Estimating the thickness of ultra thin sections for electron microscopy by image statistics

We propose a method for estimating the thickness of ultra thin histological sections by image statistics alone. Our method works for images, that are realisations of a stationary and isotropic stochastic process, and it relies on the existence of statistical image-measures that are strictly monotonic with distance. We propose to use the standard deviation of the difference between pixel values as a function of distance, and give an extremely simple, linear algorithm. Our algorithm is applied to the challenging domain of electron microscopic sections supposedly 45 nm apart, and we show that these images with high certainty belong to the required statistical class, and that the reconstructions are valid.