The induced effect,vertical disparity,and stereoscopic theory

The induced effect is an apparent slant of a frontal plane surface around a vertical axis, resulting from vertical magnification of the image in one eye. It is potentially important in suggesting a role for vertical disparity in stereoscopic vision, as proposed by Helmholtz. The paper first discusses previous theories of the induced effect and their implications. A theory is then developed attributing the effect to the process by which the stereoscopic response to horizontal disparity is scaled for viewing distance and eccentricity. The theory is based on a mathematical analysis of vertical disparity gradients produced by surfaces at various distances and eccentricities relative to the observer. Vertical disparity is shown to be an approximately linear function of eccentricity, with a slope or gradient which decreases with observation distance. The effect of vertical magnification on such gradients is analyzed and shown to be consistent with a change in the eccentricity factor, but not the distance factor, required to scale horizontal disparity. The induced effect is shown to be an appropriate stereoscopic response to a zero horizontal disparity surface at the eccentricity indicated. However, since extraretinal convergence signals provide conflicting evidence about eccentricity, they may attenuate the induced effect from its mathematically predicted value. The discomfort associated with the induced effect is attributed to this conflict.