Linear pixel shuffling for image processing: an introduction

We present a method of ordering pixels (the elements of a rectangular matrix) based on an arithmetic progression with wrap-around (modular arithmetic). For appropriate choices of the progression’s parameters based on a generalization of Fibonacci numbers and the golden mean, we achieve uniformly distributed collections of pixels formed by intervals of the pixel progression or “shuffle.” We illustrate this uniformity with a novel approach to progressive rendering of a synthetic image, and we note several opportunities for applications to other areas of image processing.