The subjective minimum number of gray levels for natural images derived by OK-quantization theory

The analog image is digitalized by the sampling and the quantization. It is well known that the maximum sampling interval is derived by the sampling theorem. On the other hand, Koshimizu introduces the OK-quantization theory for image signals, which shows the maximum quantization interval. The minimum number of gray levels is also easily given by the maximum quantization interval. We apply the OK-quantization theory to a lot of natural images and derive those of the number of minimum gray levels. However, the minimum number of gray levels is different from the minimum number of gray levels for avoiding the false contouring. In this paper, we propose the pre-processing for the probability density function of natural images in order to obtain the minimum number of gray levels for avoiding the false contouring by the OK-quantization theory.