Objects in the world, natural and artificial alike, are often bilaterally symmetric. The visual system is likely to take advantage of this regularity to encode shapes for efficient object recognition. The nature of encoding a symmetric shape, and of encoding any departure from it, is therefore an important matter in visual perception. We addressed this issue of shape encoding empirically, noting that a particular encoding scheme necessarily leads to a specific profile of sensitivity in perceptual discriminations. We studied symmetry discrimination using human faces and random dots. Each face stimulus was a frontal view of a three-dimensional (3-D) face model. The 3-D face model was a linearly weighted average (a morph) between the model of an original face and that of the corresponding mirror face. Using this morphing technique to vary the degree of asymmetry, we found that, for faces and analogously generated random-dot patterns alike, symmetry discrimination was worst when the stimuli were nearly symmetric, in apparent opposition to almost all studies in the literature. We analyzed the previous work and reconciled the old and new results using a generic model with a simple nonlinearity. By defining asymmetry as the minimal difference between the left and right halves of an object, we found that the visual system was disproportionately more sensitive to larger departures from symmetry than to smaller ones. We further demonstrated that our empirical and modeling results were consistent with Weber–Fechner's and Stevens's laws.

*p*< .0001;

*p*< .0001; and orientation,

*p*< .005; no significant effect of sign

*p*< .0001; and

*p*< .0001.]

*p*< .0001; and

*p*< .0001.]

*SD*= 20 pixels, which was 9% of the ear-to-ear distance—the specific size of this blurring kernel did not qualitatively affect our analysis). We then searched for the position of a vertical axis that minimized the left–right Euclidean (RMS) difference in pixel values, as in Figure 5. We plotted this minimal difference as a function of the two scales of asymmetry used in this paper. As shown in Figure 10, introducing asymmetry by morphing yielded an almost linear function with only a weak deceleration:

*D*(within-family) standard derivation, analogous to the within-subject confidence intervals of Loftus & Masson, 1994) from different random-dot samples at an asymmetry level. This random variation was nearly constant over the entire morphing (

*p*< .05). Thus, the model not only captured the average results, but also the trial-by-trial variations.