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3D microscopy is key in the investigation of diverse biological systems, andthe ever increasing availability of large datasets demands automatic cellidentification methods that not only are accurate, but also can imply theuncertainty in their predictions to inform about potential errors and henceconfidence in conclusions using them. While conventional deep learning methodsoften yield deterministic results, advances in deep Bayesian learning allow foraccurate predictions with a probabilistic interpretation in numerous imageclassification and segmentation tasks. It is however nontrivial to extend suchBayesian methods to cell detection, which requires specialized learningframeworks. In particular, regression of density maps is a popular successfulapproach for extracting cell coordinates from local peaks in a postprocessingstep, which hinders any meaningful probabilistic output. We herein propose adeep learning-based cell detection framework that can operate on largemicroscopy images and outputs desired probabilistic predictions by (i)integrating Bayesian techniques for the regression of uncertainty-aware densitymaps, where peak detection can be applied to generate cell proposals, and (ii)learning a mapping from the numerous proposals to a probabilistic space that iscalibrated, i.e. accurately represents the chances of a successful prediction.Utilizing such calibrated predictions, we propose a probabilistic spatialanalysis with Monte-Carlo sampling. We demonstrate this in revising an existingdescription of the distribution of a mesenchymal stromal cell type within thebone marrow, where our proposed methods allow us to reveal spatial patternsthat are otherwise undetectable. Introducing such probabilistic analysis inquantitative microscopy pipelines will allow for reporting confidence intervalsfor testing biological hypotheses of spatial distributions.

Probabilistic Spatial Analysis in Quantitative Microscopy with Uncertainty-Aware Cell Detection using Deep Bayesian Regression of Density Maps