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Traverse angle computations are a critical component of surveying, used to compute the internal angles within a closed traverse. A traverse consists of a series of connected lines forming a closed loop, often used for land boundary delineation or mapping. Calculating the internal angles ensures accuracy in the traverse geometry and is essential for checking survey data integrity.The process begins with known azimuths and bearings of the traverse sides. Internal angles at each vertex are...
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Calculating areas within irregular boundaries, such as along rivers or curved roads, is crucial in various fields, including surveying, engineering, and environmental management. Surveyors often begin by creating a traverse, a connected series of straight lines approximating the area's boundary. The coordinates of each traverse point are essential for calculating the enclosed area. The double meridian distance formula is a widely used technique for this purpose. This method utilizes the...
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DTD: Density Triangle Descriptor for 3D LiDAR Loop Closure Detection.

Kaiwei Tang1, Qing Wang1, Chao Yan1,2

  • 1School of Instrument Science and Engineering, Southeast University, Nanjing 210096, China.

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|January 10, 2026
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Summary
This summary is machine-generated.

This study introduces a novel Density Triangle Descriptor (DTD) for robust loop closure detection in simultaneous localization and mapping (SLAM). DTD significantly enhances accuracy and efficiency in complex environments, outperforming existing methods.

Keywords:
LiDAR SLAMdensity imageloop closure detectionpoint cloud descriptor

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Area of Science:

  • Robotics
  • Computer Vision
  • Artificial Intelligence

Background:

  • Simultaneous Localization and Mapping (SLAM) systems require loop closure detection for long-term consistency.
  • Existing LiDAR-based loop closure methods struggle with performance in complex environments due to reliance on limited geometric features.
  • A need exists for robust and efficient loop closure techniques in SLAM.

Purpose of the Study:

  • To introduce a novel loop closure detection method, the Density Triangle Descriptor (DTD).
  • To improve the robustness and accuracy of loop closure detection in SLAM systems.
  • To enhance computational efficiency compared to existing approaches.

Main Methods:

  • Extraction of keypoints from LiDAR-derived density images.
  • Construction of a rotation- and translation-invariant triangle-based global descriptor.
  • Modeling local neighborhoods with Gaussian distributions and deriving entropy-based local descriptors.
  • Utilizing hash indexing, entropy-based verification, and singular value decomposition for loop closure detection and pose estimation.

Main Results:

  • The proposed DTD significantly improves average F1 max score (18.30%) and EP (20.08%) compared to STD.
  • DTD achieves a 50.57% improvement in computational efficiency.
  • The method demonstrates robust performance on solid-state LiDAR with non-repetitive scanning patterns.

Conclusions:

  • The Density Triangle Descriptor (DTD) offers a robust and efficient solution for loop closure detection in SLAM.
  • DTD's invariance properties and entropy-based local descriptors enhance performance in complex environments.
  • The method shows broad applicability and generalization capabilities for various LiDAR systems.