Inverse-polar ray projection for recovering projective transformations

A ray projection in the inverse-polar space is proposed for recovering a projective transformation between two segmented images. The images are converted from their original Cartesian space to the inverse-polar space. Then, the two ray projections - one shift-invariant and the other shift-sensitive - of the inverse-polar images are computed to create two sets of data. Based on the obtained projection data, a two-step strategy is employed to recover the projective transformation. In the first step, the shift-invariant data are used to recover the four affine parameters. In the second step, the shift-sensitive data are used to recover the two projective parameters. The remaining two translation-related parameters are recovered in, e.g., an exhaustive search combined with the two-step recovery strategy. The proposed approach has been tested successfully to recover a variety of projective transformations between real images.