Catadioptric sensors that approximate wide-angle perspective projections
Catadioptric sensors that approximate wide-angle perspective projections
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近似广角透视投影的折反射传感器
DOI：
10.1109/omnvis.2000.853813
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发表时间：
2000
期刊：
影响因子：
--
通讯作者：
R. Bajcsy
中科院分区：
文献类型：
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作者：
R. A. Hicks;R. Bajcsy
我们提出了两个系列的反射表面，它们能够提供宽阔的视野，但仍然可以高度近似透视投影。这些表面是通过考虑垂直于旋转表面的轴的平面并找到控制该表面中平面的图像畸变的方程而导出的。然后，我们将此关系视为微分方程，并将畸变项规定为线性。通过为微分方程选择适当的初始条件并对其进行数值求解，我们推导出表面形状并获得对所得传感器可以近似透视投影的程度的精确估计。因此，这些表面充当计算传感器，无需在软件中处理图像即可获得场景的广角透视图。这种传感器的应用应该很广泛，包括监控、机器人和传统摄影。
We present two families of reflective surfaces that are capable of providing a wide field of view, and yet still approximate a perspective projection to a high degree. These surfaces are derived by considering a plane perpendicular to the axis of a surface of revolution and finding the equations governing the distortion of the image of the plane in this surface. We then view this relation as a differential equation and prescribe the distortion term to be linear. By choosing appropriate initial conditions for the differential equation and solving it numerically, we derive the surface shape and obtain a precise estimate as to what degree the resulting sensor can approximate a perspective projection. Thus these surfaces act as computational sensors, allowing for a wide-angle perspective view of a scene without processing the image in software. The applications of such a sensor should be numerous, including surveillance, robotics and traditional photography.