Efficiently closing loops in LiDAR-based SLAM using point cloud density maps

2.1. Methods using 3D features from point clouds

Place recognition has been widely studied in the context of camera images (Cummins and Newman, 2008; Galvez-Lopez and Tardos, 2012; Mur-Artal et al., 2015; Vysotska and Stachniss, 2016, 2019). Consequently, much research on LiDAR place recognition for loop closing has been motivated by approaches in the camera vision domain. In particular, many approaches have extended the idea of local feature descriptors to 3D point clouds (Johnson and Hebert, 1999; Rusu et al., 2009; Salti et al., 2014), discretizing the neighborhood around 3D features into a geometrical grid. They compute a descriptor from the points in this neighborhood based on their height (Bosse and Zlot, 2013), density (Frome et al., 2004; Tombari et al., 2010), or distance and angle (Rusu et al., 2008). These local feature descriptor-based methods estimate a complete 3D relative pose between the loop closures. However, they have a high computational cost to identify such feature descriptors from 3D point clouds. They are sensitive to the radially increasing sparsity of point clouds obtained from a standard spinning LiDAR.

Several methods (Kim et al., 2024; Magnusson et al., 2009; Röhling et al., 2015; Uy and Lee, 2018) take an orthogonal approach by computing one global descriptor per LiDAR scan. Magnusson et al. (2009) superimpose a voxel grid on the point clouds and approximate a normal distribution over points in each grid cell. They compute a global descriptor for the point clouds by computing a histogram over these normal distributions. More recently, Kim et al. (2024) proposed a lightweight global descriptor with SOLiD by representing point clouds in polar coordinates and discretizing them into range-elevation and azimuth-elevation directions, respectively, with each discrete bin storing the number of points. Such global descriptors are easy to store in a simple database, resulting in a faster matching process to retrieve loop closure candidates. However, global descriptor-based methods typically require revisits within small error margins around the reference pose to limit the variation in the global descriptor. They often do not generalize when detecting loop closures across LiDARs with different scanning patterns and resolutions.

2.2. Two-dimensional projection-based methods

Many recent works focus on speeding up the recognition by describing 3D point clouds by a 2D projection (Kim and Kim, 2018; Li and Li, 2021; Luo et al., 2023; Xu et al., 2023; Yuan et al., 2024). Even though such a projection results in loss of geometric information, these methods perform comparably and sometimes even better than their full 3D counterparts, especially in outdoor scenes. Among the two-dimensional projection-based methods, the cylindrical projection into range images (Chen et al., 2020; Shan et al., 2021; Steder et al., 2010, 2011) and the orthogonal projection into BEV images (Kim et al., 2021; Lu et al., 2022; Luo et al., 2021; Wang et al., 2020; Yuan et al., 2023) are widely used 2D projections.

Range image projections are equivariant to azimuthal rotations due to the underlying cylindrical projection. They can recover the relative yaw between loop closures but suffer from scale distortions due to lateral shifts in the LiDAR viewpoint. On the other hand, BEV projections preserve 2D geometry along the local ground plane, which is vital for autonomous ground robots. Among the BEV projection methods, the elevation map is widely used (Kim et al., 2021; Kim and Kim, 2018; Luo et al., 2023; Yuan et al., 2023). An elevation map preserves the maximum elevation within each discrete pillar in the BEV representation.

Scan Context by Kim and Kim (2018) is a popular LiDAR-based loop closure approach. It computes a global descriptor for each LiDAR scan using the elevation map in polar coordinates. The polar coordinates make the descriptor equivariant to in-plane rotations, thereby allowing the loop closure alignment module to estimate the relative yaw between LiDAR scans from the same location. However, the polar coordinate representation can be sensitive to in-plane translations. Scan Context++ (Kim et al., 2021) improves upon this drawback of Scan Context and computes elevation maps in Cartesian coordinates to augment the polar elevation maps. However, preserving the maximum elevation of the points after the BEV projection makes the two approaches sensitive to the vertical resolution and FoV of the LiDAR.

In contrast, BVMatch (Luo et al., 2021) proposes a density-preserving BEV projection of point clouds and a Log Gabor filtering step. It requires training a bag-of-words model to retrieve loop closure candidates, making it less suitable for real-time applications such as SLAM. Our approach also uses a density-preserving BEV projection. It generates a database of local feature descriptors from the BEV image online using the HBST data structure (Schlegel and Grisetti, 2018) for efficient operation. The use of local feature descriptors for loop closure detection has also been previously explored in the 2D LiDAR domain with traditional occupancy grid maps (Blanco et al., 2013).

Yuan et al. (2023) propose utilizing a set of geometric primitives, that is, triangles with unique side lengths, to describe a point cloud. They obtain the feature vertices of such triangles by a local BEV projection of points within voxels that lie at the boundaries of large planar regions in the environment. BTC (Yuan et al., 2024) improves upon this work by proposing a binary descriptor for a detailed representation of local geometry. They combine the triangle descriptors and the newly proposed binary descriptors to perform loop closure retrieval. The works by Yuan et al. (2023, 2024) use a local map representation of the environment by accumulating a fixed number of consecutive scans. This helps them tackle the sparsity issue present with rotating 3D LiDAR. The local maps also make their approach generalizable to LiDAR sensors with non-repetitive scanning patterns and small FoVs. We also use a local map representation to detect loop closures. However, unlike STD and BTC, we accumulate scans until a minimum displacement of the platform to ensure that the local maps capture a sufficient portion of the scene.

