# Pulp Particle Classification Based on Optical Fiber Analysis and Machine Learning Techniques

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## Abstract

**:**

## 1. Introduction

## 2. Experimental Section

## 3. Models and Methods

#### 3.1. Image Analysis Techniques

#### 3.1.1. Image Segmentation

#### 3.1.2. Particle Characterization

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#### 3.2. Machine Learning

#### 3.2.1. Data Processing

#### 3.2.2. Lasso Regression

#### 3.2.3. Support Vector Machine

#### 3.2.4. Feed-Forward Neural Network

#### 3.2.5. Recurrent Neural Network

## 4. Results

#### 4.1. Data Processing

#### 4.2. Machine Learning

#### 4.2.1. Lasso Regression

#### 4.2.2. Support Vector Machine

#### 4.2.3. Feed-Forward Neural Networks

#### 4.2.4. Recurrent Neural Networks

#### 4.3. Figures, Tables and Schemes

## 5. Discussion

#### 5.1. Image Analysis and Data Processing

#### 5.2. Machine Learning

#### 5.3. Future Investigations

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A3.**Probability density versus perimeter-based fibrillation in Dataset 1. Outliers removed from the fines and fiber stump panels.

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**Figure 1.**Particle detection algorithm using high-threshold mask ${\widehat{I}}^{\left(1\right)}$ and low-threshold mask $\stackrel{\u02c7}{I}$, where $\stackrel{\u02c7}{I}$ is used for floodfill particle domain detection. Each iteration (row) results in an identified particle domain ${D}_{\xi}$, $\xi =1,2,\dots ,{n}_{\mathrm{p}}$. The particle domains, with associated density weights ${\rho}_{ij}$, represent particles.

**Figure 2.**Average width versus contour length for pulp particles, where each object is colored according to its mean light attenuation. Example images not to scale.

**Figure 3.**The distribution of objects in each category for Dataset 2, smoothed with Gaussian kernel density functions to eliminate noise.

**Figure 4.**The accuracy of each ML model for Datasets 1 and 2 before and after their respective transformations.

Predictor | Symbol | Dataset |
---|---|---|

Contour length | ${L}_{\mathrm{c}}$ | 1, 2 |

Mean width | W | 1, 2 |

Shape factor | S | 1 |

Area-based fibrillation | ${A}_{\mathrm{F}}$ | 1 |

Perimeter-based fibrillation | ${P}_{\mathrm{F}}$ | 1 |

Projected length | ${L}_{\mathrm{p}}$ | 2 |

Mean light attenuation | $\overline{\rho}$ | 2 |

Fibrillation index | F | 2 |

Page’s and Jordan’s curl index | C | 2 |

Normalized variance | V | 2 |

Normalized max. curvature | K | 2 |

Sensitivity | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model | Data | Transf. | L. att. | Accuracy | Fiber | Fines | Ribbon | Stump | Shive | Other |

Lasso | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.964 | 0.944 | 0.989 | 0.991 | 0.970 | 0.909 | 0.200 |

2 | Yeo–J. | $\overline{\rho}$ | 0.936 | 0.917 | 0.978 | 0.972 | 0.879 | 0.909 | 0.000 | |

2 | Binary | 0.932 | 0.944 | 0.989 | 0.972 | 0.758 | 0.909 | 0.200 | ||

2 | None | $\overline{\rho}$ | 0.925 | 0.917 | 0.967 | 0.953 | 0.879 | 0.818 | 0.200 | |

2 | Yeo–J. | 0.907 | 0.917 | 0.978 | 0.925 | 0.758 | 0.909 | 0.200 | ||

2 | None | 0.904 | 0.917 | 0.978 | 0.915 | 0.758 | 0.818 | 0.400 | ||

1 | Yeo–J. | 0.765 | 0.879 | 0.882 | 0.738 | 0.602 | 0.273 | 0.222 | ||

1 | None | 0.708 | 0.759 | 0.842 | 0.690 | 0.519 | 0.455 | 0.111 | ||

SVM | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.954 | 0.917 | 0.989 | 0.981 | 0.970 | 0.818 | 0.200 |

2 | None | $\overline{\rho}$ | 0.943 | 0.917 | 1.000 | 0.981 | 0.848 | 0.818 | 0.200 | |

2 | Binary | 0.929 | 0.944 | 0.989 | 0.972 | 0.788 | 0.818 | 0.000 | ||

2 | None | 0.925 | 0.917 | 0.989 | 0.962 | 0.788 | 0.818 | 0.200 | ||

2 | Yeo–J. | $\overline{\rho}$ | 0.925 | 0.944 | 0.989 | 0.934 | 0.879 | 0.818 | 0.000 | |

