Image analysis techniques provide objective and reproducible statistics for interpreting microscopy data. At higher dimensions, three-dimensional (3D) volumetric and spatiotemporal data highlight additional properties and behaviors beyond the static 2D focal plane. However, increased dimensionality carries increased complexity, and existing techniques for general segmentation of 3D data are either primitive, or highly specialized to specific biological structures. Borrowing from the principles of 2D topological data analysis (TDA), we formulate a 3D segmentation algorithm that implements persistent homology to identify variations in image intensity. From this, we derive two separate variants applicable to spatial and spatiotemporal data, respectively. We demonstrate that this analysis yields both sensitive and specific results on simulated data and can distinguish prominent biological structures in fluorescence microscopy images, regardless of their shape. Furthermore, we highlight the efficacy of temporal TDA in tracking cell lineage and the frequency of cell and organelle replication.

Imaging platforms for generating highly multiplexed histological images are being continually developed and improved. Significant improvements have also been made in the accuracy of methods for automated cell segmentation and classification. However, less attention has focused on the quantification and analysis of the resulting point clouds, which describe the spatial coordinates of individual cells. We focus here on a particular spatial statistical method, the cross-pair correlation function (cross-PCF), which can identify positive and negative spatial correlation between cells across a range of length scales. However, limitations of the cross-PCF hinder its widespread application to multiplexed histology. For example, it can only consider relations between pairs of cells, and cells must be classified using discrete categorical labels (rather than labeling continuous labels such as stain intensity). In this paper, we present three extensions to the cross-PCF which address these limitations and permit more detailed analysis of multiplex images: topographical correlation maps can visualize local clustering and exclusion between cells; neighbourhood correlation functions can identify colocalization of two or more cell types; and weighted-PCFs describe spatial correlation between points with continuous (rather than discrete) labels. We apply the extended PCFs to synthetic and biological datasets in order to demonstrate the insight that they can generate.

Single-particle cryogenic electron microscopy (cryo-EM) is an imaging technique capable of recovering the high-resolution three-dimensional (3D) structure of biological macromolecules from many noisy and randomly oriented projection images. One notable approach to 3D reconstruction, known as Kam’s method, relies on the moments of the two-dimensional (2D) images. Inspired by Kam’s method, we introduce a rotationally invariant metric between two molecular structures, which does not require 3D alignment. Further, we introduce a metric between a stack of projection images and a molecular structure, which is invariant to rotations and reflections and does not require performing 3D reconstruction. Additionally, the latter metric does not assume a uniform distribution of viewing angles. We demonstrate the uses of the new metrics on synthetic and experimental datasets, highlighting their ability to measure structural similarity.

Cryo-electron microscopy (cryo-EM) is an imaging technique that allows the visualization of proteins and macromolecular complexes at near-atomic resolution. The low electron doses used to prevent radiation damage to the biological samples result in images where the power of noise is 100 times stronger than that of the signal. Accurate identification of proteins from these low signal-to-noise ratio (SNR) images is a critical task, as the detected positions serve as inputs for the downstream 3D structure determination process. Current methods either fail to identify all true positives or result in many false positives, especially when analyzing images from smaller-sized proteins that exhibit extremely low contrast, or require manual labeling that can take days to complete. Acknowledging the fact that accurate protein identification is dependent upon the visual interpretability of micrographs, we propose a framework that can perform denoising and detection in a joint manner and enable particle localization under extremely low SNR conditions using self-supervised denoising and particle identification from sparsely annotated data. We validate our approach on three challenging single-particle cryo-EM datasets and projection images from one cryo-electron tomography dataset with extremely low SNR, showing that it outperforms existing state-of-the-art methods used for cryo-EM image analysis by a significant margin. We also evaluate the performance of our algorithm under decreasing SNR conditions and show that our method is more robust to noise than competing methods.

In this article, we propose an algorithm for aligning three-dimensional objects when represented as density maps, motivated by applications in cryogenic electron microscopy. The algorithm is based on minimizing the 1-Wasserstein distance between the density maps after a rigid transformation. The induced loss function enjoys a more benign landscape than its Euclidean counterpart and Bayesian optimization is employed for computation. Numerical experiments show improved accuracy and efficiency over existing algorithms on the alignment of real protein molecules. In the context of aligning heterogeneous pairs, we illustrate a potential need for new distance functions.

In this work, we present a pair of tools to improve the fiducial tracking and reconstruction quality of cryo-scanning transmission electron tomography (STET) datasets. We then demonstrate the effectiveness of these two tools on experimental cryo-STET data. The first tool, GoldDigger, improves the tracking of fiducials in cryo-STET by accommodating the changed appearance of highly defocussed fiducial markers. Since defocus effects are much stronger in scanning transmission electron microscopy than in conventional transmission electron microscopy, existing alignment tools do not perform well without manual intervention. The second tool, Checkers, combines image inpainting and unsupervised deep learning for denoising tomograms. Existing tools for denoising cryo-tomography often rely on paired noisy image frames, which are unavailable in cryo-STET datasets, necessitating a new approach. Finally, we make the two software tools freely available for the cryo-STET community.

