A novel graph-theoretic and data visualization framework for spatiotemporal bubble analysis in turbulent flows

Abstract

This paper presents a novel methodology for analyzing bubble movement in turbulent flows by framing multi-object tracking as a global optimization problem on a spatiotemporal graph. Bubble detections across frames are modeled as nodes in a directed graph, with tracking addressed through a minimum cost flow algorithm. Unlike sequential trackers, our approach considers the entire temporal context to achieve globally optimal paths, reducing identity switches and fragmentation caused by occlusions and interactions. The pipeline integrates anisotropic Gaussian filtering and Otsu’s thresholding with a cost function enforcing movement and appearance consistency. Experimental validation across flow rates ($Q_1=1.0$, $Q_2=2.0$, $Q_3=3.0$) identifies distinct systems: stable homogeneous, transitional interference, and saturated aggregation-dominated. The method simultaneously measures temporal evolution of bubble count $N\left(t\right)$, mean diameter $\bar{d}\left(t\right)$, and velocity $\bar{v}\left(t\right)$, revealing critical phenomena like saturation effects where increased airflow leads to bubble aggregation rather than an increased count.