On 1-1 Bivariate Transformations Original Research Article

We study a class of one-to-one tensor mappings defined on a rectangular region of the plane. Such mappings are of interest in image processing, computer vision, biological morphology, cartography, and medical imaging. The mappings are constructed as tensor-products of univariate functions, and the main result is a set of constraints on the parameters of the mapping which assure that it is one-to-one. We illustrate the method by showing how to construct one-to-one mappings using tensor-product polynomials and tensor-product splines.