# Texture Analysis for the Bone Age Assessment from MRI Images of Adolescent Wrists in Boys

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Data Acquisition

#### 2.2. Dataset Description

#### 2.3. Data Analysis Methods and Methodology

_{norm}= μ − 3σ and max

_{norm}= μ + 3σ, and finally, thresholded, according to Equations (1) and (2):

#### 2.4. Experiment Setup

## 3. Results

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

- 1.
- First-order features

Feature Name | Formulae | |
---|---|---|

Mean | $\mu =\frac{1}{W\xb7H}{\sum}_{x=0}^{W-1}{\sum}_{y=0}^{H-1}I\left(x,y\right)={\sum}_{i=0}^{G-1}i\xb7h\left(i\right)$ | (A1) |

Variance | ${\sigma}^{2}=\frac{1}{W\xb7H}{\sum}_{x=0}^{W-1}{\sum}_{y=0}^{H-1}{(I\left(x,y\right)-\mu )}^{2}={\sum}_{i=0}^{G-1}{(i-\mu )}^{2}\xb7h\left(i\right)$ | (A2) |

Skewness | ${\sigma}^{-3}{\sum}_{i=0}^{G-1}{(i-\mu )}^{3}\xb7h\left(i\right)$ | (A3) |

Kurtosis | ${\sigma}^{-4}{\sum}_{i=0}^{G-1}{(i-\mu )}^{4}\xb7h\left(i\right)-3$ | (A4) |

Percentile | ${\sum}_{i=0}^{G-1}h\left(i\right)\ge percentile$ | (A5) |

- 2.
- Gray-level co-occurrence matrix [27]

Feature Name | Formulae | |
---|---|---|

Contrast | ${\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}{\left(i-j\right)}^{2}p(i,j)$ | (A6) |

Correlation | ${\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}\frac{ijp\left(i,j\right)-{\mu}_{i}{\mu}_{j}}{{\delta}_{i}{\delta}_{j}}$ where µ _{i} is average and δ_{i} is standard deviation for p_{i} | (A7) |

Homogeneity | ${\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}\frac{p(i,j)}{{1+\left(i-j\right)}^{2}}$ | (A8) |

Entropy | $-{\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}p\left(i,j\right){log}_{2}\left(p\left(i,j\right)\right)$ | (A9) |

Angular second moment | ${\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}{p}^{2}\left(i,j\right)$ | (A10) |

Sum average | ${\sum}_{m=1}^{G}m{p}_{sum}\left(m\right)$ | (A11) |

Sum variance | ${\sum}_{m=1}^{G}{\left(m-sum-avg\right)}^{2}{p}_{sum}\left(m\right)$ | (A12) |

Difference variance | ${\sum}_{m=1}^{G}{\left(i-{\mu}_{dif}\right)}^{2}{p}_{dif}\left(m\right)$ | (A13) |

Difference entropy | $-{\sum}_{m=1}^{G}{p}_{dif}\left(m\right)\mathrm{log}\left({p}_{sum}\left(m\right)\right)$ | (A14) |

Sum entropy | $-{\sum}_{m=1}^{G}{p}_{sum}\left(m\right)\mathrm{log}\left({p}_{sum}\left(m\right)\right)$ | (A15) |

Sum of squares | ${\sum}_{i=0}^{G-1}{\sum}_{j=0}^{G-1}{\left(i-\mu \right)}^{2}p(i,j)$ | (A16) |

- 3.
- Run-length matrix [55]

_{r}. Features derived from the run-length matrix are given in Table A3.

Feature Name | Formulae | |
---|---|---|

Short run emphasis | $\frac{1}{{n}_{r}}{\sum}_{i=0}^{G-1}{\sum}_{j=1}^{L}\frac{p(i,j)}{{j}^{2}}$ | (A17) |

Long run emphasis | $\frac{1}{{n}_{r}}{\sum}_{i=0}^{G-1}{\sum}_{j=1}^{L}p(i,j)\xb7{j}^{2}$ | (A18) |

Gray-level non-uniformity | $\frac{1}{{n}_{r}}{\sum}_{i=0}^{G-1}\left({\sum}_{j=1}^{L}p(i,j)\right)$ | (A19) |

Run-length non-uniformity | $\frac{1}{{n}_{r}}{\sum}_{j=1}^{L}\left({\sum}_{i=0}^{G-1}p(i,j)\right)$ | (A20) |

Run percent | $\frac{{n}_{r}}{W\xb7H}$ | (A21) |

- 4.
- Gradient matrix [27]

- 5.
- First order autoregressive model [56]

- 6.
- Haar wavelet transform [57]

- 7.
- Gabor transform

- 8.
- Histogram of oriented gradients [58]

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**Figure 2.**Exemplary magnetic resonance imaging. The red rectangle shows the growth region in the image on the right and bone region on the left scan.

