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

arXiv: https://arxiv.org/abs/2102.11865 · HTML: https://mlsanity.com/paper/2102.11865/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 87 references that are in the map.
- First posted on arXiv 23 Feb 2021.

## Builds on (most cited first, 30 of 30)

- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Faster R-CNN: Towards Real-Time Object Detection with Region Proposal Networks](https://mlsanity.com/paper/1506.01497/) (2015)
- [On Calibration of Modern Neural Networks](https://mlsanity.com/paper/1706.04599/) (2017)
- [You Only Look Once: Unified, Real-Time Object Detection](https://mlsanity.com/paper/1506.02640/) (2015)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [SSD: Single Shot MultiBox Detector](https://mlsanity.com/paper/1512.02325/) (2015)
- [Fast R-CNN](https://mlsanity.com/paper/1504.08083/) (2015)
- [YOLOv3: An Incremental Improvement](https://mlsanity.com/paper/1804.02767/) (2018)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [Rich feature hierarchies for accurate object detection and semantic segmentation](https://mlsanity.com/paper/1311.2524/) (2013)
- [YOLO9000: Better, Faster, Stronger](https://mlsanity.com/paper/1612.08242/) (2016)
- [On the Variance of the Adaptive Learning Rate and Beyond](https://mlsanity.com/paper/1908.03265/) (2019)
- [Spatial Pyramid Pooling in Deep Convolutional Networks for Visual Recognition](https://mlsanity.com/paper/1406.4729/) (2014)
- [TensorFlow: Large-Scale Machine Learning on Heterogeneous Distributed Systems](https://mlsanity.com/paper/1603.04467/) (2016)
- [Object Detection with Deep Learning: A Review](https://mlsanity.com/paper/1807.05511/) (2018)
- [Deep Ensembles: A Loss Landscape Perspective](https://mlsanity.com/paper/1912.02757/) (2019)
- [AutoML: A Survey of the State-of-the-Art](https://mlsanity.com/paper/1908.00709/) (2019)
- [Bayesian SegNet: Model Uncertainty in Deep Convolutional Encoder-Decoder Architectures for Scene Understanding](https://mlsanity.com/paper/1511.02680/) (2015)
- [Cell Detection with Star-convex Polygons](https://mlsanity.com/paper/1806.03535/) (2018)
- [Confidence Calibration and Predictive Uncertainty Estimation for Deep Medical Image Segmentation](https://mlsanity.com/paper/1911.13273/) (2019)
- [Bayesian Convolutional Neural Networks with Bernoulli Approximate Variational Inference](https://mlsanity.com/paper/1506.02158/) (2015)
- [End-to-end people detection in crowded scenes](https://mlsanity.com/paper/1506.04878/) (2015)
- [Rethinking the Heatmap Regression for Bottom-up Human Pose Estimation](https://mlsanity.com/paper/2012.15175/) (2020)
- [Star-convex Polyhedra for 3D Object Detection and Segmentation in Microscopy](https://mlsanity.com/paper/1908.03636/) (2019)
- [Automated Muscle Segmentation from Clinical CT using Bayesian U-Net for Personalized Musculoskeletal Modeling](https://mlsanity.com/paper/1907.08915/) (2019)
- [Deeply-Supervised Density Regression for Automatic Cell Counting in Microscopy Images](https://mlsanity.com/paper/2011.03683/) (2020)
- [Siamese Networks with Location Prior for Landmark Tracking in Liver Ultrasound Sequences](https://mlsanity.com/paper/1901.08109/) (2019)
- [Modality Attention and Sampling Enables Deep Learning with Heterogeneous Marker Combinations in Fluorescence Microscopy](https://mlsanity.com/paper/2008.12380/) (2020)
- [Utilizing Uncertainty Estimation in Deep Learning Segmentation of Fluorescence Microscopy Images with Missing Markers](https://mlsanity.com/paper/2101.11476/) (2021)

## Built on by (most cited first, 5 of 5)

- [TeSLA: Test-Time Self-Learning With Automatic Adversarial Augmentation](https://mlsanity.com/paper/2303.09870/) (2023)
- [Weakly Supervised Joint Whole-Slide Segmentation and Classification in Prostate Cancer](https://mlsanity.com/paper/2301.02933/) (2023)
- [Lean Unet: A Compact Model for Image Segmentation](https://mlsanity.com/paper/2512.03834/) (2025)
- [h-calibration: Rethinking Classifier Recalibration with Probabilistic Error-Bounded Objective](https://mlsanity.com/paper/2506.17968/) (2025)
- [Novel deep learning methods for 3D flow field segmentation and classification](https://mlsanity.com/paper/2305.11884/) (2023)

## Abstract (arXiv)

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.