Structure analysis and clustering of video data using persistent homology

This paper presents a method for clustering video data aimed at assessing postural stability using persistent homologies – a modern approach in topological data analysis characterized by high robustness to noise and variability in dynamic video data. The study is based on experimental video recordings of subjects performing the Romberg test with eyes open and closed, conducted in parallel with stabilometric testing. The developed methodological framework includes automatic segmentation of the human figure utilizing a pretrained Segment Anything Model, extraction of key anatomical points, and calculation of angular body parameters over time sequences. The resulting time series of angles are analyzed using Morse filtering to track topological changes and are represented as persistence diagrams. Subsequently, the Wasserstein metric is employed to analyze similarities and differences between the diagrams. Clustering is performed using the k-means algorithm, enabling identification of participant groups and their individual strategies for balance compensation. The results demonstrate that topological analysis of video data provides a deeper and more detailed stratification of subjects according to postural stability patterns compared to classical stabilometry. The methods reveal various strategies for equilibrium stabilization – ranging from changes in torso angles to control of the head and hands – facilitating a qualitative understanding of balance maintenance mechanisms. The authors emphasize the importance of accounting for optical distortions to enhance analysis accuracy and confirm the high reproducibility and informativeness of the proposed approach, opening prospects for personalized diagnosis and rehabilitation of patients.