2.3. Learning-based approaches

The recent popularity of deep neural networks, attributed to the widespread availability of specialized hardware and software to train such networks, has generated much interest from a LiDAR-based loop closing perspective (Chen et al., 2020; Dubé et al., 2018; Komorowski, 2021; Ma et al., 2022; Ma et al. 2024). PointNet (Qi et al., 2017b) and PointNet++ (Qi et al., 2017a) use multi-layer perceptron networks to detect local feature descriptors from point clouds. PointNetVLAD (Uy and Lee, 2018) proposes an end-to-end trained neural network that combines the local feature descriptors obtained from PointNet into a global descriptor using NetVLAD (Arandjelovic et al., 2016). SegMap (Dubé et al., 2018) segments point clouds using a region-growing algorithm and computes data-driven descriptors of these segments to detect loop closures.

BEV projections are also popular with learning-based approaches (Kim et al., 2019; Luo et al., 2023, 2025; Xu et al., 2021b). Kim et al. (2019) repurpose the Scan Context (Kim and Kim, 2018) image as a three-channel image using a jet colormap over a range of structural heights. They train a convolutional neural network using these Scan Context images and perform localization as a classification task. Xu et al. (2021b) propose an encoder-decoder network to extract descriptors from differentiable Scan Context images.

Vidanapathirana et al. (2022) use a global descriptor obtained from a sparse convolutional neural network to perform loop closures. They propose a local-consistency loss to train their approach to obtain consistent local features across revisits, which they later combine into a global descriptor using a pooling and normalization strategy.

BEVPlace (Luo et al., 2023) applies group convolutions corresponding to the S O ( 2 ) rotational group to obtain rotation equivariant local features on BEV density images and computes a global descriptor for place retrieval using NetVLAD. BEVPlace++ (Luo et al., 2025) improves upon BEVPlace by proposing a novel rotation equivariant module, which passes rotation-warped BEV density images through a convolutional neural network to extract the local features.

Recently, Ramezani et al. (2024) proposed a place recognition method based on an attentional graph neural network representation. Their approach leverages the topological relationships between consecutive LiDAR scans within a pose-graph SLAM system by generating sub-graphs according to a travel distance criterion. They use a multi-layer perceptron to encode the odometry poses and global descriptor associated with every scan within each of the sub-graphs. For a candidate pair of sub-graphs, they construct a fully connected multiplex graph from the encoded nodes and process it through an attentional graph neural network, P-GAT, to perform place recognition.

Even though learning-based approaches achieve impressive performance regarding loop closure precision and recall metrics, they typically require a computationally expensive offline pre-training step on a GPU, affecting their application to real-time loop closure detection in SLAM.

Our method also exploits the spatio-temporal information across consecutive LiDAR scans by constructing local maps as the primary representation for loop closure detection, rather than relying on individual scans. Following our earlier work (Gupta et al., 2024), we generate local maps based on a travel displacement criteria, in contrast to Yuan et al. (2023, 2024), who accumulate a fixed number of scans. This strategy helps us overcome the sparsity of rotating LiDAR and make our method agnostic to the LiDAR sensor’s scanning pattern, FoV, and resolution. We use a density-preserving BEV projection of the local maps on the local ground plane to reduce dimensionality for computational efficiency. Subsequently, we compute ORB feature descriptors (Rublee et al., 2011) from the BEV density images and store them in an HBST database (Schlegel and Grisetti, 2018) for place recognition. We mitigate the negative impact of perceptual aliasing on our feature descriptor-matching algorithm by performing a self-similarity pruning of the ORB feature descriptors (Bosse et al., 2004). Our loop closure pipeline provides a complete 3D global alignment between the local maps.

3.1. Creation of local maps

Our approach uses local point cloud maps of the environment to perform loop closures. By aggregating downsampled LiDAR scans over time, we exploit the local consistency of sequential odometry estimates to generate these local maps. We use KISS-ICP (Vizzo et al., 2023) to obtain LiDAR odometry for our pipeline.

Given an online stream of sequential point clouds { P 1 , … , P n } in the LiDAR frame and their corresponding 3D pose estimates { T 1 w , … , T n w } in the odometry frame w, we first transform the point clouds into the odometry frame, resulting in point clouds { P 1 w , … , P n w } .

Starting from a point cloud with index i, we consider k subsequent scans until the displacement ‖ t i + k - 1 - t i w w ‖ 2 exceeds a threshold τ c , where t i w ∈ ℝ 3 is the translational component of the pose estimate T i w ∈ S E ( 3 ) . Once we reach the displacement threshold τ c , we aggregate this subset of scans { P i w , … , P i + k − 1 w } into a local map M m w where m is the local map index. Specifically, we use a voxel grid-based downsampling strategy to generate the local map, using a resolution of ν_map meters per voxel. Such a downsampling strategy also ensures a uniform spatial distribution of scanned points by retaining at most 20 points per voxel. We repeat this process of local map generation sequentially, thereby generating mutually exclusive sets of consecutive point clouds, as shown in Figure 2.OPEN IN VIEWER

We transform each local map M m w into the local reference frame T i w of the first scan in the sub-sequence as follows:

M m = T i w − 1 M m w .

