Depth-Aware Machine Learning Framework for Bubble Characterization in Two-Phase Flows

TL;DR

This work addresses depth-resolved bubble characterization from a single high-speed camera by introducing a two-stage pipeline that first uses unsupervised Gaussian mixture modeling to derive a depth proxy and separate in-focus from out-of-focus bubbles, then refines segmentation with a supervised Random Forest trained on a compact, engineered feature set. Temporal stabilization ensures consistent labeling across frames despite deformation and overlap, enabling robust bubble tracking and statistics. Quantitatively, the approach achieves strong in-plane segmentation (AP ≈ 0.818 on held-out data) with low false positives and generalizes across low and high void fractions, making it practical for constrained laboratory setups. The framework provides a scalable, CPU-friendly pathway to depth-aware multiphase diagnostics with potential applicability to other deformable, occluded particle imaging problems.

Abstract

Understanding the three-dimensional motion of bubbles is essential for interpreting transport and mixing in multiphase flows, especially when bubbles deform under shear or move rapidly through the flow field. In many laboratory setups, only a single high-speed camera is available, which limits measurements to two dimensions. Traditional image-processing tools can identify bubbles only when they appear circular and isolated, but they struggle with irregularly shaped bubbles, shear-induced deformations, strong blurring, and partial overlaps. Multi-camera systems could overcome these issues, but require significant hardware additions and calibration effort. In this work, we introduce a new machine-learning framework that can detect bubbles and estimate their depth using only a single 20 kHz high-speed camera with 3 \textmu m resolution. The method first uses a large unlabeled dataset and clusters the bubbles with an unsupervised algorithm to reveal their underlying structure. These clusters provide pseudo labels, which are combined with a small set of true in-plane bubble labels to train a semi-supervised model that generalizes across different bubble appearances. These components produce a continuous depth-proxy score that indicates how close each bubble is to the imaging plane, even when bubbles are distorted or irregularly shaped. In parallel, we perform robust bubble identification using instance segmentation, which separates touching, overlapping, and elongated bubbles generated by high-velocity shear. Quantitatively, the in-plane segmentation baseline achieves strong held-out performance with Average Precision (AP) = 0.818, implying stable detection across thresholds, clutter, bubble detection Precision of 0.901, and a False-Positive Rate (FPR) near 6.1\%, hence low spurious bubbles and cleaner statistics under the tested acquisition conditions.

Figures (8)

• Figure 1: Regenerated bubble clouds for pseudo-3D visualization across depth for one frame
• Figure 2: Depth-aware bubble segmentation, overlap detection and focal-plane clustering across five consecutive frames; In-Focus: Green Clusters, Out-of-Focus: Red Clusters
• Figure 3: Bubble segmentation and clustering for a higher void fraction
• Figure 4: Representative frame employed as Ground Truths for the Random Forest supervised model, generated from kumar2025bubble.
• Figure 5: Probability density of equivalent diameter $d_{eq}$ for in-plane RF predictions compared with in-plane ground truth, showing a minor upward shift while retaining relatively high agreement in distribution shape (PDF overlap $=0.713$).