Unitary rotation of pixellated polychromatic images

TL;DR

This paper explores the mathematical properties of unitary rotations applied to pixellated polychromatic images, analyzing their invertibility, information conservation, and the oscillations caused by discrete transformations, especially in color display.

Contribution

It extends the study of unitary rotations from monochromatic to three-color images, examining oscillations and color value issues in pixel-based transformations.

Findings

Unitary rotations preserve information and are invertible.

Oscillations occur due to discrete discontinuities in the images.

Color values may fall outside the valid range [0, 1] after rotation.

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 the 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 color images.