The majority of quantitative studies on symmetry perception have employed random dot patterns, yet symmetrical random patterns are not common in nature. Here we explore symmetry perception utilizing sums of radial frequency (RF) patterns to define complex shapes. When a pair of RF patterns with different frequencies are added, the relative phase of the two components provides a precise measure of the degree of deviation from bilateral symmetry. Sums of RF2-RF7 define such diverse biological shapes as human heads, animal heads, torsos, and many fruit, so discrimination of symmetries defined by these patterns is highly relevant to biological vision. Here we show that symmetry discrimination during brief presentations is best for RF2+RF3 but becomes impossible for RF2+RF7. Further experiments demonstrate that the underlying neural mechanisms differ from those involved in random dot symmetry detection. These results were used to predict symmetry thresholds for deviations from bilateral symmetry of head shapes based on a principal components analysis of 30 female heads. Human V4 is hypothesized to be the site for symmetry discrimination of RF patterns but not of random dot patterns.