(1)

Aggregating consecutive LiDAR scans into local maps provides richer structural information than individual scans, as illustrated in Figure 3. This larger spatial context is particularly beneficial in multi-session scenarios, where local environmental changes may otherwise hinder place recognition. Furthermore, local maps generated at the same location exhibit higher similarity across different LiDAR resolutions and scanning patterns, whereas inter-LiDAR place recognition with individual scans remains a challenging data association problem, even for humans, as illustrated in Figure 3. As a result, the use of local maps improves robustness for multi-session and cross-platform loop closure detection.OPEN IN VIEWER

3.2. Ground plane detection and alignment

After generating the point cloud local map M m , we perform a BEV projection. To ensure consistency across multiple revisits, we must project the point cloud onto a consistent physical plane in the environment. The ground plane provides a natural choice for this plane and enables the computation of a stable basis for the BEV projection. In our earlier work (Gupta et al., 2024), we assumed planar sensor motion so that the ground plane remained parallel to the xy-plane of the local map’s reference frame. However, when the LiDAR follows a non-planar trajectory, the local ground plane tilts relative to the xy-plane, as shown in Figure 4. To address this, we explicitly identify the ground plane and align it with the xy-plane of the reference frame.OPEN IN VIEWER

The first step identifies candidate ground points in the local map. Semantic segmentation networks can label ground in point clouds (Paigwar et al., 2020; Xu et al., 2021a), but they require offline GPU training and add significant computational costs. Real-time CPU-based methods such as Patchwork (Lim et al., 2021) and Patchwork++ (Lee et al., 2022) operate on individual scans, so they require per-scan segmentation and careful parameter tuning. In contrast, our BEV projection requires only one approximate estimate of the local ground plane to align the entire local map at once, not a precise segmentation for every scan.

We adopt a simple sampling strategy: in a 3D LiDAR local map, the lowest-elevation points usually correspond to the ground (Hu et al., 2014). This assumption generally holds for typical outdoor sensing platforms with known extrinsics, where the ground plane lies within the LiDAR’s field of view. It also remains valid when the local map’s xy-plane is not perfectly aligned with the ground plane, since a LiDAR cannot scan below the ground surface.

We divide the local map M m into a 2D grid over the xy-plane with 1.0 m cells. In each cell, we retain only the point with the minimum z-coordinate, yielding a sparse set of candidate ground points, as shown in Figure 4. This set may still contain non-ground points where the ground is occluded or where the xy-plane is misaligned with the ground plane. To filter these, we run principal component analysis (PCA) on the normal vectors associated with the sampled points and retain only samples whose normals have a cosine similarity larger than 0.95 with the first principal component. This step removes most non-ground points and yields the ground sample set G m . The first principal component also provides a strong initial estimate of the ground orientation.

We convert this PCA estimate into an initial transform T init ∈ S E ( 3 ) for ground alignment. Specifically, we compute an axis–angle rotation that aligns the first principal component with the z-axis of the local map frame:

a = υ pc × 0 0 1 T ,

(2)

θ = arccos υ pc ⋅ 0 0 1 T ,

(3)

z init = r 2 ⋅ g ¯ m ,

(4)

To make the ground alignment robust to outliers, we refine T init with a least-squares optimization:

T m g = argmin T init ∑ ∀ g k ∈ G m w k n ^ x y ⋅ ( T init g k ) 2 ,

(5)

We compute the Jacobian J of the residual term n ^ x y ⋅ ( T init g k ) in equation (5) with respect to a perturbation Δ x = Δ t T Δ ω T T around T init on the S E ( 3 ) manifold:

J = 0 0 1 x k ′ − y k ′ 0 .

(6)

The Jacobian indicates that the optimization only updates the z-axis translation and the roll (x-axis) and pitch (y-axis), which directly correct the ground alignment.

Finally, we apply the ground-aligning transform T m g to the local map M m to obtain the aligned local map M m g whose ground plane lies on the xy-plane. The alignment step increases robustness to non-planar LiDAR motion profiles, particularly for handheld platforms. It establishes the ground plane as a robust reference plane for BEV projections during long-term revisits, since the ground surface typically remains consistent over time. We show an example of this alignment in Figure 4 and provide a detailed analysis in Section 5.3.

3.3. Density-preserving bird’s-eye-view projection

After establishing the primary representation of the environment in Sections 3.1 and 3.2, the next step is to extract informative yet distinct local feature descriptors to perform place recognition for loop closures. Rather than computing features directly on the 3D point clouds of local maps, which is computationally expensive given the spatial extent of such point clouds, we use a 2D BEV projection of the local maps as an intermediate representation for loop closure detection.

We perform the BEV projection by simply dropping the z-coordinate of all the individual points in the ground-aligned local maps M m g . Furthermore, we discretize the R 2 projection space with a resolution of ν_b meters. This results in a 2D Cartesian grid N m ( u , v ) of size W _m × H _m , where

W m = ⌊ x m u ν b ⌋ − ⌊ x m l ν b ⌋ + 1 ,

(7)

H m = ⌊ y m u ν b ⌋ − ⌊ y m l ν b ⌋ + 1 ,

(8)

x m u y m u = max x , y M m g ; x m l y m l = min x , y M m g .

(9)

However, the dimensionality reduction comes at the cost of losing the complete 3D information about the scene. Many traditional BEV projection approaches store the maximum elevation of the points in each cell (Kim et al., 2021; Kim and Kim, 2018; Li and Li, 2021; Luo et al., 2022). The maximum elevation, however, is sensitive to the distance between the scanner and the surface being scanned, as well as the LiDAR sensor’s FoV. In our pipeline, we instead store the point density in each discrete 2D cell after the projection, which is less sensitive to viewpoint changes (Luo et al., 2021).

Therefore, each cell in this grid N m ( u , v ) ∈ ℕ 0 stores the count of projected points within that cell. The BEV image I m ( u , v ) of the local map M m g is then defined as the relative point density in each cell of the grid as follows:

I m ( u , v ) = N m ( u , v ) − N min N max − N min ∈ ℝ W m × H m ,

(10)

N max = max N m ( u , v ) ; N min = min N m ( u , v ) .

