Nonlinear transformations of digitized patterns

For applying general, nonlinear shape transformations T: (ξ η)→(x, y) such that x=x(ξ, η), y=y(ξ, η), novel shooting methods are presented to avoid superfluous holes or blanks in the transformed images. Important relationships are established for the numerical methods used in image transformations and pattern recognition. Experiments have been carried out to verify the theoretical results