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

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.

Utilizing Uncertainty Estimation in Deep Learning Segmentation of Fluorescence Microscopy Images with Missing Markers

Fluorescence microscopy images contain several channels, each indicating a marker staining the sample. Since many different marker combinations are utilized in practice, it has been challenging to apply deep learning based segmentation models, which expect a predefined channel combination for all training samples as well as at inference for future application. Recent work circumvents this problem using a modality attention approach to be effective across any possible marker combination. However, for combinations that do not exist in a labeled training dataset, one cannot have any estimation of potential segmentation quality if that combination is encountered during inference. Without this, not only one lacks quality assurance but one also does not know where to put any additional imaging and labeling effort. We herein propose a method to estimate segmentation quality on unlabeled images by (i) estimating both aleatoric and epistemic uncertainties of convolutional neural networks for image segmentation, and (ii) training a Random Forest model for the interpretation of uncertainty features via regression to their corresponding segmentation metrics. Additionally, we demonstrate that including these uncertainty measures during training can provide an improvement on segmentation performance.

Modality Attention and Sampling Enables Deep Learning with Heterogeneous Marker Combinations in Fluorescence Microscopy

Fluorescence microscopy allows for a detailed inspection of cells, cellular networks, and anatomical landmarks by staining with a variety of carefully-selected markers visualized as color channels. Quantitative characterization of structures in acquired images often relies on automatic image analysis methods. Despite the success of deep learning methods in other vision applications, their potential for fluorescence image analysis remains underexploited. One reason lies in the considerable workload required to train accurate models, which are normally specific for a given combination of markers, and therefore applicable to a very restricted number of experimental settings. We herein propose Marker Sampling and Excite, a neural network approach with a modality sampling strategy and a novel attention module that together enable ($i$) flexible training with heterogeneous datasets with combinations of markers and ($ii$) successful utility of learned models on arbitrary subsets of markers prospectively. We show that our single neural network solution performs comparably to an upper bound scenario where an ensemble of many networks is na\"ively trained for each possible marker combination separately. In addition, we demonstrate the feasibility of our framework in high-throughput biological analysis by revising a recent quantitative characterization of bone marrow vasculature in 3D confocal microscopy datasets. Not only can our work substantially ameliorate the use of deep learning in fluorescence microscopy analysis, but it can also be utilized in other fields with incomplete data acquisitions and missing modalities.