(11)

To mitigate the undesired influence of dynamic objects that accumulate during local map generation, we explicitly set all image pixels N m ( u , v ) with a relative density lower than 5% to zero. This choice reflects the fact that most dynamic objects commonly found in urban environments, such as vehicles, pedestrians, and cyclists, have small vertical footprints and therefore produce low-density values.

3.4. Feature detection and pruning strategy

The BEV projection reduces the dimensionality of the local map, making feature detection for place recognition computationally efficient. The image-like BEV density representation enables us to apply well-established computer vision techniques to extract distinctive feature descriptors. Since these BEV density images preserve the geometrical, floorplan-like structure of the environment, we use ORB (Rublee et al., 2011) feature descriptors to capture relevant features. Unlike camera images, BEV images generated via orthographic projection have no scale ambiguity. We take advantage of this property by computing the ORB feature descriptors D m without applying scale-invariance adjustments, further improving computational efficiency.

Figure 5 shows an example of ORB features extracted from a BEV density image. We observe that most ORB features concentrate around high-density regions with strong gradients. These strong responses typically arise from static structures with large vertical footprints, such as building facades, trees, and light poles. In contrast, low-density regions, often corresponding to small bushes, vegetation, or dynamic objects that occasionally pass through the low-density filter, contribute few ORB features to the database. This leads to a robust behavior of our algorithm as it is not adversely affected by dynamic objects in the environment.OPEN IN VIEWER

ORB feature descriptors remain salient within a local neighborhood of the density image, but not necessarily across the entire image. As a result, environments with repetitive structures can generate self-similar feature descriptors that can confuse the feature-matching stage and cause false positives.

To improve robustness against perceptual aliasing, we prune the ORB feature descriptors within each density image using a self-similarity check inspired by Bosse et al. (2004). Specifically, we compute the nearest-neighbor match for each ORB feature descriptor based on the Hamming distance and discard any feature whose closest match lies below a threshold of τ _pr = 35 bits. This procedure eliminates self-similar feature descriptors within the same density image. This approach resembles Lowe’s ratio test (Lowe, 2004), but we apply it intra-image rather than inter-image, which avoids the cost of finding second-best matches across a larger feature descriptor database.

This pruning step filters out features from repetitive structures in the environment, such as repeating trusses on a bridge, as shown in Figure 6. This helps reduce false-positive feature matches across density images resulting from perceptual aliasing, thereby lowering the risk of incorrect loop closure detections. We present a detailed analysis of this pruning strategy and its impact on loop closure detection in Section 5.4.OPEN IN VIEWER

3.5. Feature database

Once we have the unique features within a BEV density image, we create a database to serve as a reference for place recognition. We leverage the binary domain of the ORB descriptors, using the Hamming distance embedding binary search tree (HBST) (Schlegel and Grisetti, 2018) to store the set of feature descriptors D m obtained from each density image I m , along with their corresponding map index m.

The depth of the HBST is limited by the number of bits in the binary descriptor. As a result, a query descriptor will require at most 256 bitwise comparisons with the tree’s nodes before reaching a leaf node. Each leaf node can hold a maximum of 100 descriptors, ensuring efficient feature matching. These design choices constrain the computational time for feature matching without imposing practical limitations on the usability of our approach. Unlike a clustering-based bag of words or a neural representation-based database, we use the HBST as an incrementally updated database, requiring no offline pre-training.

After obtaining a set of descriptors D m from the query local map’s BEV density image I m , we search the HBST database to find the closest match for each descriptor d j , m ∈ D m . Matches are determined using a Hamming distance threshold of 50 bits between ORB descriptors. Since the binary tree links each stored descriptor to an index m corresponding to its local map, we compile a list of feature matches between the query local map and the reference local maps in the database. These matches are subsequently verified geometrically. Figure 7 visualizes the corresponding set of feature matches between two density images, as obtained from the HBST database.OPEN IN VIEWER

3.6. Loop detection and map alignment

The geometric validation step entails performing a 2D alignment of the matched ORB features. This involves computing a 2D rigid-body transformation that optimally aligns the matched features from the binary search tree using a distance metric. Unlike the general image-alignment problem, this process is constrained to an S E ( 2 ) transformation rather than a homography. To handle outlier associations caused by the limitations of binary tree-based matching, we employ a RANSAC-based alignment strategy.

We design a RANSAC-based approach that randomly selects two feature pairs from the set of matches between a query ( I m ) and a reference ( I r ) density image. We use the Kabsch-Umeyama algorithm (Kabsch, 1976; Umeyama, 1991) to compute the relative 2D alignment between the feature pairs. We use this alignment to compute the point-wise Euclidean distance between each pair of feature matches. Feature matches with distances larger than 1.5 m (3 pixels for ν_b = 0.5 m) are considered outliers. The RANSAC process runs for a fixed number of iterations N_ransac. We require a minimum number of inliers γ from the RANSAC alignment stage to decide whether two local maps belong to the same location.

Finally, after the N_ransac iterations, we compute a Kabsch-Umeyama 2D alignment over the entire set of inlier correspondences. It provides us with a rotation matrix R ∈ S O ( 2 ) and a translation vector t ∈ R 2 , which we represent as a homogenous transformation T BEV ∈ S E ( 3 ) , having translation components only along the xy-plane, and a rotation component only about the z-axis. We scale the translation vector by the voxel size (ν_b) since the features are computed from the discretized density images.

