Tremendous strides in experimental capabilities of scanning transmission electron microscopy and scanning tunneling microscopy (STM) over the past 30 years made atomically resolved imaging routine. However, consistent integration and use of atomically resolved data with generative models is unavailable, so information on local thermodynamics and other microscopic driving forces encoded in the observed atomic configurations remains hidden. Here, we present a framework based on statistical distance minimization to consistently utilize the information available from atomic configurations obtained from an atomically resolved image and extract meaningful physical interaction parameters. We illustrate the applicability of the framework on an STM image of a FeSexTe1–x superconductor, with the segregation of the chalcogen atoms investigated using a nonideal interacting solid solution model. This universal method makes full use of the microscopic degrees of freedom sampled in an atomically resolved image and can be extended via Bayesian inference toward unbiased model selection with uncertainty quantification.