Photophysical image analysis: parameter estimation, thresholding and segmentation for images from electron-multiplying charge-coupled devices

Images acquired in fluorescence microscopy are subject to two types of noise: stochasticity in the arrival of photons at the imaging camera and subsequent noise induced by the detection system of the camera. In here, we introduce the concept photophysical image analysis (PIA) and an associated pipeline for images recorded by electron-multiplying charge-coupled device (EMCCD) cameras. Our non-heuristic methods are based on the sole assumption that the background photon arrival to the detector are described by a stationary Poisson process. We make no assumption about the signal photon statistics. We base our approach on a new closed-form analytic expression for the characteristic function for the image count recorded in an EMCCD camera. Two common image analysis tasks are addressed: thresholding, i.e., separating the image pixels into background and signal pixels based on recorded counts in each pixel, and segmentation, i.e., identifying "objects" in the image. Our pipeline for tackling these tasks use a procedure for camera noise model parameter estimation and a novel method for estimation of the photon statistics parameters directly from an image which contains both background and signal pixels. Utilizing these parameter estimates, we then introduce a new probabilistic thresholding method, where the accuracy of the thresholding is benchmarked against the Otsu method. We lastly present a segmentation method which uses the thresholding results as input. We demonstrate how the pipeline can be successfully applied to segmentation of synthetic images and experimental images of fluorescent beads and lung cell nuclei. The associated publicly available software opens up for fully automated, unsupervised, probabilistic photophysical image analysis.