Abstract: Bidirectional Texture Functions (BTF) are commonly thought to provide the most realistic perceptual experience of materials from rendered images. The key to providing efficient compression of BTFs is the decision as to how much of the data should be preserved. We use psychophysical experiments to show that this decision depends critically upon the material concerned. Furthermore, we develop a BTF derived metric that enables us to automatically set a material's compression parameters in such a way as to provide users with a predefined perceptual quality. We investigate the correlation of three different BTF metrics with psychophysically derived data. Eight materials were presented to eleven naive observers who were asked to judge the perceived quality of BTF renderings as the amount of preserved data was varied. The metric showing the highest correlation with the thresholds set by the observers was the mean variance of individual BTF images. This metric was then used to automatically determine the material-specific compression parameters used in a vector quantisation scheme. The results were successfully validated in an experiment with six additional materials and eighteen observers. We show that using the psychophysically reduced BTF data significantly improves performance of a PCAbased compression method. On average, we were able to increase the compression ratios, and decrease processing times, by a factor of four without any differences being perceived.