One-dimensional (1-D) orientation illusions induced on a test grating by a tilted and-surrounding 1-D inducing grating have a well-known angular function that exhibits both repulsion and attraction effects. Two-dimensional (2-D) orientation illusions are those induced on a test grating by 2-D image modulation, such as a pair of superimposed inducing gratings at different orientations, usually orthogonal (a plaid). Given the known angular functions induced by the plaid component gratings, two hypotheses were developed that predicted different plaid-induced illusion functions. Hypothesis 1 states that the 1-D component-induced effects simply add linearly; Hypothesis 2 states that there is an additional mechanism that responds to the virtual axes of mirror symmetry of the plaid and adds to the effect. The data of two experiments were consistent with the predictions from the second hypothesis but not the first. Possible neural substrates of mechanisms that extract axes of symmetry are discussed; it is suggested that such global symmetry axes may underlie the perceived orientation of complex shapes.