Abstract:

Addressing the issue of computer processing in the internal spherical screen projection, an internal spherical screen projection algorithm was proposed based on virtual spherical transform and virtual fisheye lens mapping. Concerning the spherical screen output distortion caused by irregular fisheye projection, a sextic polynomial of distortion correction algorithm based on the equal-solid-angle mapping function was presented to approximate any fisheye mapping function to eliminate the distortion. The six coefficients of the polynomial could be obtained via solving a linear algebra equation. The experimental results show this method is able to completely eradicate the spherical screen projection distortion. Addressing the illumination distribution modification stemming from the spherical screen projection, an illumination correction algorithm based on the cosine of the projecting angles was also proposed to eliminate the illumination distribution change. The experimental results show the illumination distribution correction method successfully recovers the originally severely modified illumination distribution into the illumination distribution almost identical to the original picture. This algorithm has theoretical instructive importance and significant practical application values for design and software development of the spherical projection systems.

Key words: Spherical Screen Projection, Fisheye lens, Virtual Sphere, Fisheye Mapping Function, Fisheye distortion correction

摘要：

针对内投式球幕投影中涉及的计算机处理过程，提出了基于虚拟球面变换和虚拟鱼眼透镜投射的内投式球幕投影算法，并针对不规则鱼眼透镜导致的球幕映像扭曲，提出了基于等立体角投影函数的六阶函数校正算法，该六阶函数的系数可通过简单求解六元一次方程获得。实验结果表明，该方法能完全消除不规则鱼眼透镜导致的球幕投影扭曲。针对球幕投影导致的图像亮度分布变异提出了基于投射角余弦修正的球幕光强校正算法。实验结果表明，该算法成功地把与输入二维图像亮度分布差异明显的球幕投影图像校正至与原始图像亮度分布高度一致的状态。该方法对球幕投影系统的设计和软件开发具有重要的理论指导意义和实践应用价值。

关键词: 球幕投影技术, 鱼眼透镜, 虚拟球面, 鱼眼投影, 鱼眼畸变校正