Although T BEV only aligns the ground-aligned local maps, we can recover the complete S E ( 3 ) pose to align the original local maps by composing T BEV with the ground-aligning transforms of the individual local maps, as shown in equation (12).

T r m = T m − 1 g T BEV T r g .

(12)

This 3D alignment serves as an initial estimate for a fine-grained registration of local maps during typical pose-graph optimization in a SLAM pipeline. A qualitative example demonstrating the effectiveness of this initial alignment is illustrated in Figure 8. Notably, one of the local maps (in blue) in this visualization contains a large trace from a dynamic object (highlighted by the green ellipse), showing that our pipeline can also detect and align loop closures even in the presence of such strong dynamics.OPEN IN VIEWER

4.1. Datasets

We conduct a comprehensive evaluation of our approach on datasets collected using a variety of LiDAR sensors with different resolutions and scanning patterns. These datasets include multiple sequences recorded in diverse urban environments across various mobile platforms.

4.2. Baseline methods used for comparison

We compare our approach against seven baseline methods, all of which provide publicly available implementations that we use for evaluation. To ensure a fair comparison, we modify their source code only to return multiple loop closure candidates per query scan rather than just the top-ranked one. Unless stated otherwise, we retain the default parameter settings in each baseline’s implementation.

4.3. Reference loop closures between local maps

Since our method computes loop closures between local maps, we also define reference loop closures at the map level for evaluation. In contrast to prior works (Jiang and Shen, 2023; Kim et al., 2021, kim et al. 2024; Kim and Kim, 2018; Yuan et al., 2023), which typically rely on simple distance-based criteria, such heuristics are insufficient in our setting. The distance-based criterion breaks down in scenarios where other objects occlude the previously seen area, the sensor has a limited FoV, or the revisits are from a significantly different viewpoint. Additionally, there is inherent ambiguity in selecting the appropriate reference frame for measuring distances between local maps.

To overcome these limitations, we define reference loop closures based on the volumetric overlap of local maps, similar to Gupta et al. (2024) and Yuan et al. (2024). We generate reference local maps using the ground-truth pose information provided by the respective datasets. We ensure that each reference local map contains the same set of scans as the corresponding local maps produced by our method. We then identify reference loop closures by selecting all pairs of local maps that exhibit more than 25% voxel-level overlap. To avoid trivial short-range closures, we skip the three consecutive local maps preceding the query local map.

We adopt the same volumetric overlap strategy for cross-sequence evaluation, but reduce the overlap threshold to 10% to accommodate potential misalignments in the global pose information between sequences.

4.4. Scan-level to map-level conversion of loop closures for baselines

The baseline methods in our evaluation operate at different scales; some detect loop closures at the individual scan level (Scan Context and SOLiD), while others work on local maps with a fixed number of scans (STD and BTC). As a result, we cannot directly evaluate them using the reference loop closures defined between local maps generated based on a travel displacement criterion. Therefore, we convert their outputs into equivalent map-level loop closures.

For scan-level approaches, we treat a loop closure between scans P i and P j as a loop closure between local maps M k and M l , where scan P i belongs to map M k and scan P j belongs to map M l .

For methods such as STD and BTC, which use smaller local maps, we first extract all scan pairs between these local maps, S m and S n , that form a loop closure. We treat each scan pair as an individual scan-level loop closure and convert it into a corresponding map-level loop closure using the same method described above.

4.5. Evaluation metrics

5.1. Intra-session loop closure detection

In this experiment, we evaluate the performance of our approach on intra-session loop closure detection. We compare against several state-of-the-art baselines by converting their detected closures to local map-level closures, as described in Section 4.4. In addition, we include a comparison with our previous conference publication, MapClosure (Gupta et al., 2024), which forms the foundation of this work. We also evaluate the local map-based baselines STD and BTC using the same 100 m travel displacement-based local maps as in our approach, referred to as STD-100 and BTC-100. However, we do not evaluate the scan-based baselines using similar local maps since scan-based methods like Scan Context and SOLiD depend on a single scan center as the reference frame, which local maps inherently lack. Handling large lateral shifts would require sampling many artificial scan centers, changing the methods’ intended use.

The quantitative results in Tables 1 and 2 show the effectiveness of our approach across multiple public and in-house datasets. Our method achieves the highest average precision in 15 of the 24 sequences and ranks second in eight of the remaining nine. In terms of recall, it achieves the best performance at 100% precision in 15 sequences and the second-best in nine others. This balance between precision and recall is also reflected in the F1 scores, where our method ranks first in 18 sequences and second in six others.

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Table 1.

Average precision (AP), maximum recall at 100% precision (R@1), and maximum F1 scores (F1 _m ) of state-of-the-art baselines and our approach for intra-session loop closure detection. Larger values indicate better performance. The best values are in bold, and the second-best values are in italics. The R@1 field is marked with “-” when the baseline cannot achieve a 100% precision upon varying its corresponding thresholding parameter.

