Marker-Based 3D Reconstruction of Aggregates with a Comparative Analysis of 2D and 3D Morphologies

Imagine you are trying to describe a very bumpy, irregular rock to a friend over the phone. If you just hold it up and show them one side, they might think it's a flat pancake. If you show them another side, they might think it's a long stick. But the rock is actually a weird, 3D lump that doesn't look like either of those things.

This is the exact problem engineers face with aggregates (the crushed rocks used to build roads, railways, and dams). For a long time, they could only look at these rocks from one angle (2D), like looking at a shadow on a wall. This gave them a distorted view of the rock's true shape, size, and how it would fit together with other rocks.

This paper introduces a clever, low-cost way to build a perfect 3D digital twin of these rocks using nothing more than a smartphone camera and some creative tricks.

Here is the breakdown of their "magic trick" in everyday terms:

1. The Problem: The "Shadow" vs. The "Real Thing"

Traditionally, to get a perfect 3D model of a rock, you needed expensive, giant machines (like medical CT scanners or high-tech laser scanners) that cost thousands of dollars. Alternatively, researchers tried taking 2D photos, but that's like trying to guess the volume of a potato by only looking at its shadow. It's often wrong.

2. The Solution: The "Turntable & Smartphone" Setup

The team built a simple setup:

The Stage: A cheap turntable (like a lazy Susan) with a white background.
The Camera: A standard smartphone (like an iPhone).
The Actor: The rock itself.

They placed the rock on the turntable and took a photo every two seconds while slowly spinning it. This created a movie of the rock from every angle.

3. The Three Magic Tricks

To turn those photos into a perfect 3D model, they used three specific "hacks":

Trick #1: The "Green Screen" Effect (Background Suppression)
Usually, when computers try to build a 3D model from photos, they get confused by the table, the shadows, and the background. It's like trying to build a statue of a person while the computer is also trying to build a statue of the chair they are sitting on.
- The Fix: They used a smart AI (a deep learning program) to act like a digital "eraser." It looked at every photo and said, "I only care about the rock; delete everything else." This left them with a clean, floating rock in a white void, making the 3D model much easier to build.
Trick #2: The "Scotch Tape" Markers (Point Cloud Stitching)
Big rocks are too heavy to spin on a small turntable. So, they had to take photos of the top half, stop, flip the rock over, and take photos of the bottom half. Now they had two separate 3D models that didn't know how to connect.
- The Fix: They drew little colored lines (purple and red) on the side of the rock. These acted like Scotch tape or puzzle pieces. The computer could easily find these lines in the photos and say, "Aha! This part of the top model matches this part of the bottom model." This allowed them to snap the two halves together perfectly without the computer getting confused.
Trick #3: The "Ruler" Markers (Scale Reference)
A 3D model made from photos is like a map without a scale. It looks right, but is it 1 inch big or 1 mile big?
- The Fix: They placed four colored dots on the corners of the turntable. Since they knew exactly how far apart those dots were (like a ruler), the computer could use them to say, "Okay, if those dots are 12 inches apart, then this rock must be 6 inches long." This gave the digital model real-world measurements.

4. The Results: It Works!

They tested this on 40 large rocks (riprap) used for erosion control.

Accuracy: They weighed the rocks underwater (the "ground truth") and compared it to the computer's 3D model. The computer was off by only 2%. That's incredibly accurate for a method using a smartphone!
The Big Discovery: When they compared the 2D photos to the 3D models, they found a huge difference.
- The Analogy: If you look at a 3D rock from the side, it might look like a flat pancake (2D). But the 3D model reveals it's actually a thick, round boulder.
- The Lesson: You cannot trust a single photo to tell you the true shape of a rock. The "shadow" is often very different from the "object."

Why Does This Matter?

This is a game-changer for construction and engineering because:

It's Cheap: You don't need a $50,000 machine; you just need a phone and a turntable.
It's Fast: You can get a perfect 3D model of a rock in minutes.
It's Better: Engineers can finally see the true shape of the rocks they use to build roads and bridges. This helps them predict how well the rocks will lock together, making structures safer and stronger.

In short: They figured out how to turn a smartphone camera into a high-tech 3D scanner using a little bit of AI, some colored markers, and a lot of spinning. It turns a blurry 2D shadow into a crystal-clear 3D reality.

1. Problem Statement

Aggregate particles are critical functional components in construction materials (e.g., asphalt, concrete, railroad ballast, and riprap). Their morphological properties (size, shape, texture) significantly influence the performance of these assemblies.

Limitations of Existing Methods:
- 2D Imaging: Traditional 2D image analysis (e.g., silhouettes from AIMS or E-UIAIA) provides limited information, often failing to capture true 3D geometry. It relies on assumptions that may not hold for complex particle shapes.
- Expensive 3D Scanning: High-fidelity 3D reconstruction using laser scanners, structured light scanners, or X-Ray CT is accurate but prohibitively expensive and often requires complex lighting or specific sample mounting.
- Existing Photogrammetry: While cost-effective, current photogrammetry methods for aggregates often rely on support pedestals to elevate small particles for "all-around" views. This limits their applicability to medium and large-sized aggregates (like riprap) which cannot be easily suspended. Additionally, standard photogrammetry often struggles with background noise and lacks robust pipelines for field conditions.

