One-dimensional mapping for estimating projective transformations.

In this paper, the 1-D mapping is studied for estimating a general projective transformation between images. First, a ray model of image patches is proposed to convert a complex projective deformation of a patch in the Cartesian space into two simple rigid shifts of radial lines in the log-polar/inverse-polar space. To capture these shifts via direct search, two types of radial image line matching, viz.

Ray projection for recovering projective transformations and illumination changes.

The ray projection and its application to recovering a projective geometric transformation and an affine lighting change between two objects are mathematically studied. A novel technique, viz., variable contour, is proposed for accurately evaluating the ray projection.