A Theoretical and Experimental Consideration on Interference in Resolutions between Sampling Theorem and OK-Quantization Theory

OK-quantization theory for the digitization in value ensures the reconstruction of the probabilistic density function of the image. This paper shows some experimental demonstrations to reduce the number of the gray levels, and shows mainly that there is a necessary but very important analytical relationship between sampling and quantization based on the equivalence relationship between two kinds of the integral, Riemann and Lebesgue integrals for calculating the volume of the image. Experimental demonstrations are also shown in this paper