In this work, we tackle the question of how to parameterize a material model (or more generically a model) such that changing one of its parameters will change the output linearly for the viewer. If it is possible to measure the amount of visual change for any small change of the parameter, then we show that building a linear parameterization is akin to inverting the cumulative difference function (integral of visual change over the range of the parameter).

With this framework and with a proper visual change function, one can linearize any material model’s parameters. For example, we provide three examples of reparameterization for roughness, edge-tint and sheen.

But we also show that visual change functions are hard to find. For example, even perceptual metrics that are learned from human subjects do not produce a consistent parameterization depending on the lighting conditions. While this is expected as human perception depends on the frequency content of the illumination, it makes it even harded to build generic linear parameterizations that are based on human vision (if not impossible).