Super-resolution images reconstructed from single molecule coordinates reveal cellular structures close to the macromolecular scale. However, a widely applicable analysis tool that can extract a quantitative description and biophysical parameters from these images is still unavailable. Here, we propose a universal analysis concept for coordinate-based super-resolution images using correlation functions. We demonstrate how this analysis can quantify diffusion, localization precision, distance and co-localization. Moreover, we developed a framework for averaging multiple images by non-linear transformations to reveal structures with much higher resolution.First, we show that the commonly used pair-distance histogram is mathematically equivalent to pixel-based correlation analysis. Therefore, many strategies of pixel-based image correlation spectroscopy can also be applied to coordinate-based super-resolution images. In particular, the computational complexity of pair-distance calculations can be decreased by pixel-binning the coordinate image and employing the Fast Fourier Transform algorithm.Second, we demonstrate that the pair-distance histogram of molecule coordinates from consecutive frames allows measuring the diffusion coefficient of membrane lipids in live cells with high spatial resolution. Our analysis can handle extremely high fluorophore densities, in contrast to conventional single-particle tracking methods. The same frame-pair histogram can analogously be used to generate a map of molecule localization precision for super-resolution images, which is still elusive information.Third, we show how coordinate-based correlation functions can be used for image alignment involving transformations beyond translation. For example, we rotationally aligned multiple images of the nuclear pore complex from yeast, which exposes the octagonal complex with high precision.Finally, we propose a new correlation function, namely the point-set distance histogram, which allowed us to quantify both co-localization and distance of Clathrin to proteins of the Golgi apparatus, even though the super-resolution images were highly corrupted by background and two-color crosstalk.