# Spot Detection for Laser Sensors Based on Annular Convolution Filtering

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## Abstract

**:**

## 1. Introduction

#### Related Work and Our Contribution

## 2. Materials and Methods: Spot Detection Using Annular Convolution Filtering

#### 2.1. The Gaussian Laser Spot

#### 2.2. ROI Determination

#### 2.3. Annular Convolution Strip

Algorithm 1: The proposed ACF algorithm. |

Input: original laser spot image with background light; |

Output: The long axis $\widehat{a}$ and the short axis $\widehat{b}$ of the estimated spot; |

Step 1: Calculate the ROI, the central coordinate, and tilt angle by using the method in Section 3.2; |

Step 2: Obtain the optimal ratio of the short axis and the long axis using the following iteration, where $a=l$, $b=1$ in the initialization; |

Set $i=1$; |

While $b<a$ |

Calculate ${r}_{i}=b/a$; |

Set $k=1$, $\overline{b}=b$; |

While $k<K$ |

Let ${a}_{ik}=a,{b}_{ik}=b$, calculate ${M}_{ik}$ by Equation (11); |

Update $a=a+\Delta a$; |

Update $b=a{r}_{i}$; |

Update $k=k+1$; |

End while |

Calculate the feature similarity ${S}_{i}$ by Equation (12); |

Update $a=l$; |

Update $b=\overline{b}+1$; |

Update $i=i+1$; |

End while |

Output the optimal ratio ${r}_{i}$ corresponding to the minimum value of S; |

Step 3: Fitting a new ellipse using the results in Step 1 and Step 2, where the ratio of the energy in this ellipse and that in ROI is chosen as the widely used value 86.5% (see [48]); |

Step 4: Output the long axis $\widehat{a}$ and the short axis $\widehat{b}$ of the ellipse in Step 3. |

**Remarks**

**1.**

## 3. Results

#### 3.1. Datasets

#### 3.1.1. Standard Dataset

#### 3.1.2. Test Dataset

#### 3.2. Compared Methods

#### 3.3. Parametric Sensitive Analysis

#### 3.4. Compared Results

## 4. Discussion and Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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Standard Data | ACF | TM | PM | AAMED | ASL | |
---|---|---|---|---|---|---|

Long axis $a$ (nm) | 158 | 159.09 | 156.41 | 167.2 | 165.93 | 168.97 |

Short axis $b$ (nm) | 132 | 132.57 | 124.63 | 133.75 | 132.75 | 135.03 |

Standard Data | ACF | TM | PM | AAMED | ASL | |
---|---|---|---|---|---|---|

Long axis $a$ (nm) | 158 | 158.64 | 154.95 | 168.1 | / | 168.53 |

Short axis $b$ (nm) | 132 | 132.2 | 123.29 | 134.05 | / | 135.1 |

Standard Data | ACF | TM | PM | AAMED | ASL | |
---|---|---|---|---|---|---|

Long axis $a$ (nm) | 158 | 159.94 | 156.7 | 171.4 | / | 169.64 |

Short axis $b$ (nm) | 132 | 133.28 | 125.17 | 137.25 | / | 136.54 |

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**MDPI and ACS Style**

Li, L.; Li, M.; Sun, W.; Li, Z.; Yang, Z.
Spot Detection for Laser Sensors Based on Annular Convolution Filtering. *Sensors* **2023**, *23*, 3891.
https://doi.org/10.3390/s23083891

**AMA Style**

Li L, Li M, Sun W, Li Z, Yang Z.
Spot Detection for Laser Sensors Based on Annular Convolution Filtering. *Sensors*. 2023; 23(8):3891.
https://doi.org/10.3390/s23083891

**Chicago/Turabian Style**

Li, Lingjiang, Maolin Li, Weijun Sun, Zhenni Li, and Zuyuan Yang.
2023. "Spot Detection for Laser Sensors Based on Annular Convolution Filtering" *Sensors* 23, no. 8: 3891.
https://doi.org/10.3390/s23083891