基于场景平面诱导单应对Sherman-Morrison公式的证明

The proof of Sherman-Morrison theorem based on the homography induced by the ocene plane

利用计算机视觉中射影重构方法来研究一类矩阵的求逆问题,首先通过场景平面诱导两幅图像之间的单应,然后利用射影重构的多义性,求出两图像单应的逆矩阵,来证明Sherman-Morrison公式.使矩阵运算的一些问题得到简化.本文给出了以其它学科来解决纯数学的一点较新的思路.

This paper studys the issue on the inverse of a class matrix by using the projective reconstruction in computer vision.It demonstrates the Sherman-Morrison formula by first inducing homography between two pictures through the ocene plane, and also amounting to the inverse matrix of homography of the two pictures through using ambiguity of projective reconstruction.Which simply the complex problem.The present paper provides a novel way of thought in solution of the mathematical problems by making use of other subjects.