Aligning Curves Under Projective Transform and its Application to Image Registration

A method to accurately align plane curves related by projective transform is described in this paper. Superior accuracy and efficiency are achieved by the use of super-curve and B-spline fusion. A super-curve is formed by superimposing two transform related and aligned curves upon each other. The B-spline fusion technique uses a single B-spline to approximate the super-curve and to align the two curves at the same time. The eight-parameter projective transform is decomposed into a simple two-parameter projective transform and an affine transform, for which a linear solution can be found. Therefore the search in the traditional eight dimensional space is reduced to a two dimensional search. The major contribution of the paper lies in the novel use of a single B-spline to represent two curves, whereas in previous approaches each curve is represented with a separate B-spline. This use of a single B-spline gives higher resolution from the two point sets instead of one. So the final result is more robustness to sampling noise. It also provides a simple and integrated framework in solving the curve matching and the transform recovery problems simultaneously.