基本矩阵的5点和4点算法(英文)

5-point and 4-point Algorithm to Determine of the Fundamental Matrix

基本矩阵 (FundamentalMatrix)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 。

The fundamental matrix encapsulates all the information between two images, and plays a very important role in camera calibration and 3D reconstruction. The following conclusions were 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 are not reported yet in the literature.