2 | Yeo–J. | 0.911 | 0.972 | 0.978 | 0.943 | 0.727 | 0.818 | 0.000 | ||

1 | Yeo–J. | 0.793 | 0.862 | 0.882 | 0.750 | 0.759 | 0.091 | 0.000 | ||

1 | None | 0.723 | 0.862 | 0.857 | 0.679 | 0.519 | 0.364 | 0.111 | ||

FFNN | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.950 | 0.889 | 0.989 | 0.991 | 0.970 | 0.818 | 0.000 |

2 | Yeo–J. | $\overline{\rho}$ | 0.936 | 0.917 | 0.989 | 0.953 | 0.939 | 0.818 | 0.000 | |

2 | Binary | 0.925 | 0.889 | 1.000 | 0.981 | 0.758 | 0.818 | 0.000 | ||

2 | Yeo–J. | 0.911 | 0.917 | 0.978 | 0.953 | 0.758 | 0.818 | 0.000 | ||

2 | None | $\overline{\rho}$ | 0.907 | 0.889 | 0.967 | 0.934 | 0.848 | 0.818 | 0.000 | |

2 | None | 0.903 | 0.917 | 0.966 | 0.953 | 0.727 | 0.818 | 0.000 | ||

1 | Yeo–J. | 0.814 | 0.879 | 0.897 | 0.798 | 0.750 | 0.364 | 0.000 | ||

1 | None | 0.795 | 0.862 | 0.882 | 0.762 | 0.722 | 0.364 | 0.111 | ||

RNN | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.936 | 0.918 | 0.977 | 0.978 | 0.928 | 0.764 | 0.047 |

2 | Yeo–J. | 0.922 | 0.928 | 0.974 | 0.936 | 0.736 | 0.764 | 0.067 | ||

2 | Binary | 0.915 | 0.931 | 0.956 | 0.966 | 0.775 | 0.730 | 0.027 | ||

2 | Yeo–J. | $\overline{\rho}$ | 0.911 | 0.934 | 0.966 | 0.941 | 0.892 | 0.709 | 0.020 | |

2 | None | 0.900 | 0.930 | 0.928 | 0.930 | 0.741 | 0.603 | 0.033 | ||

2 | None | $\overline{\rho}$ | 0.893 | 0.903 | 0.949 | 0.924 | 0.744 | 0.600 | 0.027 | |

1 | Yeo–J. | 0.786 | 0.828 | 0.816 | 0.744 | 0.784 | 0.239 | 0.174 | ||

1 | None | 0.748 | 0.855 | 0.831 | 0.762 | 0.678 | 0.076 | 0.096 |

Specificity | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|

Model | Data | Transf. | L. att. | Accuracy | Fiber | Fines | Ribbon | Stump | Shive | Other |

Lasso | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.964 | 1.000 | 0.995 | 0.983 | 0.984 | 0.993 | 1.000 |

2 | Yeo–J. | $\overline{\rho}$ | 0.936 | 0.996 | 0.974 | 0.983 | 0.980 | 0.985 | 1.000 | |

2 | Binary | 0.932 | 0.996 | 0.963 | 0.983 | 0.984 | 0.993 | 0.993 | ||

2 | None | $\overline{\rho}$ | 0.925 | 0.996 | 0.974 | 0.983 | 0.972 | 0.989 | 0.993 | |

2 | Yeo–J. | 0.907 | 0.992 | 0.953 | 0.977 | 0.976 | 0.985 | 0.996 | ||

2 | None | 0.904 | 0.992 | 0.948 | 0.977 | 0.972 | 0.989 | 0.996 | ||

1 | Yeo–J. | 0.765 | 0.966 | 0.889 | 0.946 | 0.893 | 0.994 | 0.991 | ||

1 | None | 0.708 | 0.986 | 0.841 | 0.936 | 0.847 | 0.994 | 0.989 | ||

SVM | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.954 | 1.000 | 0.995 | 0.977 | 0.980 | 0.996 | 0.993 |

2 | None | $\overline{\rho}$ | 0.943 | 0.992 | 0.979 | 0.989 | 0.980 | 0.989 | 1.000 | |

2 | Binary | 0.929 | 0.996 | 0.963 | 0.983 | 0.976 | 0.989 | 1.000 | ||

2 | None | 0.925 | 0.992 | 0.974 | 0.983 | 0.968 | 0.989 | 1.000 | ||

2 | Yeo–J. | $\overline{\rho}$ | 0.925 | 0.992 | 0.969 | 0.983 | 0.972 | 0.993 | 0.996 | |