(a) HeLiPR dataset → Ouster OS2-128
Datasets	Bridge01			Bridge02			Roundabout01			Town02			Town03
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.344	0.049	0.460	0.300	-	0.469	0.316	0.200	0.420	0.293	0.059	0.421	0.373	0.037	0.538
STD-100	0.006	-	0.048	0.024	-	0.121	0.008	0.005	0.078	0.005	0.008	0.076	0.017	-	0.133
BTC	0.733	0.005	0.730	0.644	0.009	0.719	0.627	0.220	0.689	0.651	0.034	0.703	0.584	0.022	0.678
BTC-100	0.029	-	0.171	0.247	-	0.393	0.446	0.031	0.566	0.098	-	0.286	0.013	-	0.135
SOLiD	0.136	0.079	0.211	0.181	0.009	0.226	0.072	0.015	0.121	0.098	0.008	0.167	0.106	-	0.167
LoGG3D	0.125	0.007	0.199	0.127	0.014	0.188	0.077	-	0.162	0.065	-	0.128	0.059	-	0.112
BEVPlace++	0.347	0.025	0.445	0.273	0.009	0.423	0.167	0.020	0.227	0.211	0.068	0.263	0.168	-	0.262
SC	0.186	-	0.489	0.166	-	0.558	0.217	0.144	0.412	0.151	-	0.382	0.104	-	0.351
MapClosure	0.662	0.219	0.720	0.752	0.470	0.781	0.731	0.472	0.788	0.568	0.119	0.690	0.694	0.343	0.743
Ours	0.688	0.332	0.794	0.685	0.614	0.797	0.892	0.508	0.890	0.607	0.424	0.750	0.711	0.388	0.749

(b) HeLiPR dataset → Aeva Aeries II
Datasets	Bridge01			Bridge02			Roundabout01			Town02			Town03
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.191	-	0.376	0.170	0.005	0.340	0.087	-	0.252	0.082	0.055	0.177	0.242	0.010	0.369
STD-100	0.012	-	0.080	0.056	0.005	0.168	0.021	0.009	0.082	0.000	-	0.058	0.032	-	0.113
BTC	0.609	0.076	0.722	0.511	0.010	0.679	0.377	0.176	0.483	0.259	-	0.429	0.371	0.020	0.494
BTC-100	0.033	-	0.192	0.201	-	0.392	0.157	-	0.367	0.029	-	0.150	0.033	-	0.180
SOLiD	0.378	0.166	0.451	0.156	-	0.404	0.211	0.148	0.277	0.068	0.027	0.171	0.235	-	0.338
LoGG3D	0.041	0.003	0.103	0.063	0.010	0.162	0.038	-	0.083	0.030	-	0.071	0.058	0.020	0.106
BEVPlace++	0.265	-	0.414	0.240	0.005	0.417	0.082	0.018	0.139	0.035	-	0.098	0.121	-	0.168
MapClosure	0.814	0.488	0.818	0.834	0.493	0.785	0.478	0.139	0.607	0.196	0.192	0.356	0.465	0.202	0.584
Ours	0.711	0.424	0.796	0.683	0.488	0.765	0.584	0.259	0.654	0.206	0.110	0.358	0.543	0.172	0.642

(c) HeLiPR dataset → Livox Avia
Datasets	Bridge01			Bridge02			Roundabout01			Town02			Town03
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.056	-	0.167	0.073	0.005	0.178	0.104	0.024	0.208	0.062	0.035	0.171	0.290	0.111	0.357
STD-100	0.002	-	0.025	0.013	0.010	0.065	0.015	0.012	0.056	0.000	-	0.028	0.032	-	0.107
BTC	0.111	0.040	0.293	0.211	-	0.476	0.241	0.146	0.394	0.133	0.035	0.330	0.346	0.022	0.500
BTC-100	0.011	-	0.098	0.105	-	0.288	0.050	0.037	0.175	0.000	0.018	0.034	0.010	0.022	0.079
SOLiD	0.365	0.052	0.455	0.400	0.038	0.462	0.223	0.024	0.346	0.064	-	0.098	0.212	-	0.358
LoGG3D	0.013	-	0.045	0.020	-	0.057	0.026	0.012	0.059	0.023	0.018	0.053	0.036	-	0.084
BEVPlace++	0.205	-	0.302	0.200	0.014	0.321	0.052	-	0.112	0.030	-	0.092	0.078	-	0.144
MapClosure	0.512	0.222	0.609	0.562	0.229	0.605	0.133	0.073	0.252	0.102	0.105	0.265	0.431	0.367	0.576
Ours	0.549	0.150	0.698	0.543	0.300	0.688	0.278	0.158	0.442	0.141	0.088	0.269	0.464	0.267	0.587

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Table 2.

Average precision (AP), maximum recall at 100% precision (R@1), and maximum F1 scores (F1 _m ) of state-of-the-art baselines and our approach for intra-session loop closure detection. Larger values indicate better performance. The best values are in bold, and the second-best values are in italics. The R@1 field is marked with “-” when the baseline cannot achieve a 100% precision upon varying its corresponding thresholding parameter.

(a) MulRan dataset → Ouster OS1-64
Datasets	KAIST01			KAIST02			Riverside01			Riverside02			Sejong01
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.545	0.030	0.655	0.462	0.258	0.640	0.329	-	0.488	0.443	0.067	0.619	0.016	-	0.143
STD-100	0.097	0.007	0.262	0.080	-	0.232	0.203	0.104	0.318	0.103	0.045	0.202	0.000	0.000	0.000
BTC	0.680	0.007	0.756	0.605	0.103	0.736	0.916	0.865	0.927	0.645	-	0.854	0.289	0.364	0.909
BTC-100	0.293	0.007	0.502	0.224	0.010	0.447	0.615	0.292	0.706	0.456	0.214	0.609	0.000	0.000	0.000
SOLiD	0.356	0.104	0.462	0.457	0.433	0.604	0.505	0.271	0.582	0.471	0.326	0.558	0.010	-	0.133
LoGG3D	0.246	0.022	0.362	0.290	-	0.353	0.337	0.021	0.412	0.225	0.022	0.319	0.001	-	0.018
BEVPlace++	0.387	0.111	0.421	0.418	0.237	0.464	0.490	0.062	0.556	0.428	0.168	0.451	0.195	0.091	0.444
SC	0.176	-	0.550	0.169	0.402	0.636	0.240	0.417	0.684	0.190	0.404	0.587	0.162	0.182	0.424
MapClosure	0.671	0.437	0.777	0.790	0.505	0.828	0.902	0.885	0.946	0.831	0.708	0.876	0.083	0.182	0.421
Ours	0.733	0.400	0.838	0.852	0.588	0.876	0.885	0.896	0.945	0.843	0.629	0.877	0.364	0.546	0.706

