Geometric correction of digital images using orthonormal decomposition

We have developed an algorithm which can be used to correct the geometric distortion of digital images. The method uses an orthonormal decomposition and a two-dimensional Horner's scheme to construct and evaluate a polynomial equation of arbitrary degree in two independent variables. This numerical scheme for geometric correction combines several methods selected on the basis of their computation efficiency and numerical stability. The differences and advantages of this numerical scheme are compared with methods found in the image processing literature. The algorithm presented here has a reduced number of mathematical operations, is flexible and numerically stable. Based on the least-squares criteria, the algorithm provides corrected pixel positions with an accuracy equal to or better than the pixel size.