Probabilistic spatial analysis in quantitative microscopy with uncertainty-aware cell detection using deep Bayesian regression

The investigation of biological systems with three-dimensional microscopy demands automatic cell identification methods that not only are accurate but also can imply the uncertainty in their predictions. The use of deep learning to regress density maps is a popular successful approach for extracting cell coordinates from local peaks in a postprocessing step, which then, however, hinders any meaningful probabilistic output. We propose a framework that can operate on large microscopy images and output probabilistic predictions (i) by integrating deep Bayesian learning for the regression of uncertainty-aware density maps, where peak detection algorithms generate cell proposals, and (ii) by learning a mapping from prediction proposals to a probabilistic space that accurately represents the chances of a successful prediction. Using these calibrated predictions, we propose a probabilistic spatial analysis with Monte Carlo sampling. We demonstrate this in a bone marrow dataset, where our proposed methods reveal spatial patterns that are otherwise undetectable.