Estimation Of Homography Based On The Common Self-polar Triangle Of Sphere Images

The plane projective transformation(Homography)is one of the significant tools of computer vision algorithms and has widely applications.Under the paracatadioptric camera,based on the common self-polar triangle of sphere image and antipodal sphere image,the method of homography estimation is presented.The projection process of a space sphere under the paracatadioptric camera has two steps.In the first step,a space sphere is projected onto the unit viewing sphere to form a pair of antipodal circles.In the second step,the intersection point of the virtual camera optical axis and the unit viewing sphere is taken as the projection center,and the pair of the antipodal circles on the unit viewing sphere are projected onto the image plane to form two disjoint conics.Since EoH estimates homography based on the common self-polar triangle between two image planes,two image planes are obtained by taking a space sphere from two different angles.Firstly,the equations of sphere image and antipodal sphere image of a space sphere on two image planes are obtained.Secondly,the eigenvalues and eigenvectors of the matrices on these two image planes are calculated respectively,thus,the common self-polar triangles of sphere image and antipodal sphere image on the two image planes are obtained.And three pairs of line correspondences are obtained by matching the eigenvalues.The fourth pair of line correspondence is obtained by connecting a set of intersection points of the common self-polar triangle and the conics.This pair of line correspondence is located in the common self-polar triangle.Because homography matrix has eight degrees of freedom,a pair of line correspondences provides two equations about the elements of homography matrix.Four pairs of line correspondences are sufficient to estimate homography matrix.Then,another pair of lines by connecting the intersection points of the common self-polar triangle and the conics is used to verify the validity of homography matrix obtained by the proposed method.Based on the platform of MATLAB R2016a,the feasibility and validity of this method are verified with simulate experiments and real experiments.