Encoding true-color images with a limited palette via soft vector clustering as an instance of dithering multidimensional signals

• We introduce a general dithering scheme for multidimensional signals.
• This dithering scheme is based on stochastic (soft) vector quantization.
• We provide the formulae of the upper-bound of the quantization noise of this dithering.
• We provide a visual instance of the behavior of this dithering with true-color images.
• This is also a new method of the optimal encoding of true-color images with a limited palette.

One of the classic problems of digital image processing is to encode true-color images for the optimal viewing on displays with a limited set of colors. A major manifestation of optimal viewing in this regard is to maximally remove parasitic artifacts in the degraded encoded images such as the contouring effect. Several robust attempts have been made to solve this problem over the past 50 years, and the first contribution of this paper is to introduce a simple – yet effective – novel solution that is based on soft vector clustering.The other contribution of this paper is to propose the application of the soft clustering methodology deployed in our color-encoding solution for the dithering of multidimensional signals. Dithering essentially adds controlled noise to the analog signal upon its digitization so that the resulting quantization noise is dispersed over a much wider band of the frequency domain and is therefore less perceptible in the digitized signal. This comes of course at the price of more overall quantization noise. Dithering is a vital operation that is performed via well-known simple schemes upon the analog-to-digital conversion of one-dimensional signals; however, the published literature is still missing a general neat scheme for the dithering of multidimensional signals that is able to handle arbitrary dimensionality, arbitrary number and distribution of quantization centroids, and with computable and controllable noise power. This gap is also filled by this paper.