On optimal image digitization

Nielsen et al. recently addressed the problem of determining the optimal discretization grid and quantization depth when a given bivariate function f(x, y) has to be described with a predetermined number of bits. This was done under the assumption that the function value range and mean "fluctuation rates" in the x and y direction are given, and that ideal point sampling with zero-order-hold interpolation is used in reconstructing the image. This correspondence outlines an alternative approach, based on the assumption that f (x, y) is the sample function of a 2-D stationary stochastic process with a known covariance function. We use standard integral sampling and obtain closed form solutions under the assumption that f(x, y) is (the sample of) a homogeneous and separable Markov process.