# An Elevation Ambiguity Resolution Method Based on Segmentation and Reorganization of TomoSAR Point Cloud in 3D Mountain Reconstruction

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## Abstract

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## 1. Introduction

- (1)
- A robust segmentation method combing DBSCAN and GMM is proposed. Compared with the traditional segmentation methods, the proposed method provides better segmentation of the TomoSAR mountain point cloud with intersection.
- (2)
- Motivated by segmentation, an ingenious reorganization method is given. Through elevation extension and combination, reorganization allows to construct all possible results of elevation ambiguity resolution instead of estimating the elevation ambiguity number point by point.
- (3)
- By analyzing the distribution law of TomoSAR point cloud, geometric constraints are given to ensure the automatic extraction of the real point cloud. If geometric constraints are not used, the processor needs to interpret and judge one by one from all the reorganization results.

## 2. Array TomoSAR System

## 3. Distribution Law of TomoSAR Point Cloud

#### 3.1. Geometric Distortion

#### 3.2. Compressive Sensing-Based Layover Solution

#### 3.3. Cause of Elevation Ambiguity

#### 3.4. Distribution Law of TomoSAR Point Cloud

- (1)
- The real point cloud satisfies the boundary constraint in the elevation direction. There is a monotonic increasing relationship between the elevation and ground. Therefore, the elevation values of the points without elevation ambiguity are all within the upper and lower elevation boundaries. As shown in Figure 5, the incidence angle of points ${P}_{1}$ to ${P}_{5}$ increases with the ground. According to (11), the elevation values of points ${P}_{1}$ to ${P}_{5}$ increase with the ground. Using the reduction to absurdity, if the elevation value does not increase with the ground distance, ${P}_{6}$ will be illuminated. Since ${P}_{6}$ is located in the shadow area, it cannot be illuminated;
- (2)
- The real point cloud satisfies the elevation continuity constraint. If there is no shadowing, the elevation continuously increases. Otherwise, holes will be included in the point cloud. However, the near end and the far end of the hole area have equal elevation values. As shown in Figure 5, there is a shadowing between ${P}_{5}$ and ${P}_{7}$. The incidence angles of points ${P}_{5}$ and ${P}_{7}$ are the same. In the same way, the elevation values of points ${P}_{5}$ and ${P}_{7}$ are the same. Thus, the elevation continuity of the real point cloud is always satisfied.

- (1)
- The elevation difference between the real target and the ambiguity target is an integer multiple of the discrete numbers in an elevation period;
- (2)
- The layover points whose elevation difference is an integer multiple of the discrete number will intersect;
- (3)
- For the points in the same period, the elevation is increasing, and the elevation ambiguity number is equal;
- (4)
- The elevation values of the points at the near end and the far end of the hole area are continuous.

## 4. The Segmentation and Reorganization-Based Method

#### 4.1. Segmentation

#### 4.2. Reorganization

## 5. Experimental Results and Analysis

#### 5.1. Simulation Experiments

#### 5.1.1. Data Set

#### 5.1.2. Segmentation Results

#### 5.1.3. Reorganization Results

#### 5.2. Real Experiments

#### 5.2.1. Data Set

#### 5.2.2. Segmentation Results

#### 5.2.3. Reorganization Results

#### 5.3. 3D Mountain Reconstruction Results

## 6. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Abbreviations

TomoSAR | Tomographic Synthetic Aperture Radar |

3D | Three-dimentional |

DBSCAN | Density-Based Spatial Clustering of Applications with Noise |

GMM | Gaussian Mixture Model |

ERS-1 | European Remote Sensing 1 |

ERS-2 | European Remote Sensing 2 |

CS | Compressive Sensing |

TSAC | Three-Step Automatic Clustering |

MS | Mean Shift |

AIRCAS | Aerospace Information Research Institute, Chinese Academy of Sciences |

RIP | Restricted Isometry Property |

ALOS | Advanced Land Observing Satellite “DAICHI” |

BIC | Bayesian Information Criterion |

EM | Expectation Maximum |

EPR | Elevation Position Result |

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**Figure 5.**The observation geometry on the ground-height plane of the airborne array TomoSAR. The terrain marked as dark red can be illuminated, and the terrain marked as black indicates the shadowing area.

**Figure 9.**Simulated scenes: (

**a**) the subscene in ground range geometry; (

**b**) the truth point cloud; (

**c**) the simulated original point cloud; (

**d**) the reference true value. The color maps in (

**a**,

**c**) represent scattering intensity. The colors in (

**d**) represent outliers (−1) and elevation ambiguity number.

**Figure 10.**Segmentation results of the simulated data: (

**a**) DBSCAN; (

**b**) TSAC; (

**c**) GMM; (

**d**) the proposed segmentation method. The different categories are color-coded.

**Figure 11.**The intermediate results of TSAC for the abnormal category in Figure 10: (

**a**) the Gaussian image; (

**b**,

**c**) the Gaussian image and range-elevation map after performing MS for the lower density points; (

**d**) the range-elevation map after performing the third density-based clustering. The color on the left figure represents the density of points, and the color on the other figures represents different categories.

