Learning 3D biophysical cell properties from 2D images and cell-population statistics
Authors: Santiago Hernández-Orozco, Hector Zenil
Organizations: Algocyte | Oxford Immune Algorithmics, Oxford University Innovation & London Institute for Healthcare Engineering, UK · Algorithmic Dynamics Lab, Department of Biomedical Computing, School of Biomedical Engineering and Imaging Sciences, King’s Institute for AI, King’s College London, UK
Inferring 3D cellular properties from 2D microscopy is difficult when a reference instrument reports only population statistics rather than labels for individual cells. Here we develop a population-supervised framework that maps single 2D red-cell images to latent biophysical quantities and aggregates them to mean corpuscular volume, red-cell distribution width and mean corpuscular haemoglobin. The model combines shared local inference, a biophysically structured decoder for volume and haemoglobin, learned instance weighting and device-specific calibration. We formalise conditions under which aggregate observations identify restricted instance predictors, show why population agreement does not by itself identify single-cell properties or 3D geometry, and derive the dispersion penalty induced by subset mean matching. The development dataset comprises 390 specimens and 1,105 acquisitions across six devices, with reported Pearson correlations of 0.86--0.98 against a Sysmex analyser. The framework provides a testable route from 2D images and population supervision to 3D cellular biophysics without claiming explicit 3D reconstruction.
Figures & tables
Figure 1: Representative 100×100 masked RGB input crops illustrating variation in apparent morphology, focus and segmentation. Images are reproduced without intensity adjustment and enlarged by nearest-neighbour replication.
Index
Reported Pearson correlation
Reference
MCV
0.94–0.96
Sysmex analyser
RDW
0.86–0.92
Sysmex analyser
MCH
0.94–0.98
Sysmex analyser
Table 1: Reported Pearson correlations against a Sysmex analyser in the development data [ 11 ] .
Stage
Operations
Output shape
Input
Masked RGB crop
B×3×100×100
Block 1
Two 3×3 convolutions, BN, ReLU; pool 2
B×32×50×50
Block 2
Two 3×3 convolutions, BN, ReLU; pool 2
B×64×25×25
Block 3
Two 3×3 convolutions, BN, ReLU; pool 5
B×128×5×5
Block 4
3×3 convolution, BN, ReLU; adaptive pool
B×256×1×1
Embedding
Flatten; linear 256→D ; ReLU
B×D
Table 2: Convolutional encoder and scalar-head architecture. B denotes the crop minibatch size and D the embedding dimension.
Appendix figures & tables1 asset
Supplementary material from the paper’s appendix.
Appendix
Figure D.1: Synthetic subsampling diagnostic. All size-two subsets of (70,80,100,110) fL are enumerated after scaling deviations about 90 fL by a . Expected mean-target loss equals (250/3)a2 . The vertical reference marks the generating dispersion.
Highly multiplexed microscopy enables rich spatial characterization of tissues at single-cell resolution, yet most analyses rely on two-dimensional sections despite inherently three-dimensional tissue organization. Acquiring dense volumetric data in spatial proteomics remains costly and technically challenging, leaving practitioners to choose between 2D sections or 3D serial sections under limited imaging budgets. In this work, we study how sampling geometry impacts the stability of commonly used spatial statistics, and we introduce a geometry-aware reconstruction module that enables sparse yet consistent 3D analysis from serial sections. Using controlled simulations, we show that planar sampling reliably recovers global cell-type abundance but exhibits high variance for local statistics such as cell clustering and cell-cell interactions, particularly for rare or spatially localized populations. We observe consistent behavior in real multiplexed datasets, where interaction metrics and neighborhood relationships fluctuate substantially across individual sections. To support sparse 3D analysis in practice, we present a reconstruction approach that links cell projections across adjacent sections using phenotype and proximity constraints and recovers single-cell 3D centroids using cell-type-specific shape priors. We further analyze the trade-off between section spacing, coverage, and redundancy, identifying acquisition regimes that maximize reconstruction utility under fixed imaging budgets. We validate the reconstruction module on a public imaging mass cytometry dataset with dense axial sampling and demonstrate its downstream utility on an in-house CODEX dataset by enabling structure-level 3D analyses that are unreliable in 2D. Together, our results provide diagnostic tools and practical guidance for deciding when 2D sampling suffices and when sparse 3D reconstruction is warranted.
Label-free single-cell imaging offers a scalable, non-invasive alternative to fluorescence-based cytometry, yet inferring molecular phenotypes directly from bright-field morphology remains challenging. We present a unified Deep Learning (DL) framework that jointly performs White Blood Cell (WBC) classification and continuous protein-expression regression from label-free Differential Phase Contrast (DPC) images. Our model employs a Hybrid architecture that fuses convolutional fine-grained texture features with transformer-based global representations through a learnable cross-branch gating module, enabling robust morpho-molecular inference from DPC images. To support downstream interpretability, we further incorporate a Large Language Model (LLM) that generates concise, biologically grounded summaries of the predicted cell states. Experiments on the Berkeley Single Cell Computational Microscopy (BSCCM) and Blood Cells Image benchmarks demonstrate strong performance, achieving a 91.3% WBC classification accuracy and a 0.72 Pearson correlation for CD16 expression regression on BSCCM. These results underscore the promise of label-free single-cell imaging for cost-effective hematological profiling, enabling simultaneous phenotype identification and quantitative biomarker estimation without fluorescent staining. The source code is available at https://github.com/saqibnaziir/Single-Cell-Phenotyping.
Saqib Nazir, Ardhendu Behera
Department of Computer Science, Edge Hill University, UK
Self-supervised learning in fluorescence microscopy often relies on 2D projections, despite the inherently three-dimensional nature of cells. We present a systematic comparison of 2D and 3D masked autoencoders (MAE-2D vs. MAE-3D) on volumetric microscopy data. Under matched architectures and training protocols, MAE-3D consistently outperforms 2D max-projection and slice-based variants on downstream single-cell tasks. We further align visual representations with a pretrained protein language model (ESM2) and show that cross-modal supervision yields larger gains for volumetric models. Channel cross-attention and frequency-domain regularization are critical for leveraging 3D spatial context. On protein--protein interaction prediction, our best model achieves a ROC--AUC of 0.86, while on protein localization it reaches an AUCmicro of 0.95 and an F1micro of 0.74, demonstrating competitive performance on both tasks. Overall, our findings highlight the potential of volumetric modeling and multimodal alignment for representation learning in single-cell microscopy.
Institute of AI for Health & Helmholtz AI, Computational Health Center, Helmholtz Munich – German Research Center for Environmental Health, Neuherberg, Germany · Munich Center for Machine Learning (MCML), Munich, Germany · Department of Medicine III, Ludwig-Maximilian-University Hospital, Munich, Germany +2