Turski Jacek
Department of Mathematics and Statistics, University of Houston-Downtown, Houston, TX 77002, USA.
Vision Res. 2016 Feb;119:73-81. doi: 10.1016/j.visres.2015.11.001. Epub 2016 Jan 21.
We study geometric properties of horopters defined by the criterion of equality of angle. Our primary goal is to derive the precise geometry for anatomically correct horopters. When eyes fixate on points along a curve in the horizontal visual plane for which the vergence remains constant, this curve is the larger arc of a circle connecting the eyes' rotation centers. This isovergence circle is known as the Vieth-Müller circle. We show that, along the isovergence circular arc, there is an infinite family of horizontal horopters formed by circular arcs connecting the nodal points. These horopters intersect at the point of symmetric convergence. We prove that the family of 3D geometric horopters consists of two perpendicular components. The first component consists of the horizontal horopters parametrized by vergence, the point of the isovergence circle, and the choice of the nodal point location. The second component is formed by straight lines parametrized by vergence. Each of these straight lines is perpendicular to the visual plane and passes through the point of symmetric convergence. Finally, we evaluate the difference between the geometric horopter and the Vieth-Müller circle for typical near fixation distances and discuss its possible significance for depth discrimination and other related functions of vision that make use of disparity processing.
我们研究由角度相等标准定义的双眼单视界的几何特性。我们的主要目标是推导解剖学上正确的双眼单视界的精确几何形状。当眼睛注视水平视觉平面上某条曲线上的点时，双眼的聚散度保持不变，这条曲线是连接眼睛旋转中心的圆的较大弧段。这个等聚散度圆被称为维特 - 米勒圆。我们表明，沿着等聚散度圆弧，存在由连接节点的圆弧形成的无限多个水平双眼单视界。这些双眼单视界在对称会聚点相交。我们证明三维几何双眼单视界族由两个垂直分量组成。第一个分量由以聚散度、等聚散度圆上的点以及节点位置的选择为参数的水平双眼单视界组成。第二个分量由以聚散度为参数的直线形成。这些直线中的每一条都垂直于视觉平面并经过对称会聚点。最后，我们评估了典型近注视距离下几何双眼单视界与维特 - 米勒圆之间的差异，并讨论了其对于深度辨别以及利用视差处理的其他相关视觉功能可能具有的意义。