**Figure 12.**The results of the elevation ambiguity resolution acquired by (

**a**) region growing and (

**b**) our method. The red dots indicate the seeds.

**Figure 14.**Range-elevation maps of the original point cloud: (

**a**) slice 1; (

**b**) slice 2; (

**c**) slice 3; (

**d**) slice 4; (

**e**) slice 5. The colormap represents the normalized scatetring intensity.

**Figure 15.**Slices on range-elevation plane of the segmentation results. From top to bottom: slice 1 to slice 5. From left to right: DBSCAN, TSAC, GMM, and the proposed segmentation method. The different categories are color-coded.

**Figure 16.**Slices on range-elevation plane after elevation ambiguity resolution. From top to bottom: slice 1 to slice 5. From left to right: region growing and the proposed method. The red dot represents the seed.

**Figure 17.**Comparison of the 3D point clouds before and after the elevation ambiguity resolution. From top to bottom: slice 1 to slice 5. From left to right: the original point cloud, the real point cloud in radar coordinate system, and the real point cloud in geodetic coordinate system.

**Figure 18.**Slices of the real point cloud, the Elevation Position Result (EPR), the DSM data, and the DEM data. The left are the slices on range-elevation plane, and the right are the slices on ground-height plane.

**Figure 20.**Three-dimensional (3D) images of the Huangniba mountain area: (

**a**,

**b**) are the stereograph and the top view of AW3D30 DSM, respectively; (

**c**,

**d**) are the stereograph and the top view of our result, respectively.

**Figure 22.**Three-dimensional (3D) images under different viewing angles: (

**a**,

**b**) are the images under view([114,22]); (

**c**,

**d**) are the images under view([105,40]); (

**e**,

**f**) are the images under view([−115,58]). For view([az,el]), az and el are the azimuth and elevation angles of the line of sight in the geodetic coordinate system. The left images are produced by AW3D30 DSM data and Google Earth. The right images are obtained from array TomoSAR.

**Figure 23.**(

**a**,

**b**) The stereograph and the top view of the 3D reconstruction image with the absolute height error as the color map; (

**c**) the histogram of the absolute height error.

Parameter | Symbol | Value |
---|---|---|

Center frequency | ${f}_{c}$ | 10 GHz |

Bandwidth | ${B}_{w}$ | 500 MHz |

Maximum baseline length | B | 2 m |

Baseline interval | b | 0.2 m |

Horizontal inclination of baseline | $\beta $ | 0 deg |

Flight height | H | 3.5 km |

Central incidence angle | ${\theta}_{c}$ | 35 deg |

DBSCAN | TSAC | GMM | Proposed | |
---|---|---|---|---|

Purity | 0.76 | 0. 92 | 0.91 | 0.93 |

${N}_{c}$ | 3 | 10 | 8 | 6 |

np | pn | pp | Tpp | comp (%) | cor (%) | Q (%) | |
---|---|---|---|---|---|---|---|

Reg. | 78 | 292 | 6548 | 5310 | 90.14 | 77.63 | 65.11 |

Pro. | 78 | 292 | 6548 | 6461 | 97.51 | 94.46 | 92.23 |

Combination | Boundary Constraint | Continuity Constraint | |
---|---|---|---|

slice 1 | 8 | 2 | 1 |

slice 2 | 27 | 1 | 1 |

slice 3 | 64 | 8 | 1 |

slice 4 | 6561 | 6561 | 1 |

slice 5 | 729 | 729 | 1 |

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## Share and Cite

**MDPI and ACS Style**

Li, X.; Zhang, F.; Li, Y.; Guo, Q.; Wan, Y.; Bu, X.; Liu, Y.; Liang, X.
An Elevation Ambiguity Resolution Method Based on Segmentation and Reorganization of TomoSAR Point Cloud in 3D Mountain Reconstruction. *Remote Sens.* **2021**, *13*, 5118.
https://doi.org/10.3390/rs13245118

**AMA Style**

Li X, Zhang F, Li Y, Guo Q, Wan Y, Bu X, Liu Y, Liang X.
An Elevation Ambiguity Resolution Method Based on Segmentation and Reorganization of TomoSAR Point Cloud in 3D Mountain Reconstruction. *Remote Sensing*. 2021; 13(24):5118.
https://doi.org/10.3390/rs13245118

**Chicago/Turabian Style**

Li, Xiaowan, Fubo Zhang, Yanlei Li, Qichang Guo, Yangliang Wan, Xiangxi Bu, Yunlong Liu, and Xingdong Liang.
2021. "An Elevation Ambiguity Resolution Method Based on Segmentation and Reorganization of TomoSAR Point Cloud in 3D Mountain Reconstruction" *Remote Sensing* 13, no. 24: 5118.
https://doi.org/10.3390/rs13245118