# Multiscale Spatial Polygonal Object Granularity Factor Matching Method Based on BPNN

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## Abstract

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## 1. Introduction

## 2. Methodology

#### 2.1. MSPOM Similarity Evaluation Indices Combined with Minimum Bounding Rectangle (MBR)

#### 2.1.1. Distance Similarity

#### 2.1.2. Overlap Rate of Area

#### 2.1.3. Direction Similarity

#### 2.1.4. Shape Similarity

#### 2.2. Granularity Factor Evaluation Index (GFEI)

#### 2.3. Matching Model Based on BPNN (BPM)

- When $p\ge 0.5$, the matching result is “match”; furthermore, the closer the value of $p$ is to 1 or the value of $1-p$ is to 0, the more similar the matching pair.
- When $p<0.5$, the matching result is “does not match”; furthermore, the closer the value of $p$ is to 0 or the value of $1-p$ is to 1, the more dissimilar the matching pair.

#### 2.4. Matching Workflow

- Step 1: In the preparation stage, the data are preprocessed, which includes format conversion, topology checking, and geometric coordinate transformation. The purpose of preprocessing is to resolve systematic errors between data from different sources [47].
- Step 2: The matching stage is the focus of this study, which includes BPM training, first-matching, and last-matching. Model training is performed to acquire the geometric features and matching results of the training data. In first-matching, 1:1 and 1:N candidate matching pairs are detected using the MBR combinatorial optimization [48] (MBRCO) algorithm. MBRCO uses the objects’ MBR to replace them so as to find their candidate matching objects, and adopts the combination threshold to avoid the excessive calculation of the exhaustive method, which can quickly and effectively screen the candidate matching pairs. Then, 1:1 and 1:N correspondences are obtained using the trained BPM. In final matching, spatial districts (SDs) are divided based on Delaunay triangulation, in which the remaining unmatched objects (M:N and 1:0) are distributed. The M:N candidate matching pairs are detected using the MBRCO algorithm and the M:N correspondences are obtained using the trained BPM. The remaining unmatched objects are 1:0 correspondences.
- Step 3: In the evaluation stage, we evaluate the matching results by comparing them with the results of manual inspection.

## 3. Experiments and Discussion

#### 3.1. GFEI Index Analysis

#### 3.2. Experimental Data

#### 3.3. Model Training

#### 3.3.1. Sample Selection

#### 3.3.2. Models and Parameters

- BPM: We established a three-layer BPNN structure. The activation function was a logistic function, number of nodes in the hidden layer was 9, momentum factor was 0.9, learning efficiency was 0.01, and maximum number of iterations was 1000.
- MLRM: The confidence interval of parameter estimation was 95%, maximum number of iterations was 1000, convergence value of parameters was ${10}^{-6}$, and singularity tolerance was ${10}^{-8}$.
- SRM: The random number state was 1, kernel function was the radial basis function, and gamma value was 20.

#### 3.4. Experimental Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 8.**Comparison of $P$ (Accuracy), $R$ (Recall), and ${F}_{1}$ (F1-Measure evaluation) of the four matching models, multivariate logistic regression matching model (MLRM), SVM regression matching model (SRM), Matching Model Based on Backpropagation Neural Network (BPM), and empirical weight matching model (EWM).

**Figure 9.**Comparison of the number of correct matching pairs and missing matching pairs of MLRM, SRM, BPM, and EWM.

**Table 1.**Experimental results of the four similarity evaluation indices (Section 2.1).

Matching Type | Matching Pair | ${\mathit{S}}_{\mathit{d}\mathit{i}\mathit{s}}$ | ${\mathit{S}}_{\mathit{o}\mathit{l}\mathit{p}}$ | ${\mathit{S}}_{\mathit{d}\mathit{i}\mathit{r}}$ | ${\mathit{S}}_{\mathit{s}\mathit{h}\mathit{a}\mathit{p}\mathit{e}}$ | ${\mathit{S}}_{\mathit{a}\mathit{l}\mathit{l}}$ | $\mathit{R}\left(\mathit{S}\right)$ |
---|---|---|---|---|---|---|---|

1:1 | ${a}_{1}:{b}_{23}$ | 0.745 | 0.859 | 0.973 | 0.742 | 0.830 | Match |

${a}_{2}:{b}_{4}$ | 0.709 | 0.909 | 0.971 | 0.882 | 0.868 | Match | |

${a}_{3}:{b}_{16}$ | 0.805 | 0.922 | 0.998 | 0.943 | 0.917 | Match | |

${a}_{7}:{b}_{11}$ | 0.721 | 0.865 | 0.922 | 0.778 | 0.822 | Match | |

${a}_{8}:{b}_{12}$ | 0.940 | 0.903 | 0.992 | 0.813 | 0.912 | Match | |

${a}_{9}:{b}_{14}$ | 0.739 | 0.848 | 0.943 | 0.803 | 0.833 | Match | |

1:N | ${a}_{4}:{b}_{24},{b}_{25},{b}_{26}$ | 0.779 | 0.496 | 0.902 | 0.643 | 0.705 | Not recognized |