(b) NCLT dataset → Velodyne HDL-32E; IPB-Car dataset → Ouster OS1-128; IPB-Backpack dataset → Hesai Pandar-128
Datasets	NCLT 2012-01-08			NCLT 2013-04-05			IPB-car			IPB-backpack
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.429	0.286	0.621	0.219	0.417	0.588	0.219	0.068	0.344	0.261	0.139	0.323
STD-100	0.000	0.018	0.035	0.000	0.000	0.000	0.013	0.016	0.042	0.000	-	0.053
BTC	0.333	-	0.654	0.104	0.083	0.333	0.470	0.036	0.607	0.302	0.236	0.383
BTC-100	0.319	-	0.544	0.000	0.083	0.154	0.331	0.112	0.448	0.000	0.083	0.154
SOLiD	0.092	0.018	0.153	0.092	0.018	0.153	0.078	0.012	0.120	0.216	0.014	0.365
LoGG3D	0.070	-	0.161	0.019	-	0.060	0.014	-	0.045	0.215	-	0.355
BEVPlace++	0.154	-	0.274	0.101	0.167	0.286	0.196	0.028	0.297	0.370	0.125	0.398
SC	0.144	-	0.495	0.031	-	0.444	0.168	-	0.426	0.253	0.083	0.358
MapClosure	0.321	0.089	0.500	0.307	-	0.571	0.899	0.272	0.906	0.169	0.181	0.306
Ours	0.703	0.321	0.796	0.506	0.500	0.727	0.929	0.404	0.909	0.361	0.361	0.540

Our method provides a robust solution for loop closure detection within a SLAM pipeline, where false positives must be minimized (Bailey and Durrant-Whyte, 2006; Blanco et al., 2013; Lowry et al., 2016). The precision-recall curves in Figure 9 show that our approach (red) consistently outperforms baselines across datasets with varied sensor setups. It maintains high precision over a broad range of recall values, eliminating the need for careful tuning of the inlier threshold in RANSAC or additional outlier rejection schemes in the pose-graph optimization.OPEN IN VIEWER

The evaluations on the HeLiPR dataset demonstrate the versatility of our method across different LiDAR sensors in varied urban environments. Our method consistently ranks among the top two methods across all metrics. In several sequences, our current approach ranks second only to MapClosure. However, the precision-recall curves in Figure 9 reveal a key advantage: our method maintains a higher precision than MapClosure, ensuring that detected loop closures remain accurate.

The HeLiPR Bridge sequences, which exhibit strong perceptual aliasing, highlight the effectiveness of our pruning strategy. While overall metrics in Table 1 may appear comparable between our method and MapClosure, our precision-recall curves in the first row of Figure 9 terminate earlier at a higher precision value than MapClosure, which also holds in comparison to other baselines. This behavior reflects our deliberate choice to prioritize precision over recall in perceptually ambiguous scenes. By doing so, we improve robustness, reduce sensitivity to the inliers threshold (γ), and lower the risk of false loop closures. The Town sequences present additional challenges with narrow alleyways, wide boulevards, and numerous dynamic objects such as pedestrians and cars. Even under these conditions, our approach ranks among the top two methods, showing its resilience in complex urban environments.

Additionally, the results on HeLiPR Bridge sequences provide insight into how the baselines perform under different levels of dynamic activity in the scene. The Bridge01 sequence, recorded at night, contains relatively few dynamic objects, whereas Bridge02, recorded during the day, includes substantially more dynamic participants. Since both sequences capture the same driving environment, we can directly compare their results to assess how dynamic objects affect loop closure detection. Our method performs consistently in terms of average precision and F1 score, highlighting its robustness to such dynamic elements. As expected, scan-based methods also show little to no variation in the metrics across these sequences, since individual scans are not significantly affected by dynamic objects due to the short temporal window of a single LiDAR scan.

The ground alignment strategy introduced in Section 3.2 further strengthens performance on datasets with non-planar LiDAR motion, such as the NCLT dataset and our self-recorded IPB-Backpack sequence. As shown in Table 2, our method outperforms Scan Context, BEVPlace++, and MapClosure, which assume planar motion for the BEV projection. We achieve the best values across all three metrics, except for average precision on the IPB-Backpack dataset, where the performance gap to BEVPlace++ remains marginal. Consistent BEV projection onto the local ground plane during revisits, even under varying pitch and roll, drives this performance. On the IPB-Car dataset, recorded in hilly terrain with vegetation and elevation changes, our method achieves almost 100% average precision, with a near-perfect precision-recall curve, confirming its robustness to complex ground plane variations.

The results also confirm the importance of local maps for extracting meaningful structural information for place recognition and loop closure detection. Among the baselines, only STD, BTC, and MapClosure perform competitively, and all rely on local maps. Nonetheless, our evaluation of STD and BTC with the same local maps as our pipeline, referred to as STD-100 and BTC-100, shows that our method’s advantage does not stem solely from larger local map sizes, but from the full algorithmic design.

