Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties
Authors: Zahra Tabatabaei, Diana Soto Aguilar, Jose C. Bonilla, Mathias P. Clausen, Jon Sporring
Organizations: Department of Computer Science, University of Copenhagen, Denmark. · Department of Green Technology, University of Southern Denmark, Denmark. · Department of Food Science, University of Copenhagen, Denmark.
Abstract
We propose a novel computational toolbox that integrates Topological Data Analysis (TDA), Differential Box Counting (DBC), Multifractal Partition (MFP), and Local Binary Patterns (LBP), applied to time-lapse super-resolution STED microscopy images of sodium caseinate gelation induced by glucono-delta-lactone (GDL) at 30 °C and 40 °C and two GDL concentrations (1.8% and 3.5% w/v). TDA tracked topological loops, closed ring-like structures reflecting protein network interconnectivity, via max-Betti-1 curves, which revealed a lag phase of dispersed aggregates, a sharp decay coinciding with network percolation and the rheologically observed sol-gel transition, and a post-gelation increase corresponding to network rearrangements. These topological transitions were corroborated by DBC and MFP as these methods were able to resolve changes in structural complexity and spatial heterogeneity. The toolbox was validated on simulated fractal images prior to experimental application. Together, these descriptors provided sensitivity to subtle microstructural transitions that bulk rheology captured as averaged bulk mechanical responses. This integrated approach provides a robust quantitative tool for characterizing complex microstructure in food and material science with evolving microstructural dynamics. Code is available at https://github.com/Zahratabatabaei/Delifood_CV_paper.git
Molecular dynamics (MD) simulations generate trajectories in a high-dimensional configuration space whose analysis critically depends on molecular descriptors, typically handcrafted observables or learned kinetic embeddings. Designing descriptors that are both expressive and broadly applicable, however, remains challenging. We study persistent homology (PH) as a general-purpose representation for MD and introduce the masked Flood complex, a protein-tailored modification of a recently introduced simplicial complex construction that emphasizes inter-residue structure at low computational cost. Vectorized persistence diagrams then provide information-rich, geometry-aware summaries of protein conformations, which we evaluate on protein class prediction, frame-level observable regression, and Markov state model (MSM) estimation from learned low-dimensional coordinates in a single shared representation space. Results on the mdCATH dataset show that PH-based descriptors are competitive across tasks, with masked Flood PH yielding the most consistent overall performance. Further, when using topologically-informed MSMs as a drop-in replacement within the recent MarS-FM framework for generative modeling of protein conformations, we obtain consistently better ensemble statistics than MSMs based on physical observables. Finally, we explore the transferability of the generative model to qualitatively different, fast folding, proteins.
Flow in porous media is difficult to address using standard analytical or numerical methods due to its complexity. However, since synthetic representations of porous media are easy to produce and data from physical experiments are becoming more widely available, the problem is well-suited to studies that include machine learning (ML) techniques. We discuss a number of features that can be extracted from such data, and their utility as input variables into a standard ML algorithm. These features include structural measures describing the geometry of the porous media, topological measures describing the connectivity, and network measures obtained by modeling the porous media as simplified pore networks. These features enable the prediction of the permeability of the considered (synthetic) porous materials using ML techniques that also leverage the separately computed exact permeability (ground truth). Comparing results obtained using different input variables helps develop a better understanding of the utility of various measures for predicting permeability based on the porous media structure. We show, in particular, that topological data analysis (TDA) provides a useful set of features that can be easily combined with ML to yield meaningful results.
Topological data analysis (TDA), particularly persistent homology (PH), captures geometric structural properties in medical images (e.g., connected components, loops, shape characteristics), which conventional pixel-level deep learning approaches often neglect. While many topological descriptors are known for converting persistence diagrams (PDs) or raw images into topological feature vectors, existing methods mostly default to a single fixed descriptor (e.g., persistence images), leaving the diversity of topological representations largely unexplored. To the best of our knowledge, there is no known large language model (LLM)-based agentic framework that can automatically determine the most suitable topological descriptors for a given image dataset and produce the corresponding topological feature vectors for downstream tasks. To fill this gap, we propose \textbf{TopoAgent}, an LLM-based agentic framework that automates topology learning for medical image analysis.TopoAgent operates through a Perception--Reasoning--Action--Reflection loop supported by 21 domain-specific tools and dual memory that accumulates experience across runs. Its skill set is distilled from systematic evaluation of 15 topological descriptors across 26 datasets with six classifiers. TopoAgent analyzes input images and their topological characteristics, reasons about which topological descriptors best suit the input, and determines the optimal descriptor and its configuration, all without task-specific training.