A statistical method for crack pre-detection in 3D concrete images

TL;DR

This work tackles crack detection in large-scale 3D concrete CT images by introducing a statistical pre-localization framework that identifies regions likely to contain cracks with controlled error rates. The approach combines a computationally light Maximal Hessian Entry filter, geometry-driven statistics on a regular cube partition, and a spatial CUSUM-based change-point test coupled with adaptive local FDR weighting (LAWS) to detect anomalous regions while using an empirical null learned from homogeneous data. It demonstrates robust performance on semi-synthetic and real CT volumes, with linear runtime and no need for large annotated datasets, thereby enabling targeted, resource-efficient high-resolution segmentation. The framework is designed to integrate with DL models, reducing training and inference costs and providing an interpretable pre-processing step in large-scale CT inspection pipelines, with potential for training data generation and joint use with segmentation networks.

Abstract

In practical applications, effectively segmenting cracks in large-scale computed tomography (CT) images holds significant importance for understanding the structural integrity of materials. Classical image-processing techniques and modern deep-learning models both face substantial computational challenges when applied directly to high resolution big data volumes. This paper introduces a statistical framework for crack pre-localization, whose purpose is not to replace or compete with segmentation networks, but to identify, with controlled error rates, the regions of a 3D CT image that are most likely to contain cracks. The method combines a simple Hessian-based filter, geometric descriptors computed on a regular spatial partition, and a spatial multiple testing procedure to detect anomalous regions while relying only on minimal calibration data, rather than large annotated datasets. Experiments on semi-synthetic and real 3D CT scans demonstrate that the proposed approach reliably highlights regions likely to contain cracks while preserving linear computational complexity. By restricting subsequent high resolution segmentation to these localized regions, deep-learning models can be trained and operate more efficiently, reducing both training runtime as well as resource consumption. The framework thus offers a practical and interpretable preprocessing step for large-scale CT inspection pipelines.

Figures (17)

• Figure 1: 7-step processing pipeline diagram for crack pre-ocalization in 3D concrete images
• Figure 2: Representative 2D slices from the VoroCrack3D dataset JUNG2024110474. The top row shows original semi-synthetic CT images of NC and HPC with different crack patterns (samples 7a and 8a), while the bottom row displays their corresponding ground truth masks. Each volume has a spatial resolution of $400^3$ voxels.
• Figure 3: Results of crack segmentation on two semi-synthetic samples (7a-NC and 8a-NC) from the VoroCrack3D dataset JUNG2024110474. Each row corresponds to a test image (original and ground truth images), followed by the results of the Frangi filter, Sheet filter, and Maximal Hessian Entry filter.
• Figure 4: Performance of the Frangi, Sheet, and Maximal Hessian Entry filters evaluated using precision, recall, F1, and IoU. The top row shows results for normal concrete, and the bottom row shows results for high-performance concrete.
• Figure 5: Application of the Frangi, Sheet, and Maximal Hessian Entry filters to real 3D CT images of concrete with cracks. Each row corresponds to a different input dimensions $850 \times 400 \times 1050$, $800 \times 650 \times 1150$, respectively. The first column shows 2D slices of the original images, followed by the segmentation results obtained using the three filters.