DTD: Density Triangle Descriptor for 3D LiDAR Loop Closure Detection.

Loop closure detection is essential for improving the long-term consistency and robustness of simultaneous localization and mapping (SLAM) systems. Existing LiDAR-based loop closure approaches often rely on limited or partial geometric features, restricting their performance in complex environments. To address these limitations, this paper introduces a Density Triangle Descriptor (DTD). The proposed method first extracts keypoints from density images generated from LiDAR point clouds, and then constructs a triangle-based global descriptor that is invariant to rotation and translation, enabling robust structural representation. Furthermore, to enhance local discriminative ability, the neighborhood around each keypoint is modeled as a Gaussian distribution, and a local descriptor is derived from the entropy of its probability distribution. During loop closure detection, candidate matches are first retrieved via hash indexing of triangle edge lengths, followed by entropy-based local verification, and are finally refined by singular value decomposition for accurate pose estimation. Extensive experiments on multiple public datasets demonstrate that compared to STD, the proposed DTD improves the average F1 max score and EP by 18.30% and 20.08%, respectively, while achieving a 50.57% improvement in computational efficiency. Moreover, DTD generalizes well to solid-state LiDAR with non-repetitive scanning patterns, validating its robustness and applicability in complex environments.