Fixed Points of a Generalized Discrete Baker's Transformation

In this note we investigate the fixed point sets for the iterations of a generalization of the two-dimensional discrete baker's transformation. In particular, we will derive explicit formulas for the fixed points, and the number of fixed points. Moreover, we will show that the set of all fixed points is a closed set. This generalizes the some of known results for the classical baker's transformation

Adaptive color quantization using the baker's transformation

International audienceIn this article we propose an original technique to reduce the number of colors contained in an image. This method uses the "Bakers Transformation", which obtains a statistically suitable mixture of the pixels of the image. mm this mixture, we can extract several samples, which present the same characteristics as the initial image. The concept we imagined is to consider these samples as potential pallets of colors. These pallets make it possible to do an adaptive quantization of the efiectiue number of colors. We consider, and we put in competition, three methods to obtain a single pallet. Firstly, we present the "Baker 's Transformation". Secondly, we present methods to have a single pallet. Third part is dedicated to results illustrating the good visual quality reached by the quantized images. Finally, we present a comparison between our method and three classical methods of quantization