A new spin on color quantization

Abstract

We address the problem of image color quantization using a maximum entropy based approach. Focusing on pixel mapping we argue that adding thermal noise to the system yields better visual impressions than that obtained from a simple energy minimization. To quantify this observation, we introduce the coarse-grained quantization error, and seek the optimal temperature which minimizes this new observable. By comparing images with different structural properties, we show that the optimal temperature is a good proxy for complexity at different scales. Noting that the convoluted error is a key observable, we directly minimize it using a Monte Carlo algorithm to generate a new series of quantized images. Adopting an original approach based on the informativity of finite size samples, we are able to determine the optimal convolution parameter leading to the best visuals. Finally, we test the robustness of our method against changes in image type, color palette and convolution kernel.

Multiscale Relevance of Natural Images

“…For the sake of simplicity, let us consider the case of an initial grayscale palette projected on binary values {0, 255} (B&W). We implement a stochastic mapping procedure using the Boltzmann distribution P(c|h ij ) ∝ e −(hij −c) 2 /T , where h ij is the original color of pixel with coordinates ij, c ∈ {0, 255} the color in the reduced palette, and T a temperature parameter, see [44]. T = 0 corresponds to the choice of the closest color in the reduced palette, while T → ∞ leads to uniform noise.…”

Multiscale relevance of natural images

“…For the sake of simplicity, let us consider the case of an initial grayscale palette projected on binary values (b&w). We implement a stochastic mapping procedure using the Boltzmann distribution , where is the original color of pixel with coordinates ij , the color in the reduced palette, and T a temperature parameter, see 49 . Note that this probability density is obtained from the maximal entropy distribution related to the minimization of the Mean-Squared Error (MSE) between the original and mapped images.…”