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Deep Learning-Based Tracking and Lineage Reconstruction of Ligament Breakup

This paper presents a two-stage deep learning framework that combines Faster R-CNN for object detection and a Transformer-augmented MLP for temporal modeling to automatically track ligament breakup, reconstruct parent-child lineages, and quantify fragmentation statistics in liquid sheet disintegration, overcoming the limitations of conventional tracking methods in handling one-to-many fragmentation events.

Original authors: Vrushank Ahire, Vivek Kurumanghat, Mudasir Ganaie, Lipika Kabiraj

Published 2026-04-13

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CC BY 4.0

Original authors: Vrushank Ahire, Vivek Kurumanghat, Mudasir Ganaie, Lipika Kabiraj

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are watching a high-speed video of a water balloon popping. As it bursts, the water doesn't just disappear; it stretches into long, thin strings (like taffy) called ligaments, which then snap apart into tiny, individual drops.

Scientists want to study this process to improve things like fuel injectors in cars or pesticide sprayers. But there's a problem: this happens incredibly fast, and the water strings and drops are constantly changing shape, overlapping, and splitting. Trying to track them manually is like trying to follow a single thread in a tangled ball of yarn while someone is spinning it at 100 miles per hour.

This paper presents a new AI "super-sleuth" that solves this tracking problem in two smart steps.

Step 1: The "Eagle-Eye" Detective (Finding the Objects)

First, the AI needs to know what it is looking at in every single frame of the video. Is that a long string (ligament) or a round drop (droplet)?

The Challenge: The researchers didn't have enough real photos of these exploding water sheets to teach the AI. Teaching a computer usually requires thousands of labeled examples, and drawing boxes around every drop in a high-speed video takes forever.
The Creative Solution: Instead of just taking more photos, they built a "digital sandbox." They took the real strings and drops they did have, cut them out, and pasted them into new, computer-generated backgrounds.
- Analogy: Imagine you have a few real photos of cats. To teach a computer to recognize cats, you don't just take more photos of the same cats. You cut the cats out of the photos and paste them onto different backgrounds (a park, a living room, a beach) to create hundreds of new "fake" cat photos.
- The Result: The AI learned to spot ligaments and droplets with high accuracy, even when they were tiny or clumped together, by studying this mix of real and "sandbox" images.

Step 2: The "Time-Traveling" Detective (Connecting the Dots)

Once the AI knows what the objects are, it has to figure out what happened to them in the next frame. This is where most old tracking systems fail.

The Old Way: Traditional tracking is like a game of "Musical Chairs" where every person must have exactly one seat. If a person splits into two, the system gets confused because it can't assign two seats to one person. It assumes a one-to-one match: "This drop in Frame 1 is the same drop in Frame 2."
The Problem: In reality, one long string (ligament) often snaps and turns into three or four drops. This is a one-to-many event.
The New Solution: The researchers built a second AI brain that acts like a family tree generator. Instead of asking, "Is this the same object?", it asks, "What is the relationship between these two objects?"
- Move: "I am the same object, just moved slightly."
- Breakup: "I was the parent string, and I just split into these three children drops."
- None: "We are strangers; we have no connection."

The AI uses "physics clues" to make these decisions. It looks at how far objects moved, how much they overlap, and how their size changed.

Analogy: Imagine watching a family reunion. If you see one person walking alone, you know they are just moving. If you see one person suddenly followed by three smaller people running in the same direction, your brain instantly understands: "That parent just had triplets!" The AI does this mathematically, spotting the "parent" string and its "child" drops instantly.

Why This Matters

By combining these two steps, the researchers can now automatically build a complete family tree of the liquid breakup. They can see exactly how many drops came from one string, how big they are, and how fast they are moving.

The "Perfect Recall" Trick: The most impressive part is that the AI never misses a "breakup" event. Even if it's unsure about other things, it is programmed to catch every single time a string snaps. This is crucial because if you miss a breakup, the whole family tree is broken, and the data is useless.

The Bottom Line

This paper teaches computers to watch a liquid explosion and understand the story behind it. It doesn't just see "dots and lines"; it understands the drama of parent strings splitting into child drops. This helps engineers design better sprays for engines, medicine, and farming, all by letting a computer do the heavy lifting of tracking thousands of tiny, fast-moving pieces of liquid.

1. Problem Statement

The disintegration of liquid sheets into ligaments and droplets (atomization) is a complex, multi-scale process critical to applications like fuel injection, pharmaceuticals, and additive manufacturing. Analyzing this process via high-speed shadowgraphy presents significant challenges:

Complex Dynamics: Objects are dense, overlapping, and undergo rapid shape changes.
Limitations of Conventional Tracking: Standard multi-object tracking algorithms (e.g., SORT, DeepSORT) enforce strict one-to-one temporal associations. They fail to model one-to-many fragmentation events, where a single parent ligament breaks into multiple child droplets.
Data Scarcity: Obtaining large, manually annotated datasets for high-speed spray imaging is time-consuming and tedious.
Gap in Literature: Existing deep learning approaches focus on frame-by-frame detection or simple tracking but lack explicit modeling of fragmentation lineage (parent-child relationships) and the reconstruction of breakup trees.