**Figure 3.**The result of regression algorithms for all cases examined for data describing bone images (metric). The real age is presented by blue circles and estimated age with a regression algorithm is depicted by orange dots. The samples are ordered on the y axis with increasing age. (

**a**) DICOM T1-weighted, (

**b**) DICOM T2-weighted, (

**c**) PNG T1-weighted, and (

**d**) PNG T2-weighted.

**Figure 4.**The result of regression algorithms for all examined cases for data describing growth region images (metric). The real age is given as a blue circle and age estimated with a regression algorithm is depicted as orange dot. The samples are ordered on the y axis with increasing age. (

**a**) DICOM T1-weighted, (

**b**) DICOM T2-weighted, (

**c**) PNG T1-weighted, and (

**d**) PNG T2-weighted.

Parameter | T1-Weighted | T2-Weighted |
---|---|---|

Slice thickness | 3 mm | 3 mm |

Repetition Time | 435 ms | 2749 ms |

Echo Time | 16 ms | 106 ms |

Number of averages | 2 | 2 |

Spacing | 3.5 mm | 3.5 mm |

Echo train length | 23 | 23 |

Bandwidth | 81 MHz | 97 MHz |

**Table 2.**Quantitative regression parameters for different types of data and bone images (metric). Results for 3 features derived from 15 by applying principal component analysis.

Data | R^{2} | RMSE | MSE | MAE |
---|---|---|---|---|

DICOM T1-weighted | 0.9383 | 0.4584 | 0.2101 | 0.3300 |

DICOM T2-weighted | 0.7510 | 0.8365 | 0.6997 | 0.6229 |

PNG T1-weighted | 0.7283 | 0.9344 | 0.8732 | 0.6922 |

PNG T2-weighted | 0.8711 | 0.5731 | 0.3284 | 0.4429 |

**Table 3.**Quantitative regression parameters for different types of data and growth region images (metric). Results for 3 features derived from 15 by applying principal component analysis.

Data | R^{2} | RMSE | MSE | MAE |
---|---|---|---|---|

DICOM T1-weighted | 0.8041 | 0.8194 | 0.6714 | 0.6142 |

DICOM T2-weighted | 0.6621 | 1.4104 | 1.9892 | 1.0969 |

PNG T1-weighted | 0.6743 | 1.0550 | 1.1130 | 0.8740 |

PNG T2-weighted | 0.5216 | 1.1058 | 1.2228 | 0.9228 |

**Table 4.**Results of performance of the presented method and other solutions for the estimation of bone age based on hand.

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## Share and Cite

**MDPI and ACS Style**

Obuchowicz, R.; Nurzynska, K.; Pierzchala, M.; Piorkowski, A.; Strzelecki, M.
Texture Analysis for the Bone Age Assessment from MRI Images of Adolescent Wrists in Boys. *J. Clin. Med.* **2023**, *12*, 2762.
https://doi.org/10.3390/jcm12082762

**AMA Style**

Obuchowicz R, Nurzynska K, Pierzchala M, Piorkowski A, Strzelecki M.
Texture Analysis for the Bone Age Assessment from MRI Images of Adolescent Wrists in Boys. *Journal of Clinical Medicine*. 2023; 12(8):2762.
https://doi.org/10.3390/jcm12082762

**Chicago/Turabian Style**

Obuchowicz, Rafal, Karolina Nurzynska, Monika Pierzchala, Adam Piorkowski, and Michal Strzelecki.
2023. "Texture Analysis for the Bone Age Assessment from MRI Images of Adolescent Wrists in Boys" *Journal of Clinical Medicine* 12, no. 8: 2762.
https://doi.org/10.3390/jcm12082762