One challenge in exploring the internal representation of faces is the lack of controlled stimuli transformations. Researchers are often limited to verbalizable transformations in the creation of a dataset. An alternative approach to verbalization for interpretability is finding image-based measures that allow us to quantify image transformations. In this study, we explore whether PCA could be used to create controlled transformations to a face by testing the effect of these transformations on human perceptual similarity and on computational differences in Gabor, Pixel and DNN spaces. We found that perceptual similarity and the three image-based spaces are linearly related, almost perfectly in the case of the DNN, with a correlation of 0.94. This provides a controlled way to alter the appearance of a face. In experiment 2, the effect of familiarity on the perception of multidimensional transformations was explored. Our findings show that there is a positive relationship between the number of components transformed and both the perceptual similarity and the same three image-based spaces used in experiment 1. Furthermore, we found that familiar faces are rated more similar overall than unfamiliar faces. That is, a change to a familiar face is perceived as making less difference than the exact same change to an unfamiliar face. The ability to quantify, and thus control, these transformations is a powerful tool in exploring the factors that mediate a change in perceived identity.