ΔE values (ΔE ≤ 1.0) in the GSP space, where ΔE represents the Euclidean distance between predicted and measured coordinates, confirming the model's reliable predictive performance. The model offers a scalable, quantitative basis for physically consistent colour prediction in subtractive systems, with potential applications in pigment formulation, digital calibration, and optical modelling of coloured materials.