Quantifying the effect of X-ray scattering for data generation in real-time defect detection

TL;DR

This work tackles how X-ray scattering affects data generation for in-line defect detection by using Monte-Carlo X-ray simulations to create paired training datasets with and without scattering and evaluating DCNN performance via POD curves. The authors model a defect-detection task in cylindrical objects with an ellipsoidal cavity and train a segmentation network on both data variants, linking accuracy to defect size through $s_{90}$ and $s_{90/95}$ metrics. They show that excluding scattering from training data often has limited impact (typically $<5\%$ in $s_{90}$) except in high SPR regimes where performance gaps can reach up to about $15\%$, and that SPR and defect size jointly govern the necessity of simulating scattering. The results provide a practical, task-driven framework for deciding the fidelity required in synthetic X-ray data generation, with broad applicability to other industrial imaging problems and openly available code and data for replication.

Abstract

Background: X-ray imaging is widely used for the non-destructive detection of defects in industrial products on a conveyor belt. In-line detection requires highly accurate, robust, and fast algorithms. Deep Convolutional Neural Networks (DCNNs) satisfy these requirements when a large amount of labeled data is available. To overcome the challenge of collecting these data, different methods of X-ray image generation are considered. Objective: Depending on the desired degree of similarity to real data, different physical effects should either be simulated or can be ignored. X-ray scattering is known to be computationally expensive to simulate, and this effect can greatly affect the accuracy of a generated X-ray image. We aim to quantitatively evaluate the effect of scattering on defect detection. Methods: Monte-Carlo simulation is used to generate X-ray scattering distribution. DCNNs are trained on the data with and without scattering and applied to the same test datasets. Probability of Detection (POD) curves are computed to compare their performance, characterized by the size of the smallest detectable defect. Results: We apply the methodology to a model problem of defect detection in cylinders. When trained on data without scattering, DCNNs reliably detect defects larger than 1.3 mm, and using data with scattering improves performance by less than 5%. If the analysis is performed on the cases with large scattering-to-primary ratio ($1 < SPR < 5$), the difference in performance could reach 15% (approx. 0.4 mm). Conclusion: Excluding the scattering signal from the training data has the largest effect on the smallest detectable defects, and the difference decreases for larger defects. The scattering-to-primary ratio has a significant effect on detection performance and the required accuracy of data generation.

Figures (10)

• Figure 1: General scheme of defect detection via X-ray imaging. An X-ray acquisition system is used to make a projection of the product of interest. Defects affect projection intensity even if they are inside the product, and can be detected by analyzing the projection.
• Figure 2: Application-driven approach to evaluate the difference between simulation with and without scattering. First, a large number of 3D volumes is generated by combining different variations of object and defect geometry. Two forward projection methods are used to transform the 3D volumes into X-ray projections. Each dataset containing a variety of projections is used to train a DCNN. They are applied to the same collection of test data with scattering. The performance of the DCNNs is evaluated using POD curves.
• Figure 3: Different distributions of the X-ray signal that are computed with a Monte-Carlo algorithm: distribution of primary photons registered by the detector (a), distribution of scattered photons (b), scattering-to-primary ratio (c), projection image without scattering after pre-processing (d), projection image with scattering (e).
• Figure 4: Example of a POD curve and its relation to accuracy for a single projection: (a) the correlation between $F_1$ score and defect size for all projections in the test set, (b) a histogram computed after binning the defect size indicating that the fraction of projections with $F_1>50\%$ increases with defect size, (c) the POD curve representing a probability of $F_1>50\%$ with the smallest detectable defect $s_{90}$ and its higher bound highlighted.
• Figure 5: Examples of projections corresponding to different generated volumes.