摘要:
基本矩阵(Fundamental Matrix)是两幅图像之间的基本约束,在摄像机标定和三维重建
中起着至关重要的作用.本文证明,当摄像机在两幅图像之间的运动为纯平移运动时,给定5对
图像对应点,如果其中的4对对应点为共面空间点的投影(称为共面对应点),则可以线性确定基
本矩阵.另外,如果摄像机不是5参数模型(完全针孔模型),而是4参数模型(畸变因子为零),则
此时仅使用该4对共面对应点即可线性确定基本矩阵.据我们所知,这些结果在文献中还没有类
似的报导.
Abstract:
The fundamental matrix encapsulates all the information between two images, and
plays a very important role in camera calibration and 3D reconstruction. In this paper, the following
conclusions have been rigorously proved: If the camera motion is of a pure translation, then
given 5 point correspondences across two images, the fundamental matrix can be linearly determined
if four correspondences of the 5 ones are from coplanar space points (called coplanar correspondences).
In addition, we show that if the distortion factor in the pinhole camera model is
null, then the fundamental matrix can be linearly determined by only these 4 coplanar correspondences.
To our knowledge, such results have not been reported yet in the literature.
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