发表机构
Hunter College and the Graduate Center, City University of New York（纽约市立大学亨特学院及研究生院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究视觉感知垂直方向受视野影响的规律，提出方向序参量模型，表明李 - 马丁规则源于此模型，能紧密匹配组合系数，解释感知垂直和视线水平，经试验数据证实其跨视野组合的次可加性，且基于刺激侧可图像计算。
AI 中文摘要
视觉感知的垂直方向会受到视野方向内容的影响。李和马丁（2005a，2005b）报告了这种诱导垂直（VPV）的三个规律：倾斜的外周线会使其随方向线性移动；两条线的组合近似线性；对称倾斜相互抵消。我们表明这三个规律都源于一个原理。诱导垂直是刺激方向在双角度域中第一圆矩的辐角的一半，即\(\phi=\frac{1}{2}\arg c_1\)，其中\(c_1=\sum_j A_j e^{i2\gamma_j}\)（每条线以其角度的两倍计数）。等效地，它是方向结构张量的主轴或方向总体向量；我们称之为方向序参量模型（PLUMB）。角度加倍是必然的：方向是有向的（\(\theta\equiv\theta+\pi\)），所以圆均值读出必须是双角度的，并且线性跟踪、组合和抵消是任何此类读出的特征性表现，而非单独的发现。李和马丁的二线、三线和四线组合系数随后能紧密匹配，角度上没有每个配置的自由参数；其大小来自一个质量作用长度函数（他们的图5，三个常数）。数据反驳了完全求和，但对于长线并未将该模型与简单平均区分开；决定性的无参数测试是短线情况和在\(45^\circ\)处为零的\(|\cos 2\theta|\)强度定律。作为两个半视野上的和与差来读取，相同的序参量产生感知垂直和视线水平，恢复了沙维特、李和马丁（2013）的反向规则；他们的30名观察者的试验数据证实了预测的跨视野组合的次可加性。该解释基于刺激侧且可通过图像计算，将诱导垂直和视线水平与经典图像方向描述符联系起来。
英文摘要
Li and Matin (2005a, 2005b) reported three regularities of the induced visually-perceived vertical (VPV): a roll-tilted line shifts the vertical nearly linearly with its orientation; two lines combine nearly linearly; symmetric tilts cancel. All three follow from one principle. The induced vertical -- a stimulus-side axis, not yet the observer's setting -- is half the argument of the first circular moment of the stimulus orientation distribution in the doubled-angle domain, phi = (1/2) arg(c_1) with c_1 = sum_j A_j exp(i 2 gamma_j). We call this the orientation order-parameter model (PLUMB), and prove c_1 is the unique additive, salience-homogeneous spin-2 axial summary. Director symmetry rules out the odd rotational orders, so the doubling is the lowest available; linear pooling and positive homogeneity then fix c_1 within that rung. Li and Matin's 2-, 3-, and 4-line coefficients are matched with no per-configuration free parameters in the angles, one published saturating length-gain function setting the gain; the orthogonal and square configurations have a first moment of exactly zero, so there is no angle to fit. The data refute complete summation but cannot separate the account from simple averaging for long lines; the decisive tests are short lines and the |cos 2theta| coherence law vanishing at 45 degrees. A further, substantive assumption decomposes the signal per hemifield into sum and difference readouts, making perceived eye level (VPEL) the antisymmetric counterpart of VPV and recovering Shavit, Li, and Matin's (2013) reversed integration rules. Trial-level data (30 observers) confirm the predicted sign and null structure; the sub-additive magnitude is a gain read from the data, not derived. The account is stimulus-side, computed before body/gravity weighting, and image-computable, linking both percepts to classical image-orientation descriptors.
Comments45 pages, 14 figures
