  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.
