2026/07/22 by A. Y. Shavit · 1 voice
#q-bio.NC #stat.AP
The visually perceived vertical is biased by the orientation content of the visual field. Li and Matin (2005a, 2005b) reported three regularities of this induced vertical (VPV): a roll-tilted peripheral line shifts it about linearly with orientation; two lines combine about linearly; and symmetric tilts cancel. We show all three follow from one principle. The induced vertical is half the argument of the first circular moment of stimulus orientation in the doubled-angle domain, ϕ=(1)/(2)arg c1 with c1=∑j Aj ei2γj (each line counted at twice its angle). Equivalently it is the principal axis of the orientation structure tensor, or an orientation population vector; we call it the orientation order-parameter model (PLUMB). The angle-doubling is forced: orientation is a director (θ≡θ+π), so a circular-mean readout must be the doubled-angle one, and linear tracking, combination, and cancellation are signatures of any such readout, not separate findings. Li and Matin's 2-, 3-, and 4-line combination coefficients are then closely matched with no per-configuration free parameters in the angles; the magnitudes come from one mass-action length function (their Fig. 5, three constants). The data refute complete summation but do not separate the model from simple averaging for long lines; the decisive parameter-free tests are the short-line regime and a |cos 2θ| strength law with a null at 45^∘. Read as a sum and a difference across the two hemifields, the same order parameter yields perceived vertical and eye level, recovering the reversed rules of Shavit, Li and Matin (2013); their 30-observer trial data confirm the predicted sub-additive cross-field combination. The account is stimulus-side and image-computable, linking induced vertical and eye level to classical image-orientation descriptors.