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