2 | Yeo–J. | 0.911 | 0.992 | 0.953 | 0.971 | 0.968 | 0.996 | 1.000 | ||

1 | Yeo–J. | 0.793 | 0.959 | 0.922 | 0.951 | 0.901 | 0.996 | 0.994 | ||

1 | None | 0.723 | 0.964 | 0.852 | 0.943 | 0.871 | 0.996 | 0.989 | ||

FFNN | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.950 | 1.000 | 0.995 | 0.977 | 0.984 | 0.985 | 0.996 |

2 | Yeo–J. | $\overline{\rho}$ | 0.936 | 0.996 | 0.974 | 0.977 | 0.980 | 0.993 | 0.996 | |

2 | Binary | 0.925 | 0.996 | 0.958 | 0.983 | 0.984 | 0.985 | 0.996 | ||

2 | Yeo–J. | 0.911 | 0.992 | 0.953 | 0.971 | 0.976 | 0.993 | 0.996 | ||

2 | None | $\overline{\rho}$ | 0.907 | 1.000 | 0.942 | 0.971 | 0.980 | 0.985 | 0.996 | |

2 | None | 0.903 | 0.992 | 0.958 | 0.965 | 0.972 | 0.985 | 1.000 | ||

1 | Yeo–J. | 0.814 | 0.969 | 0.930 | 0.946 | 0.921 | 0.994 | 0.994 | ||

1 | None | 0.795 | 0.981 | 0.907 | 0.946 | 0.896 | 0.996 | 0.994 | ||

RNN | 2 | Binary | ${\overline{\rho}}^{\prime}$ | 0.936 | 0.989 | 0.994 | 0.985 | 0.983 | 0.985 | 0.991 |

2 | Yeo–J. | 0.922 | 0.991 | 0.940 | 0.978 | 0.971 | 0.991 | 0.999 | ||

2 | Binary | 0.915 | 0.984 | 0.971 | 0.981 | 0.977 | 0.988 | 0.988 | ||

2 | Yeo–J. | $\overline{\rho}$ | 0.911 | 0.988 | 0.965 | 0.982 | 0.970 | 0.991 | 0.997 | |

2 | None | 0.900 | 0.978 | 0.951 | 0.960 | 0.966 | 0.989 | 0.996 | ||

2 | None | $\overline{\rho}$ | 0.893 | 0.978 | 0.946 | 0.958 | 0.971 | 0.989 | 0.997 | |

1 | Yeo–J. | 0.786 | 0.975 | 0.947 | 0.944 | 0.856 | 0.992 | 0.989 | ||

1 | None | 0.748 | 0.959 | 0.921 | 0.919 | 0.885 | 0.998 | 0.994 |

Dataset | Transform. | Light att. | Kernel | $\mathbf{\Gamma}$ | $\mathit{\gamma}$ |
---|---|---|---|---|---|

1 | None | linear | 10 | 0.01 | |

1 | Yeo–Johnson | RBF | 10 | 0.1 | |

2 | None | $\overline{\rho}$ | linear | 100 | 0.01 |

2 | None | linear | 0.1 | 0.01 | |

2 | Yeo–Johnson | $\overline{\rho}$ | RBF | 100 | 0.01 |

2 | Yeo–Johnson | linear | 1 | 0.01 | |

2 | Binary | ${\overline{\rho}}^{\prime}$ | linear | 100 | 0.01 |

2 | Binary | linear | 10 | 0.01 |

Layer | Hidden Units | Activation Type |
---|---|---|

LSTM | 124 | ReLU |

GRU1 | 32 | Tanh |

GRU2 | 16 | Tanh |

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## Share and Cite

**MDPI and ACS Style**

Lindström, S.B.; Amjad, R.; Gåhlin, E.; Andersson, L.; Kaarto, M.; Liubytska, K.; Persson, J.; Berg, J.-E.; Engberg, B.A.; Nilsson, F.
Pulp Particle Classification Based on Optical Fiber Analysis and Machine Learning Techniques. *Fibers* **2024**, *12*, 2.
https://doi.org/10.3390/fib12010002

**AMA Style**

Lindström SB, Amjad R, Gåhlin E, Andersson L, Kaarto M, Liubytska K, Persson J, Berg J-E, Engberg BA, Nilsson F.
Pulp Particle Classification Based on Optical Fiber Analysis and Machine Learning Techniques. *Fibers*. 2024; 12(1):2.
https://doi.org/10.3390/fib12010002

**Chicago/Turabian Style**

Lindström, Stefan B., Rabab Amjad, Elin Gåhlin, Linn Andersson, Marcus Kaarto, Kateryna Liubytska, Johan Persson, Jan-Erik Berg, Birgitta A. Engberg, and Fritjof Nilsson.
2024. "Pulp Particle Classification Based on Optical Fiber Analysis and Machine Learning Techniques" *Fibers* 12, no. 1: 2.
https://doi.org/10.3390/fib12010002