Discrete invertible affine transformations

The theory and algorithm of a general method that constructs one-to-one mappings on an n-dimensional digital lattice are presented. The mapping is constructed so that any given equivolume affine transformation can be approximated. Equivolume affine transformations include translation, reflection, and skew. It is shown that (n²-1) fundamental skew transformations, n fundamental translations, and some reflective transformations are sufficient to represent arbitrary equivolume affine transformation. One-to-one integer approximation of the fundamental transformations and approximation error propagation rules are described. Minimum error decomposition algorithms for the equivolume affine transformation in n-dimensional space and two-dimensional space are proposed