Okatani Takayuki, Deguchi Koichiro
Graduate School of Information Sciences, Tohoku University, 6-6-09 Aramaki Aza Aoba, Sendai, 980-8579 Japan.
IEEE Trans Pattern Anal Mach Intell. 2005 Dec;27(12):1845-55. doi: 10.1109/TPAMI.2005.235.
This paper presents a method for calibrating a projector-camera system that consists of multiple projectors (or multiple poses of a single projector), a camera, and a planar screen. We consider the problem of estimating the homography between the screen and the image plane of the camera or the screen-camera homography, in the case where there is no prior knowledge regarding the screen surface that enables the direct computation of the homography. It is assumed that the pose of each projector is unknown while its internal geometry is known. Subsequently, it is shown that the screen-camera homography can be determined from only the images projected by the projectors and then obtained by the camera, up to a transformation with four degrees of freedom. This transformation corresponds to arbitrariness in choosing a two-dimensional coordinate system on the screen surface and when this coordinate system is chosen in some manner, the screen-camera homography as well as the unknown poses of the projectors can be uniquely determined. A noniterative algorithm is presented, which computes the homography from three or more images. Several experimental results on synthetic as well as real images are shown to demonstrate the effectiveness of the method.
本文提出了一种用于校准由多个投影仪（或单个投影仪的多个姿态）、一个相机和一个平面屏幕组成的投影仪-相机系统的方法。我们考虑在没有关于屏幕表面的先验知识以直接计算单应性的情况下，估计屏幕与相机图像平面之间的单应性，即屏幕-相机单应性的问题。假设每个投影仪的姿态未知，但其内部几何结构已知。随后表明，屏幕-相机单应性仅可从投影仪投射并由相机获取的图像中确定，最多相差一个具有四个自由度的变换。此变换对应于在屏幕表面选择二维坐标系时的任意性，当以某种方式选择此坐标系时，屏幕-相机单应性以及投影仪的未知姿态可唯一确定。提出了一种非迭代算法，该算法从三个或更多图像计算单应性。展示了在合成图像和真实图像上的几个实验结果，以证明该方法的有效性。