Cryogenic electron tomography (cryoET) is capable of determining in situ biological structures of molecular complexes at near-atomic resolution by averaging half a million subtomograms. While abundant complexes/particles are often clustered in arrays, precisely locating and seamlessly averaging such particles across many tomograms present major challenges. Here, we developed TomoNet, a software package with a modern graphical user interface to carry out the entire pipeline of cryoET and subtomogram averaging to achieve high resolution. TomoNet features built-in automatic particle picking and three-dimensional (3D) classification functions and integrates commonly used packages to streamline high-resolution subtomogram averaging for structures in 1D, 2D, or 3D arrays. Automatic particle picking is accomplished in two complementary ways: one based on template matching and the other using deep learning. TomoNet’s hierarchical file organization and visual display facilitate efficient data management as required for large cryoET datasets. Applications of TomoNet to three types of datasets demonstrate its capability of efficient and accurate particle picking on flexible and imperfect lattices to obtain high-resolution 3D biological structures: virus-like particles, bacterial surface layers within cellular lamellae, and membranes decorated with nuclear egress protein complexes. These results demonstrate TomoNet’s potential for broad applications to various cryoET projects targeting high-resolution in situ structures.

Supervised deep learning approaches can artificially increase the resolution of microscopy images by learning a mapping between two image resolutions or modalities. However, such methods often require a large set of hard-to-get low-res/high-res image pairs and produce synthetic images with a moderate increase in resolution. Conversely, recent methods based on generative adversarial network (GAN) latent search offered a drastic increase in resolution without the need of paired images. However, they offer limited reconstruction of the high-resolution (HR) image interpretable features. Here, we propose a robust super-resolution (SR) method based on regularized latent search (RLS) that offers an actionable balance between fidelity to the ground truth (GT) and realism of the recovered image given a distribution prior. The latter allows to split the analysis of a low-resolution (LR) image into a computational SR task performed by deep learning followed by a quantification task performed by a handcrafted algorithm based on interpretable biological features. This two-step process holds potential for various applications such as diagnostics on mobile devices, where the main aim is not to recover the HR details of a specific sample but rather to obtain HR images that preserve explainable and quantifiable differences between conditions.

We revisit the topic of common lines between projection images in single-particle cryo-electron microscopy (cryo-EM). We derive a novel low-rank constraint on a certain 2n × n matrix storing properly scaled basis vectors for the common lines between n projection images of one molecular conformation. Using this algebraic constraint and others, we give optimization algorithms to denoise common lines and recover the unknown 3D rotations associated with the images. As an application, we develop a clustering algorithm to partition a set of noisy images into homogeneous communities using common lines, in the case of discrete heterogeneity in cryo-EM. We demonstrate the methods on synthetic and experimental datasets.

Hyperplexed in-situ targeted proteomics via antibody immunodetection (i.e., >15 markers) is changing how we classify cells and tissues. Differently from other high-dimensional single-cell assays (flow cytometry, single-cell RNA sequencing), the human eye is a necessary component in multiple procedural steps: image segmentation, signal thresholding, antibody validation, and iconographic rendering. Established methods complement the human image evaluation, but may carry undisclosed biases in such a new context, therefore we re-evaluate all the steps in hyperplexed proteomics. We found that the human eye can discriminate less than 64 out of 256 gray levels and has limitations in discriminating luminance levels in conventional histology images. Furthermore, only images containing visible signals are selected and eye-guided digital thresholding separates signal from noise. BRAQUE, a hyperplexed proteomic tool, can extract, in a marker-agnostic fashion, granular information from markers which have a very low signal-to-noise ratio and therefore are not visualized by traditional visual rendering. By analyzing a public human lymph node dataset, we also found unpredicted staining results by validated antibodies, which highlight the need to upgrade the definition of antibody specificity in hyperplexed immunostaining. Spatially hyperplexed methods upgrade and supplant traditional image-based analysis of tissue immunostaining, beyond the human eye contribution.

We develop a novel method for image segmentation of 3D confocal microscopy images of emerging hematopoietic stem cells. The method is based on the theory of persistent homology and uses an optimal threshold to select the most persistent cycles in the persistence diagram. This enables the segmentation of the image’s most contrasted and representative shapes. Coupling this segmentation method with a meshing algorithm, we define a pipeline for 3D reconstruction of confocal volumes. Compared to related methods, this approach improves shape segmentation, is more ergonomic to automatize, and has fewer parameters. We apply it to the segmentation of membranes, at subcellular resolution, of cells involved in the endothelial-to-hematopoietic transition (EHT) in the zebrafish embryos.