Linear Solving the Infinite Homography Matrix from Epipole

The infinite homography matrix plays an important role in affine reconstruction. The new constraint between the homography of the infinity plane and the epipole is that the epipolar geometry can get a new equation after analyze. According to the new constraint, the infinite homography matrix can be linear solved, and the affine reconstruction can be also gotten through the triangulation principle. Compared with the approach of literatures, it avoids solving the vanish points and the vanish lines and needs not the information of the homography of a space plane. If the correspondences epipoles and matching points in two images are known, the infinite homography matrix can be linear solving. Using the relationship between absolute conic and infinite homography matrix to solve the camera´s intrinsic parameters. The feasibility of the approach can be seen from the simulation experiments. Real experiments indicate that the approach has really high robustness.