Better Global Polynomial Approximation for Image Rectification

When using images to locate objects, there is the problem of correcting for distortion and misalignment in the images. An elegant way of solving this problem is to generate an error correcting function that maps points in an image to their corrected locations. We generate such a function by fitting a polynomial to a set of sample points. The objective is to identify a polynomial that passes “sufficiently close” to these points with “good” approximation of intermediate points. In the past, it has been difficult to achieve good global polynomial approximation using only sample points. We report on the development of a global polynomial approximation algorithm for solving this problem.