2. Methodology

The authors propose a two-stage deep learning framework that separates spatial recognition from temporal inference to reconstruct the full lineage of ligament breakup.

Stage I: Spatial Analysis (Object Detection)

Goal: Detect and classify ligaments and droplets in individual high-speed image frames.
Architecture: A Faster R-CNN detector with a ResNet-50 backbone and Feature Pyramid Network (FPN).
Data Strategy (Morphology-Preserving Synthetic Generation):
- To address data scarcity, the authors developed a synthetic data generation strategy that preserves physical plausibility.
- Instead of standard augmentations (rotation/flipping), they extract "clean" ligament and droplet masks from real images and reassemble them into new composite images with randomized spatial arrangements and noise-matched backgrounds.
- This ensures the model learns realistic object morphologies without introducing physically impossible configurations.
Training: The model is trained on a mix of original and synthetic data to improve generalization across varying object densities and scales.

Stage II: Temporal Relationship Inference

Goal: Determine the relationship between objects in consecutive frames ( $t$ and $t+1$ ).
Formulation: A pairwise classification problem where object pairs are classified into three categories:
1. MOVE (0): Continuation of the same object.
2. BREAKUP (1): A parent object fragments into a child (one-to-many).
3. NONE (-1): No physical relationship.
Feature Engineering: Instead of raw image pixels, the model uses physics-informed geometric features derived from bounding boxes and masks:
- Centroid distance (absolute and normalized by area).
- Bounding Box Intersection-over-Union (IoU).
- Area ratio ( $A_{child}/A_{parent}$ ).
- Type consistency (Ligament vs. Droplet).
Architecture: A Transformer-augmented Multilayer Perceptron (TransformerMLP). This architecture was chosen to model complex, non-linear interactions between the geometric features, outperforming standard MLPs and Residual networks.
Lineage Reconstruction: The outputs are organized into a Directed Acyclic Graph (DAG). A mass conservation constraint is applied to select the most physically plausible set of children when multiple breakup candidates exist, enabling the reconstruction of fragmentation trees.

3. Key Contributions

Two-Stage Framework: A novel architecture integrating Faster R-CNN for detection and a Transformer-based classifier for temporal lineage, explicitly handling one-to-many fragmentation events.
Morphology-Preserving Synthetic Data: A data generation strategy that creates physically realistic synthetic training samples, achieving high performance ( $F_1$ score up to 0.872) even with limited ground-truth annotations.
Physics-Informed Tracking: Moving beyond visual similarity, the temporal classifier uses geometric features (area, displacement, overlap) to infer breakup events, addressing the severe class imbalance inherent in atomizing flows.
Automated Lineage Extraction: The system automatically reconstructs fragmentation trees, extracting statistics such as fragment multiplicity, parent-child area ratios, and droplet size distributions.

4. Experimental Results

The study was conducted on high-speed shadowgraphy images of a Carbopol gel jet (0.10 wt.%) impinging at a Weber number of ~400.

Stage I (Detection):
- Optimal Configuration: The best performance was achieved with a mix of 200 original images and 50 synthetic images (Exp1) or 250 original + 250 synthetic (Exp3), yielding a held-out test $F_1$ score of 0.872.
- Insight: Synthetic data is most effective when it complements rather than replaces original data. Purely synthetic training or excessive synthetic ratios led to reduced localization fidelity.
- Performance: The model successfully distinguished between ligaments and droplets, with ligament detection outperforming droplet detection due to the latter's small size and overlap.
Stage II (Temporal Classification):
- Best Model: The TransformerMLP significantly outperformed other architectures (BasicMLP, ResidualMLP, etc.).
- Metrics: Achieved 86.1% accuracy, 93.2% precision, and 0.887 $F_1$ score on the held-out test set.
- Critical Breakup Recall: The model achieved perfect recall (1.00) for BREAKUP events. This is crucial because missing a fragmentation event permanently breaks the lineage tree; high sensitivity here ensures the integrity of the reconstructed history.
- Class Imbalance: Despite the dataset being heavily skewed toward "NONE" (non-related) pairs, the model effectively identified rare fragmentation events.

5. Significance and Conclusion

This work represents a significant advancement in the automated analysis of multiphase flows:

Beyond One-to-One Tracking: It solves the fundamental limitation of conventional tracking by explicitly modeling fragmentation, allowing for the reconstruction of parent-child lineages.
Physical Interpretability: By using physics-informed features and mass conservation constraints, the framework ensures that the reconstructed breakup trees are physically plausible, not just statistically probable.
Efficiency: The synthetic data strategy drastically reduces the need for labor-intensive manual annotation, making high-fidelity spray analysis more accessible.
Impact: The framework enables the automated extraction of critical breakup statistics (e.g., fragment multiplicity, size distributions) that are essential for optimizing industrial atomization processes.

In summary, the paper presents a robust, end-to-end deep learning solution that transforms high-speed imaging data into quantitative, lineage-resolved breakup statistics, bridging the gap between computer vision and fluid dynamics.