BRDF models are ubiquitous tools for the representation of material appearance. However, there is now an astonishingly large number of different models in practical use. Both a lack of BRDF model standardisation across implementations found in different renderers, as well as the often semantically different capabilities of various models, have grown to be a major hindrance to the interchange of production assets between different rendering systems. Current attempts to solve this problem rely on manually finding visual similarities between models, or mathematical ones between their functional shapes, which requires access to the shader implementation, usually unavailable in commercial renderers. We present a method for automatic translation of material appearance between different BRDF models, which uses an image-based metric for appearance comparison, and that delegates the interaction with the model to the renderer. We analyse the performance of the method, both with respect to robustness and visual differences of the fits for multiple combinations of BRDF models. While it is effective for individual BRDFs, the computational cost does not scale well for spatially-varying BRDFs. Therefore, we further present a parametric regression scheme that approximates the shape of the transformation function and generates a reduced representation which evaluates instantly and without further interaction with the renderer. We present respective visual comparisons of the remapped SVBRDF models for commonly used renderers and shading models, and show that our approach is able to extrapolate transformed BRDF parameters better than other complex regression schemes.