# Industrial X-ray Image Analysis with Deep Neural Networks Robust to Unexpected Input Data

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## Abstract

**:**

## 1. Introduction

## 2. Background

## 3. Materials and Methods

#### 3.1. OOD Detector Model

#### Residual Image Analysis

#### 3.2. Binary Classifier Model Trained with Supervised-Learning

#### 3.3. Datasets

## 4. Results

## 5. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Overview of the AE model with encoder (${\mathrm{E}}_{i}$) and decoder (${\mathrm{D}}_{i}$) blocks. Adapted from [37] with permission from ASME.

**Figure 2.**Examples of patches in the training and test datasets: (

**a**) is weld okay, accepted weld, (

**b**,

**c**) are high contrast defects, (

**d**) is a mid-contrast defect, and (

**e**) is a low contrast defect. Adapted from [37] with permission from ASME.

**Figure 3.**Examples of perturbed defect patches in the training dataset; (

**a**) real defect, (

**b**) okay weld, (

**c**) okay plus real defect patch, and (

**d**) okay weld plus a synthetic natural image-based defect patch; (

**a**–

**c**) are adapted from [37] with permission from ASME.

**Figure 4.**Examples of synthetic defect and anomaly indications inserted into weld okay patches: (

**a**) circular hollow inclusion, (

**b**) dogbone inclusion, (

**c**) elongated inclusion, (

**d**) partial circle inclusion, and (

**e**) raster.

**Figure 5.**Results for the high contrast real defects test dataset; (

**a**) is input, (

**b**) is the residual image, residual analysis kernel results are for average kernel in (

**c**) and standard deviation in (

**d**). Above the patch is the maximum value indicated. Kernels above thresholds are indicated in (

**e**) with blue ($\langle I\rangle $ and $\sigma $), green ($\sigma $), and orange ($\langle I\rangle $).

**Figure 6.**Results for the mid-contrast real defects test dataset. (

**a**) is input, (

**b**) is the residual image, residual analysis kernel results are for average kernel in (

**c**) and standard deviation in (

**d**). Above the patch is the maximum value indicated. Kernels above thresholds are indicated in (

**e**) with blue ($\langle I\rangle $ and $\sigma $), green ($\sigma $), and orange ($\langle I\rangle $).

**Figure 7.**Results for the synthetic partial circle inclusion test dataset. (

**a**) is input, (

**b**) is the residual image, residual analysis kernel results are for average kernel in (

**c**) and standard deviation in (

**d**). Above the patch is the maximum value indicated. Kernels above thresholds are indicated in (

**e**) with blue ($\langle I\rangle $ and $\sigma $), green ($\sigma $), and orange ($\langle I\rangle $).

**Figure 8.**Results for the exotic synthetic raster anomaly. (

**a**) is input, (

**b**) is the residual image, residual analysis kernel results are for average kernel in (

**c**) and standard deviation in (

**d**). Above the patch is the maximum value indicated. Kernels above thresholds are indicated in (

**e**) with blue ($\langle I\rangle $ and $\sigma $), green ($\sigma $), and orange ($\langle I\rangle $).

**Figure 9.**Residual image analysis results for the high contrast real defects test dataset. The $\langle I\rangle $ distribution is given in (

**a**), the $\sigma $ distribution in (

**b**), and in (

**c**) $\sigma $ versus $\langle I\rangle $ is plotted. Observe that the histograms have different scales than the scatter plot.

**Figure 10.**Receiver operating characteristics curve (

**a**), accuracy versus false positives (

**b**), and precision versus true positives (

**c**) for the high and mid-contrast real defects test datasets. All values are in fractions.

**Figure 11.**AE model sliding window results for the test dataset. Trained with the SNI perturbation dataset. (

**a**) is the original input, (

**b**) is the residuals, and (

**c**) is the kernel analysis results thresholded with thresholds resulting in an FPR at $0.1\%$ on a patch level.

**Figure 12.**Kernel residual analysis results for the AE model trained on accepted welds as well as those with defects, but without any perturbation dataset. The $\langle I\rangle $ distribution is given in (

**a**), the $\sigma $ distribution in (

**b**), and in (

**c**) $\sigma $ versus $\langle I\rangle $ is plotted.

**Figure 13.**Results for the AE model trained on both accepted welds and those with defects, a synthetic raster anomaly test sample. (

**a**) is input, (

**b**) is the residual image, the residual analysis kernel results are for average kernel in (

**c**) and standard deviation in (

**d**). Above the patch is the maximum value indicated. Kernels above thresholds are indicated in (

**e**) with blue ($\langle I\rangle $ and $\sigma $), green ($\sigma $), and orange ($\langle I\rangle $).

**Table 1.**Overview of the different datasets utilized. For the experimental data, the original sample count refers to the number of unique patches extracted with random translation and rotation from the original full-sized image input; for the synthetic data, the original sample count refers to the number of unique random realizations. See the text for details.

