Unitary rotation of pixellated polychromatic images

Abstract

Unitary rotations of polychromatic images on finite two-dimensional pixellated screens provide invertibility, group composition, and thus conservation of information. Rotations have been applied on monochromatic image data sets, where we now examine closer the Gibbs-like oscillations that appear due to discrete “discontinuities” of the input images under unitary transformations. Extended to three-color images, we examine here the display of color at the pixels where, due to oscillations, some pixel color values may fall outside their required common numerical range [0,1], between absence and saturation of the red, green, and blue formant colors we choose to represent the images.