# Coarse X-ray Lumbar Vertebrae Pose Localization and Registration Using Triangulation Correspondence

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## Abstract

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## 1. Introduction

- To pinpoint the posture area of the lumbar vertebrae in environments with a low contrast. Figure 1 depicts the position of the vertebrae that must be located. Thus, each stance is observed to be difficult to execute.
- To register two sides of view for reconstructing a three-dimensional model.

## 2. Materials and Methods

#### 2.1. Materials

#### 2.1.1. X-ray Image of Human Lumbar Spine

#### 2.1.2. Speeded up Robust Features (SURF)

#### 2.1.3. Delaunay Triangulation

#### 2.1.4. Dataset

#### 2.2. Methodology

#### 2.2.1. Region of Interest Segmentation (ROI)

#### 2.2.2. Triangulation Using Delaunay’s Approach

Algorithm 1 Delaunay triangulation | |

Algorithm | Delaunay($P$) |

Input | a set $P$ of $n$ point in ${\mathit{\mathbb{R}}}^{2}$ |

Output | $\mathcal{D}\mathcal{T}\left(P\right)$ |

1. | compute a triangulation $\mathcal{T}$ of $P$ |

2. | Initialize a stack containing all the edges of $\mathcal{T}$ |

3. | While stack is non-empty |

4. | do pop $ab$ from stack and unmark it |

5. | if $ab$ is illegal then |

6. | do flip $ab$ to $cd$ |

7. | for $xy\in \left\{ac,cb,bd,da\right\}$ |

8. | do if $xy$ is not marked |

9. | then mark $xy$ and push it on stack |

10. | return $\mathcal{T}$ |

#### 2.2.3. Vertebrae Pose Localization

Algorithm 2 Delaunay’s edge counting algorithm | |

Algorithm | Delaunay Edge Counting |

input | directed graph (DT) $G=\left(V,E\right)$ with edge lengths $\lambda :E\to {\mathit{\mathbb{R}}}_{>0}$ |

data | priority queue $Q$ with keys $\mathrm{dist}[\cdot ]$, number of edge $v$ |

1. | initialization |

2. | while $Qnotempty$ do |

3. | $extractv\leftarrow Q$ with minimum $\mathrm{dist}\left[v\right]$; push $v\to S$ |

4. | foreach vertex $w$ such that $\left(v,w\right)\in E$ do |

5. | path discovery //-shorter path to $w$? |

6. | if $\mathrm{dist}\left[w\right]>\mathrm{dist}\left[v\right]+\lambda \left(v,w\right)$ then |

7. | $\mathrm{dist}\left[w\right]\leftarrow \mathrm{dist}\left[v\right]+\lambda \left(v,w\right)$ |

8. | Insert/update $w\to Q$ with new key; $\sigma \left[w\right]\leftarrow 0$; |

9. | $\mathrm{Pred}\left[w\right]\leftarrow \text{}\mathrm{empty}\text{}\mathrm{list}$ |

10. | path counting |

11. | if $\mathrm{dist}\left[w\right]=\mathrm{dist}\left[v\right]+\lambda \left(v,w\right)$ then |

12. | $\sigma \left[w\right]\leftarrow \sigma \left[w\right]+\sigma \left[v\right]$ |

13. | append $v\to \mathrm{Pred}\left[w\right]$ |

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Table 1.**Description of the experimented dataset which collected from Burapha University Hospital, Thailand.

List | Description | Unit | |
---|---|---|---|

1. | Image type | Normal X-ray (Plain film) | - |

2. | Body part | Lumbar spine (LSPINE) | - |

3. | View | AP view and LA view | - |

4. | Numbers of patients | 3600 | records |

5. | Numbers of images | 7200 | images |

6. | Numbers of disorder patient | 621 | records |

7. | Numbers of spinal disorders | 788 | cases |

8. | Dataset size | 18.5 | GB |

9. | Ground truth | - Lumbar vertebrae positions.
- Spondylolisthesis diagnosis.
- Bertolotti’s syndrome
| - |

10. | Ground truth type | Four corner coordinates points. | - |

11. | File types | JPG (image) and CSV (ground truth) | - |

12. | Locations | Thailand, Chonburi, Burapha University Hospital (BUH) | - |

13. | Years of records | 2000–2021 | - |

14. | Age range | (6–97) | years old |

15. | Image dimension | Original | - |

16. | Motivation | Delivering gold standard lumbar spine dataset of Thais for researchers around the world to develop and improve performance of the segmentation algorithms on the lumbar spine. | - |

Dataset | Confusion Matrix | |||
---|---|---|---|---|

Accuracy | Recall | Precision | FNR | |

Good | 87.60 | 88.32 | 84.24 | 11.56 |

Medium | 81.38 | 86.55 | 83.11 | 16.20 |

Low | 71.97 | 81.23 | 79.73 | 18.51 |

Average | 80.32 | 85.37 | 82.36 | 15.42 |

Method | Evaluation | ||
---|---|---|---|

JM | HD | PAD | |

Proposed approach | 0.82 | 10.87 | 2.33 |

Watershed | 0.54 | 46.28 | 5.19 |

DRLSE | 0.77 | 27.98 | 4.63 |

Region growing | 0.81 | 32.89 | 4.48 |

Method | Average Time Usages (s) | |||
---|---|---|---|---|

Good | Medium | Lowth | Average time | |

Proposed approach | 0.92 | 1.04 | 1.36 | 1.11 |

Watershed | 1.33 | 1.89 | 1.92 | 1.71 |

DRLSE | 1.74 | 1.79 | 1.81 | 1.78 |

Region growing | 1.56 | 1.88 | 2.21 | 1.88 |

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## Share and Cite

**MDPI and ACS Style**

Yookwan, W.; Limchareon, S.; Lee, S.-H.; Jang, J.-S.; Lee, D.; Chinnasarn, K.
Coarse X-ray Lumbar Vertebrae Pose Localization and Registration Using Triangulation Correspondence. *Processes* **2023**, *11*, 61.
https://doi.org/10.3390/pr11010061

**AMA Style**

Yookwan W, Limchareon S, Lee S-H, Jang J-S, Lee D, Chinnasarn K.
Coarse X-ray Lumbar Vertebrae Pose Localization and Registration Using Triangulation Correspondence. *Processes*. 2023; 11(1):61.
https://doi.org/10.3390/pr11010061

**Chicago/Turabian Style**

Yookwan, Watcharaphong, Sornsupha Limchareon, Sang-Hun Lee, Jun-Su Jang, Daesung Lee, and Krisana Chinnasarn.
2023. "Coarse X-ray Lumbar Vertebrae Pose Localization and Registration Using Triangulation Correspondence" *Processes* 11, no. 1: 61.
https://doi.org/10.3390/pr11010061