Traditionally, texture perception has been studied using artificial textures made of random dots or repeated shapes. At the same time, computer algorithms for natural texture synthesis have improved dramatically. We seek to unify these two fields through a psychophysical assessment of a particular computational model, providing insight into which statistics are most vital for natural texture perception. We employ Portilla and Simoncelli's texture synthesis algorithm, a parametric model that mimics computations carried out in human vision. We find an intriguing interaction between texture type (periodic, structured, or 3-D textures) and image statistics (autocorrelation function and filter magnitude correlations), suggesting different representations may be employed for these texture families under pre-attentive viewing.