Topological texture analysis of microscopy images of dynamic casein gelation and its relation to rheological properties

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 {\deg}C and 40 {\deg}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