Ivo Fabian Sbalzarini

Through digital imaging, microscopy has evolved from primarily being a means for visual observation of life at the micro- and nano-scale, to a quantitative tool with ever-increasing resolution and throughput. Artificial intelligence, deep neural networks, and machine learning (ML) are all niche terms describing computational methods that have gained a pivotal role in microscopy-based research over the past decade. This Roadmap encompasses key aspects of how ML is applied to microscopy image data, with the aim of gaining scientific knowledge by improved image quality, automated detection, segmentation, classification and tracking of objects, and efficient merging of information from multiple imaging modalities. We aim to give the reader an overview of the key developments and an understanding of possibilities and limitations of ML for microscopy. It will be of interest to a wide cross-disciplinary audience in the physical sciences and life sciences.

We propose a method for variable selection in the intensity function of spatial point processes that combines sparsity-promoting estimation with noise-robust model selection. As high-resolution spatial data becomes increasingly available through remote sensing and automated image analysis, identifying spatial covariates that influence the localization of events is crucial to understand the underlying mechanism. However, results from automated acquisition techniques are often noisy, for example due to measurement uncertainties or detection errors, which leads to spurious displacements and missed events. We study the impact of such noise on sparse point-process estimation across different models, including Poisson and Thomas processes. To improve noise robustness, we propose to use stability selection based on point-process subsampling and to incorporate a non-convex best-subset penalty to enhance model-selection performance. In extensive simulations, we demonstrate that such an approach reliably recovers true covariates under diverse noise scenarios and improves both selection accuracy and stability. We then apply the proposed method to a forestry data set, analyzing the distribution of trees in relation to elevation and soil nutrients in a tropical rain forest. This shows the practical utility of the method, which provides a systematic framework for robust variable selection in spatial point-process models under noise, without requiring additional knowledge of the process.

We investigate the computational power of particle methods, a well-established class of algorit hms with applications in scientific computing and computer simulation. The computational power of a compute model determines the class of problems it can solve. Automata theory allows describing the computational power of abstract machines (automata) and the problems they can solve. At the top of the Chomsky hierarchy of formal languages and grammars are Turing machines, which resemble the concept on which most modern computers are built. Although particle methods can be interpreted as automata based on their formal definition, their computational power has so far not been studied. We address this by analyzing Turing completeness of particle methods. In particular, we prove two sets of restrictions under which a particle method is still Turing powerful, and we show when it loses Turing powerfulness. This contributes to understanding the theoretical foundations of particle methods and provides insight into the powerfulness of computer simulations.17 pages, 23 appendix pages

Long-range morphogen gradients have been proposed to form by morphogen diffusion from a localized source to distributed sinks in the target tissue. The role of the complex tissue geometry in this process is, however, less well understood and has not been explicitly resolved in existing models. Here, we numerically reconstruct pore-scale 3D geometries of zebrafish epiboly from light-sheet microscopy volumes. In these high-resolution 3D geometries, we simulate Fgf8a gradient formation in the tortuous extracellular space. Our simulations show that when realistic embryo geometries are considered, a source-diffusion-degradation mechanism with additional binding to extracellular matrix polymers is sufficient to explain emergence and robust maintenance of Fgf8a gradients. The predicted normalized gradient is robust against changes in source and sink rates but sensitive to changes in the pore connectivity of the extracellular space, with lower connectivity leading to steeper and shorter gradients. This demonstrates the importance of considering realistic geometries when studying morphogen gradients.

It is shown that regularizing the signal gradient statistics during training of deep‐learning models of super‐resolution fluorescence microscopy improves the generated images. Specifically, regularizing the images in the training data set is proposed to have gradient and Laplacian statistics closer to those expected for natural‐scene images. The BioSR data set of matched pairs of diffraction‐limited and super‐resolution images is used to evaluate the proposed regularization in a state‐of‐the‐art generative deep‐learning model of super‐resolution microscopy, the Conditional Variational Diffusion Model (CVDM). Since the proposed regularization is applied as a preprocessing step to the training data, it can be used in conjunction with any supervised machine‐learning model. However, its utility is limited to images for which the prior is appropriate, which in the BioSR data set are the images of filamentous structures. The quality and generalization power of CVDM trained with and without the proposed regularization are compared, showing that the new prior yields images with clearer visual detail and better small‐scale structure.

We use a combination of unsupervised clustering and sparsity-promoting inference algorithms to learn locally dominant force balances that explain macroscopic pattern formation in self-organized active particle systems. The self-organized emergence of macroscopic patterns from microscopic interactions between self-propelled particles can be widely observed in nature. Although hydrodynamic theories help us better understand the physical basis of this phenomenon, identifying a sufficient set of local interactions that shape, regulate and sustain self-organized structures in active particle systems remains challenging. We investigate a classic hydrodynamic model of self-propelled particles that produces a wide variety of patterns, such as asters and moving density bands. Our data-driven analysis shows that propagating bands are formed by local alignment interactions driven by density gradients, while steady-state asters are shaped by a mechanism of splay-induced negative compressibility arising from strong particle interactions. Our method also reveals analogous physical principles of pattern formation in a system where the speed of the particle is influenced by the local density. This demonstrates the ability of our method to reveal physical commonalities across models. The physical mechanisms inferred from the data are in excellent agreement with analytical scaling arguments and experimental observations.