Dataset | Original Sample Count | Augmented Sample Count |
---|---|---|

Train weld okay | 27,454 | 164,724 |

Train defects | 11,705 | 70,230 |

Train synthetic natural image indications | 112,000 | |

Train synthetic, circular indication | 5000 | |

Train synthetic, partial circle inclusion | 5000 | |

Test weld okay | 3480 | |

Test defect, high contrast | 3396 | |

Test defect, mid-contrast | 2898 | |

Test defect, low contrast | 1830 | |

Test, synthetic, five different types | 200 |

**Table 2.**Results for the supervised–trained patch-level binary classifier. The TPR is given as the average and the spread $(\mathrm{max}-\mathrm{min})/2)$ within parenthesis, at $0.1\%$ FPR. For the training data, D is for defects, SC is for synthetic circular indication, SPC is for synthetic partial circular inclusion, SNI is for synthetic natural image indications.

TPR Average and Spread $[\%]$ | ||||
---|---|---|---|---|

Training Data | D | D + SC | D + SC + SPC | D + SNI |

Test Dataset | ||||

Defects high contrast | $78\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $83\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $84\phantom{\rule{0.166667em}{0ex}}\left(4\right)$ | $85\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ |

Defects mid-contrast | $45\phantom{\rule{0.166667em}{0ex}}\left(7\right)$ | $74\phantom{\rule{0.166667em}{0ex}}\left(4\right)$ | $77\phantom{\rule{0.166667em}{0ex}}\left(7\right)$ | $76\phantom{\rule{0.166667em}{0ex}}\left(4\right)$ |

Defects low contrast | $15\phantom{\rule{0.166667em}{0ex}}\left(10\right)$ | $23\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $17\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ | $21\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ |

Synthetic circular hollow inclusion | $46\phantom{\rule{0.166667em}{0ex}}\left(11\right)$ | $69\phantom{\rule{0.166667em}{0ex}}\left(24\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

Synthetic dogbone inclusion | $45\phantom{\rule{0.166667em}{0ex}}\left(14\right)$ | $48\phantom{\rule{0.166667em}{0ex}}\left(11\right)$ | $97\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ | $97\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ |

Synthetic elongated inclusion | $24\phantom{\rule{0.166667em}{0ex}}\left(7\right)$ | $24\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $70\phantom{\rule{0.166667em}{0ex}}\left(8\right)$ | $86\phantom{\rule{0.166667em}{0ex}}\left(7\right)$ |

Synthetic partial circle inclusion | $31\phantom{\rule{0.166667em}{0ex}}\left(6\right)$ | $33\phantom{\rule{0.166667em}{0ex}}\left(9\right)$ | $89\phantom{\rule{0.166667em}{0ex}}\left(6\right)$ | $90\phantom{\rule{0.166667em}{0ex}}\left(6\right)$ |

Synthetic raster | $71\phantom{\rule{0.166667em}{0ex}}\left(27\right)$ | $98\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $97\phantom{\rule{0.166667em}{0ex}}\left(5\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

**Table 3.**Results for the unsupervised–trained autoencoder model, OOD detector. The TPR is given as the average and the spread $(\mathrm{max}-\mathrm{min})/2)$ within parenthesis, at $0.1\%$ FPR. Results are shown for training with weld okay and different perturbation datasets, where D denotes the real defect dataset and SNI is the synthetic natural image indications dataset.

TPR Average and Spread $[\%]$ | |||
---|---|---|---|

Perturbation Dataset | None | D | SNI |

Test Dataset | |||

Defects high contrast | $50\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ | $79\phantom{\rule{0.166667em}{0ex}}\left(9\right)$ | $94\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ |

Defects mid-contrast | $6\phantom{\rule{0.166667em}{0ex}}\left(5\right)$ | $69\phantom{\rule{0.166667em}{0ex}}\left(17\right)$ | $90\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ |

Defects low contrast | $0\phantom{\rule{0.166667em}{0ex}}\left(1\right)$ | $16\phantom{\rule{0.166667em}{0ex}}\left(6\right)$ | $26\phantom{\rule{0.166667em}{0ex}}\left(7\right)$ |

Synthetic circular hollow inclusion | $12\phantom{\rule{0.166667em}{0ex}}\left(10\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

Synthetic dogbone inclusion | $10\phantom{\rule{0.166667em}{0ex}}\left(2\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

Synthetic elongated inclusion | $3\phantom{\rule{0.166667em}{0ex}}\left(1\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

Synthetic partial circle inclusion | $4\phantom{\rule{0.166667em}{0ex}}\left(3\right)$ | $99\phantom{\rule{0.166667em}{0ex}}\left(1\right)$ | $99\phantom{\rule{0.166667em}{0ex}}\left(1\right)$ |

Synthetic raster | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ | $100\phantom{\rule{0.166667em}{0ex}}\left(0\right)$ |

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**MDPI and ACS Style**

Lindgren, E.; Zach, C. Industrial X-ray Image Analysis with Deep Neural Networks Robust to Unexpected Input Data. *Metals* **2022**, *12*, 1963.
https://doi.org/10.3390/met12111963

**AMA Style**

Lindgren E, Zach C. Industrial X-ray Image Analysis with Deep Neural Networks Robust to Unexpected Input Data. *Metals*. 2022; 12(11):1963.
https://doi.org/10.3390/met12111963

**Chicago/Turabian Style**

Lindgren, Erik, and Christopher Zach. 2022. "Industrial X-ray Image Analysis with Deep Neural Networks Robust to Unexpected Input Data" *Metals* 12, no. 11: 1963.
https://doi.org/10.3390/met12111963