A response-surface framework for empirical modeling of nonlinear color enhancement operators in HSL space

This work presents a data-driven framework for empirically characterizing nonlinear color enhancement operators through controlled measurements in HSL space. The approach combines synthetic probe images, response-surface fitting, and structured validation to derive explicit functional approximations of operator behavior without assuming knowledge of the internal implementation. As a case study, the framework is applied to a widely used commercial Vibrance adjustment. Measurements show that the saturation increment depends jointly on hue and initial saturation and cannot be represented by separable models. A two-dimensional chromatic surface is therefore estimated using a Fourier representation in hue with saturation-dependent coefficients. Residual analysis on real images reveals systematic lightness variations, motivating an extended three-dimensional formulation in which both saturation and lightness increments depend on ( S, H, L). Validation on synthetic and real images shows that this formulation substantially improves reconstruction accuracy. The work demonstrates a general methodology for empirical response-surface modeling of complex color operators when only black-box access is available.