Unitary rotation of square-pixellated images

摘要

The unitary rotation of square-pixellated images is based on the finite su(2)-oscillator model, which describes systems whose values for position, momentum and energy, are discrete and finite. In a two-dimensional position space, this allows the construction of angular momentum states, orthonormal and complete, for which rotations are defined as multiplication by phases that carry the rotation angle. The decomposition of a digital square images in terms of these angular momentum states determines a unitary (hence invertible) rotation of the image, whose kernel can be computed as a four-dimensional array of real numbers.