Transformer-based three-dimensional crack detection in lava tubes: from a terrestrial analogue toward lunar subsurface exploration

Technical Summary: Transformer-based 3D Crack Detection in Lava Tubes

Problem Statement
Assessing the structural integrity of lava tubes is critical for future lunar subsurface exploration, where these formations are prime candidates for human habitats due to their radiation shielding and thermal stability. However, current methods for automated crack detection are inadequate for natural lava tubes. Conventional tunnel inspection relies on known, regular cross-sections (e.g., cylindrical), an assumption violated by the irregular, continuously varying polygonal cross-sections of lava tubes. Furthermore, these environments contain primary volcanic textures (shelves, flow marks, stalactites) at scales comparable to the cracks themselves, creating significant noise for vision-based or standard LiDAR analysis. Existing machine learning approaches often struggle with the sparsity, disorder, and complex geometry of point cloud data in these unstructured scenes, particularly when distinguishing true fractures from geological mimics.

Methodology
The authors introduce LavaCrack_PT, a Transformer-based deep learning model designed for 3D crack detection in unstructured point clouds. The workflow consists of three main components:

1. Data Acquisition and Annotation:

   • Site: Xianren Cave (Hainan, China), selected as a terrestrial analogue for its diverse cross-sectional morphologies and scale variations.
   • Sensor: Leica RTC360 LiDAR scanner (60m range, 1mm+10ppm precision) used in 30 stations to capture the tube's geometry.
   • Dataset: The point cloud was segmented into 175 evenly spaced orthogonal cross-sections. A total of 671 cracks were manually annotated by experts (split 8:2 for training and testing), covering straight, curved, and rockfall terrains. Cracks were classified by position (roof, wall, floor) based on normalized height ($z_{norm}$).

2. Model Architecture (LavaCrack_PT):

   • Backbone: Built upon PointTransformerV2, the model features a five-level multi-scale hierarchical backbone. This structure utilizes grouped vector attention and partition-based pooling to capture both fine-grained local details (crack boundaries) and long-range dependencies (thread-like crack continuity). Feature dimensions double at each level ($32 \to 1024$) while point counts are downsampled ($N \to N/16$).
   • Loss Function: To address the severe class imbalance between background and thin cracks, the authors propose an Enhanced Dice (E-Dice) loss. This includes an adaptive smoothing factor ($\alpha$) calculated dynamically based on the ratio of foreground to total points, combined with a weighted Cross-Entropy (CE) loss to further emphasize rare crack classes.

3. Analysis Framework:

   • The trained detector was applied to the full tube inventory to generate a field map of 893 elongated cracks.
   • Crack orientations were statistically analyzed relative to the local tube axis and radial direction to test against thermoelastic stress-field predictions.

Key Results

• Detection Performance: LavaCrack_PT achieved a mean Intersection over Union (mIoU) of 0.6930 and a mean class accuracy (mAcc) of 0.8027 on the test set. It outperformed CNN-based, graph-based, and other Transformer-based baselines.
• Robustness: The model demonstrated stability across:
  • Terrain: Straight sections, bends, and rockfall zones (where occlusion mimics cracks).
  • Scale: Extremely narrow cracks (near point-cloud resolution) and extremely wide cracks.
  • Density: High, medium, and low-density point clouds, maintaining fewer false negatives than baselines even at lower densities.
• Geological Validation: The detector identified a distinct position-dependent orientation pattern:
  • Roof cracks: Predominantly axis-parallel (mean angle ~53.7° relative to the tube axis).
  • Wall cracks: Predominantly transverse/radial (mean angle ~69.4°).
  • Floor cracks: Essentially absent (consistent with rockfall mantling).
  • This partition aligns with elastic-shell theory and 2D elastic-strength models, which predict longitudinal tensile stress on the roof and circumferential tension on the walls.

Significance and Claims
The paper positions this work as a bridge between terrestrial analogues and lunar exploration, making the following specific claims:

1. Validation of Stress Models: The study provides the first field-measured, 3D crack inventory that empirically validates stress-field predictions for lava tubes without relying on ground truth from lunar missions. It confirms that while the bulk orientation of cracks may appear isotropic, the position-dependent partition (roof vs. wall) matches theoretical stress regimes.
2. Physical Basis for Transfer: The authors argue that transferring an Earth-trained detector to the Moon is physically justified. The governing thermoelastic stress (Equation 1) depends on material properties (basalt composition, thermal expansion, modulus) rather than gravity. While gravity scales the size of the tube (allowing larger spans on the Moon), it does not alter the mechanism of crack formation or the dimensionless stress field geometry. Therefore, the geometric signatures learned on Earth should remain valid on the Moon.
3. Methodological Transferability: The workflow (LiDAR acquisition $\to$ Transformer segmentation $\to$ morphological analysis) is presented as a self-contained pipeline ready for lunar deployment. The model's robustness to point-cloud density variations suggests it can adapt to different sensing configurations anticipated in lunar missions.
4. Engineering Implications: The identification of transverse, radially oriented wall cracks as a specific population is highlighted as critical for engineering safety, as their propagation could undermine the load-bearing capacity of the arch shell, a risk distinct from the more numerous roof cracks.

The paper concludes that this Earth-validated workflow offers a transferable basis for future Moon subsurface exploration, treating the terrestrial observation as a rigorous test of the underlying mechanics that govern lunar lava tube integrity.