This paper investigates the role of transformations and similarity in a perceptual task, the same-different paradigm. Representational Distortion (RD) theory measures similarity by the complexity required to distort compared object representations. In an experiment, participants compared pairs of geometric shapes that varied across two dimensions (shape and color). We then modelled data using a variety of model of similarity. RD yielded accurate fits and compared favourably with various models of Structural Alignment. Results highlighted the relationship between transformations and low-level stimulus properties.