3d shape and scene layout are often misperceived when viewing stereoscopic displays. For example, viewing from the wrong distance alters an object's perceived size and shape. It is crucial to understand the causes of such misperceptions so one can determine the best approaches for minimizing them. The standard model of misperception is geometric. The retinal images are calculated by projecting from the stereo images to the viewer's eyes. Rays are back-projected from corresponding retinal-image points into space and the ray intersections are determined. The intersections yield the coordinates of the predicted percept. We develop the mathematics of this model. In many cases its predictions are close to what viewers perceive. There are three important cases, however, in which the model fails: 1) when the viewer's head is rotated about a vertical axis relative to the stereo display (yaw rotation); 2) when the head is rotated about a forward axis (roll rotation); 3) when there is a mismatch between the camera convergence and the way in which the stereo images are displayed. In these cases, most rays from corresponding retinal-image points do not intersect, so the standard model cannot provide an estimate for the 3d percept. Nonetheless, viewers in these situations have coherent 3d percepts, so the visual system must use another method to estimate 3d structure. We show that the non-intersecting rays generate vertical disparities in the retinal images that do not arise otherwise. Findings in vision science show that such disparities are crucial signals in the visual system's interpretation of stereo images. We show that a model that incorporates vertical disparities predicts the percepts associated with improper viewing of stereoscopic displays. Improving the model of misperceptions will aid the design and presentation of 3d displays.

中文翻译：

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立体显示中的误解：视觉科学视角。

在观看立体显示器时，3d 形状和场景布局经常被误解。例如，从错误的距离观看会改变物体的感知大小和形状。了解这种误解的原因至关重要，这样人们就可以确定将它们最小化的最佳方法。误解的标准模型是几何的。视网膜图像是通过将立体图像投影到观看者的眼睛来计算的。光线从相应的视网膜图像点反向投影到空间中，并确定光线的交叉点。交叉点产生预测感知的坐标。我们开发了这个模型的数学。在许多情况下，它的预测接近观众的感知。然而，在三种重要的情况下，模型会失败：1）当观众的 头部相对于立体显示器绕垂直轴旋转（偏航旋转）；2）当头部围绕一个正向轴旋转时（滚动旋转）；3) 当相机会聚与立体图像的显示方式不匹配时。在这些情况下，来自相应视网膜图像点的大多数光线不相交，因此标准模型无法提供 3d 感知的估计。尽管如此，在这些情况下的观看者具有连贯的 3d 感知，因此视觉系统必须使用另一种方法来估计 3d 结构。我们表明非相交光线在视网膜图像中产生垂直差异，否则不会出现。视觉科学的发现表明，这种差异是视觉系统解释立体图像的关键信号。我们展示了一个包含垂直差异的模型可以预测与立体显示不当观看相关的感知。改进误解模型将有助于 3d 显示的设计和呈现。