${a}_{5}:{b}_{15},{b}_{17},{b}_{18},{b}_{19},{b}_{20}$ | 0.811 | 0.359 | 0.885 | 0.684 | 0.685 | Not recognized | |

${a}_{6}:{b}_{6},{b}_{8}$ | 0.822 | 0.874 | 0.988 | 0.784 | 0.867 | Match | |

M:N | ${a}_{10},{a}_{11}:{b}_{1},{b}_{2},{b}_{3},{b}_{5}$ | 0.776 | 0.598 | 0.890 | 0.646 | 0.726 | Not recognized |

**Table 2.**Test results of GFEI. (where ${S}_{all}{}^{\prime}$ represents the total similarity values of the matching pairs after the 1:1 weighted processing).

Matching Type | Matching Pair | ${\mathit{R}}_{\mathit{p}\mathit{s}\mathit{d}}$ | ${\mathit{M}}_{\mathit{p}\mathit{s}\mathit{d}}$ | ${\mathit{S}}_{\mathit{p}\mathit{s}\mathit{d}}$ | $\mathit{G}\mathit{F}\mathit{E}\mathit{I}$ | ${\mathit{N}}_{\mathit{G}\mathit{F}\mathit{E}\mathit{I}}$ | ${\mathit{S}}_{\mathit{a}\mathit{l}\mathit{l}}{}^{\u2019}$ |
---|---|---|---|---|---|---|---|

1:1 | ${a}_{1}:{b}_{23}$ | 1 | 1.8 | 1.249 | 0.113 | 0.75 | 0.790 |

${a}_{2}:{b}_{4}$ | 1 | 0.113 | 0.75 | 0.809 | |||

${a}_{3}:{b}_{16}$ | 1 | 0.113 | 0.75 | 0.833 | |||

${a}_{7}:{b}_{11}$ | 1 | 0.113 | 0.75 | 0.786 | |||

${a}_{8}:{b}_{12}$ | 1 | 0.113 | 0.75 | 0.831 | |||

${a}_{9}:{b}_{14}$ | 1 | 0.113 | 0.75 | 0.792 | |||

1:N | ${a}_{4}:{b}_{24},{b}_{25},{b}_{26}$ | 3 | 0.091 | 0.86 | 0.783 | ||

${a}_{5}:{b}_{15},{b}_{17},{b}_{18},{b}_{19},{b}_{20}$ | 5 | 0.063 | 1 | 0.842 | |||

${a}_{6}:{b}_{6},{b}_{8}$ | 2 | 0.108 | 0.775 | 0.821 | |||

M:N | ${a}_{10},{a}_{11}:{b}_{1},{b}_{2},{b}_{3},{b}_{5}$ | 2 | 0.108 | 0.775 | 0.751 |

$\mathbf{Dataset}\text{}\mathit{A}$ | $\mathbf{Dataset}\text{}\mathit{B}$ | |
---|---|---|

Place | Zhoushan, China | |

Area | $36{\text{}\mathrm{km}}^{2}$ | |

Scale | 1:2000 | 1:10,000 |

Production time | 2012 | 2009 |

No. of polygons | 6774 | 778 |

Models | TP | FP | AM | FN | P | R | ${\mathit{F}}_{1}\text{}$ |
---|---|---|---|---|---|---|---|

MLRM | 631 | 42 | 14 | 91 | 91.8% | 87.4% | 89.5% |

81.1% | 5.4% | 1.8% | 11.7% | ||||

SRM | 667 | 15 | 14 | 82 | 95.8% | 89.1% | 92.3% |

85.7% | 1.9% | 1.8% | 10.5% | ||||

BPM | 687 | 6 | 14 | 71 | 97.2% | 90.6% | 93.8% |

88.3% | 0.8% | 1.8% | 9.1% | ||||

EWM | 619 | 51 | 14 | 94 | 90.5% | 86.8% | 88.6% |

79.6% | 6.6% | 1.8% | 12.1% |

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## Share and Cite

**MDPI and ACS Style**

Zhu, D.; Cheng, C.; Zhai, W.; Li, Y.; Li, S.; Chen, B.
Multiscale Spatial Polygonal Object Granularity Factor Matching Method Based on BPNN. *ISPRS Int. J. Geo-Inf.* **2021**, *10*, 75.
https://doi.org/10.3390/ijgi10020075

**AMA Style**

Zhu D, Cheng C, Zhai W, Li Y, Li S, Chen B.
Multiscale Spatial Polygonal Object Granularity Factor Matching Method Based on BPNN. *ISPRS International Journal of Geo-Information*. 2021; 10(2):75.
https://doi.org/10.3390/ijgi10020075

**Chicago/Turabian Style**

Zhu, Daoye, Chengqi Cheng, Weixin Zhai, Yihang Li, Shizhong Li, and Bo Chen.
2021. "Multiscale Spatial Polygonal Object Granularity Factor Matching Method Based on BPNN" *ISPRS International Journal of Geo-Information* 10, no. 2: 75.
https://doi.org/10.3390/ijgi10020075