Triple-stochastic models and palm-trees: spatial point processes in super-resolution data

Recent advances in super-resolution fluorescence microscopy, such as MINFLUX, enable the localisation of single molecules with nanometre precision. These developments offer new opportunities to investigate molecular organisation at an unprecedented spatial scale. However, the increasing resolution of microscopy data introduces new challenges in analysis - particularly in detecting and characterising spatial structure within noisy, sparse, and complex datasets.<br/><br/>Template matching, a common analysis approach, typically relies on extensive a priori information and subjective decision-making. Its dependence on predefined structural models and manual selection introduces the risk of bias and may limit its generalisability. This work investigates an alternative strategy: modelling localisation data as spatial point patterns, and applying statistical tools grounded in point process theory to determining repeating structure(s) in the data.<br/><br/>Here, we describe a Python-based simulator for the generation of MINFLUX-like data under stochastic processes; Poisson distributed centroids surrounded by unseen, one-or-more repeating structures that form the parent locations for the Gaussian distributed measurements, or localisations, that MINFLUX detects. Simulated datasets arising from this simulator will be used to explore and compare our spatial point process and Palm distribution approach against the methods currently used.<br/><br/>This work seeks to move beyond template matching, toward more generalisable and interpretable spatial statistical approaches for high-resolution molecular imaging, that can answer two key questions from MINFLUX-like point pattern datasets: is there repeating structure, and if so, what is it?