2. Methodology

The authors propose a flexible, cost-effective, marker-based photogrammetry approach using Structure-from-Motion (SfM) to reconstruct high-fidelity 3D models of individual aggregate particles.

A. Equipment Setup

Hardware: A standard digital camera (demonstrated with an iPhone XR), a tripod, a turntable (30.5 cm diameter), and a white cardboard background.
Procedure: The camera is fixed at a 30–45° angle. The aggregate is placed on the turntable, and multi-view images are captured by manually rotating the table (approx. 30° per shot). For larger particles that cannot fit on a turntable, the camera can be moved around the static object.

B. Key Technical Innovations

To overcome the limitations of standard SfM, the authors introduced three specific design features:

Background Suppression via Deep Learning:
- Standard SfM reconstructs the entire scene, including the background, requiring time-consuming manual cleaning.
- Solution: The authors implemented a U2-Net deep learning architecture for salient object detection. This generates a foreground mask for each image, suppressing background noise during the bundle adjustment optimization. This allows for "noise-free" reconstruction without manual cleaning.
- Benefit: The system is robust to different background colors and lighting conditions (field-ready) after a one-time training on ~100 image-mask pairs.
Robust Point Cloud Stitching with Object Markers:
- Large aggregates often require multiple reconstruction runs (scanning different sides) because they cannot be rotated 360° in a single setup.
- Solution: Two distinct colored markers (head-tail patterns in purple and red) are drawn directly on the aggregate surface.
- Process: After partial reconstructions, these markers are manually labeled in a few views to establish consistent 3D coordinates. This enables robust registration and stitching of partial point clouds into a complete model, overcoming the failure of automatic registration algorithms on feature-poor surfaces.
Scale Referencing with Background Markers:
- To convert the local coordinate system to a physical scale, colored Ground Control Points (GCPs) are placed at the corners of the turntable/background.
- Known distances between these markers provide the scale factor for the final 3D model.

C. Workflow

Preparation: Set up equipment and tune the segmentation network for the environment.
Capture: Place aggregate, label object markers, and capture multi-view images (30 views per side).
Reconstruction: Generate masks $\rightarrow$ Execute SfM $\rightarrow$ Label markers $\rightarrow$ Stitch point clouds $\rightarrow$ Generate textured mesh/point cloud.

3. Key Contributions

Cost-Effective 3D Pipeline: Developed a workflow using consumer-grade cameras and open-source/commercial photogrammetry software (extended Agisoft Metashape) to achieve high-fidelity 3D models.
Scalability: Successfully demonstrated the reconstruction of medium-to-large aggregates (up to 15.2 cm / 6 inches, specifically RR3 riprap), overcoming the size limitations of previous pedestal-based photogrammetry methods.
Automation & Robustness: Integrated deep learning for background suppression and custom markers for stitching, eliminating the need for manual cleaning and enabling operation in varied lighting/background conditions.
Comparative Analysis: Provided a rigorous statistical comparison between 2D and 3D morphological metrics, highlighting the discrepancies between single-view 2D analysis and true 3D geometry.

4. Results and Validation

Accuracy Validation: The reconstructed volumes of 10 dolomite aggregate samples were compared against ground-truth measurements obtained via water displacement (ASTM D6473).
- Mean Percentage Error (MPE): +2.0%, indicating a slight systematic overestimation.
- Reasons for Overestimation: Minor pixel deviation in marker labeling, porous surface textures (micro-texture filled with water in real life but reconstructed as flat faces), and the inherent nature of SfM optimization.
- Comparison: The raw volume accuracy (MPE +2.0%) outperformed a previous 3-view volumetric estimation method (which required complex correction factors to achieve ~3.6% MAPE).
Morphological Comparison (2D vs. 3D):
- Flat and Elongated Ratio (FER): 3D FER values were consistently higher than the average 2D FER derived from multi-view images. 2D analysis tends to underestimate the elongation because single views often miss the true longest dimension.
- Sphericity/Circularity: 3D sphericity was consistently higher than average 2D circularity.
- Variability: The Coefficient of Variation (CoV) for 2D FER was higher (10–20%) than for 2D circularity (<10%), suggesting that aspect ratio is more sensitive to viewing angle than roundness.
- Key Finding: 2D analysis (even multi-view averages) generally captures intermediate ratios of the 3D principal dimensions rather than the true 3D extremes. This implies that using 2D data to infer 3D properties requires caution or correction factors.

5. Significance and Future Implications

Quality Assurance/Quality Control (QA/QC): The method provides a low-cost, field-deployable tool for obtaining precise 3D morphological data for aggregate inspection, crucial for pavement and railway engineering.
Research & Simulation: The high-fidelity 3D models can be used to build libraries for Discrete Element Modeling (DEM) and Finite Element Modeling (FEM), where accurate particle geometry is essential for simulating interlocking and stress distribution.
Field Applicability: The design is extensible to field conditions (e.g., stockpiles) by adapting the background suppression network and using mobile camera movement instead of a turntable.
Future Work: The authors recommend further research to develop correction factors that can reliably translate 2D morphological statistics into accurate 3D properties, potentially streamlining current inspection processes.