In contrast, scan-based global descriptor approaches such as Scan Context and SOLiD fail to achieve consistent performance. Scan Context, designed for rotating LiDAR sensors, performs poorly in the HeLiPR Ouster OS2-128 and MulRan sequences due to its strong dependence on viewpoint. SOLiD, designed to handle LiDARs with different FoVs, performs better on the HeLiPR Aeva Aeries II and Livox Avia sequences but still falls short of local map-based methods. These trends highlight the inherent difficulty in constructing global descriptors for single LiDAR scans.

The weak performance of LoGG3D further illustrates this limitation. Without spatio-temporal aggregation or dimensionality reduction, LoGG3D remains highly sensitive to the point density within each scan. Trained exclusively on sequences from the MulRan dataset with Ouster OS1-64, it performs well only on that dataset and generalizes poorly elsewhere. It fails to reach 100% precision even at low recall values in most sequences, underscoring the need to retrain such methods for each sensor setup.

BEVPlace++, also a learning-based method, performs more robustly than LoGG3D does due to its density-preserving BEV projection. However, it struggles on NCLT and IPB-Backpack sequences because of its assumption of planar motion for BEV projection.

Overall, these experiments confirm our core claim: our method delivers state-of-the-art performance in intra-session loop closure detection across datasets and LiDAR platforms. By leveraging local maps as the core representation, our pipeline balances precision and recall, remains robust under perceptual aliasing, adapts to non-planar motion, and generalizes across different sensor characteristics, all without requiring changes to the pipeline parameters.

5.2. Inter-session and inter-LiDAR loop closure detection

In this experiment, we evaluate the performance of our approach for inter-session and inter-LiDAR loop closure detection and compare it against state-of-the-art baselines introduced in Section 4.2. We select sequences spanning revisit intervals from a few weeks to several years to test the robustness under diverse temporal conditions.

Our pipeline architecture remains fundamentally the same in this scenario, with only minor modifications. We store the ground alignment transformations for each local map together with the HBST database from the reference sessions. For a given query session, we match the ORB features against the reference database without adding any features from the query session to the database. Then, using the ground alignment transforms of the corresponding local map from the reference session and the query local map, we compute a complete S E ( 3 ) pose estimate to align the loop closure between the two sessions.

We first evaluate inter-session loop closures using the same LiDAR sensor. The precision-recall curves in Figure 10 and the metrics reported in Table 3 reveal trends consistent with the intra-session results. Our method consistently achieves the highest recall at 100% precision across different LiDARs and revisit periods, confirming its reliability in challenging conditions. The precision-recall curves highlight this robustness, as they terminate earlier but maintain high precision. Our method also ranks among the top two in average precision and maximum F1 scores, with BTC being the only baseline matching our overall performance. Other baselines often fail to reach 100% precision or achieve it only at very low recall, except in the MulRan KAIST01–KAIST03 sequences.OPEN IN VIEWER

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Table 3.

Average precision (AP), maximum recall at 100% precision (R@1), and maximum F1 scores (F1 _m ) of state-of-the-art baselines and our approach for inter-session loop closure detection between sequences recorded with the same LiDAR sensor. Larger values indicate better performance. Best values are in bold, and the second-best values are in italics. The R@1 field is marked with “-” when the baseline cannot achieve a 100% precision upon varying its corresponding thresholding parameter.

(a) Conventional spinning LiDAR sensors
Datasets	MulRan						NCLT			HeLiPR
Revisit period	≈2 months						> 1 year			2 weeks			4 weeks
Reference seq.	KAIST01			Sejong02			2012-01-08			Bridge02			Town01
Query seq.	KAIST03			Sejong03			2013-04-05			Bridge03			Town03
LiDAR	Ouster OS1-64			Ouster OS1-64			Velodyne HDL-32E			Ouster OS2-128			Ouster OS2-128
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.451	0.223	0.529	0.095	-	0.224	0.297	0.241	0.408	0.220	-	0.396	0.266	0.084	0.360
BTC	0.635	0.309	0.740	0.378	0.005	0.526	0.465	0.311	0.605	0.490	0.001	0.647	0.461	0.259	0.636
SOLiD	0.472	0.085	0.435	0.022	-	0.055	0.153	-	0.307	0.157	0.004	0.223	0.239	0.024	0.276
LoGG3D	0.342	0.027	0.424	0.017	-	0.069	0.179	-	0.312	0.152	0.005	0.205	0.149	0.002	0.222
BEVPlace++	0.547	0.276	0.575	0.053	-	0.149	0.238	0.017	0.308	0.335	0.002	0.468	0.316	0.025	0.350
SC	0.160	0.445	0.643	0.039	-	0.140	0.252	-	0.426	0.205	-	0.500	0.247	-	0.479
Ours	0.725	0.633	0.835	0.203	0.037	0.346	0.464	0.411	0.637	0.472	0.300	0.638	0.497	0.437	0.664

(b) Unconventional hybrid solid-state and solid-state, non-spinning LiDAR sensors
Datasets	HeLiPR
Revisit period	2 weeks						4 weeks
Reference seq.	Bridge02						Town01
Query seq.	Bridge03						Town03
LiDAR	Livox Avia			Aeva Aeries II			Livox Avia			Aeva Aeries II
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.087	-	0.168	0.171	0.001	0.319	0.238	0.066	0.283	0.226	0.088	0.270
BTC	0.161	0.001	0.368	0.391	0.008	0.593	0.295	0.198	0.442	0.415	0.068	0.549
SOLiD	0.151	0.002	0.209	0.163	0.013	0.212	0.218	0.058	0.248	0.224	0.066	0.254
LoGG3D	0.039	-	0.125	0.065	-	0.158	0.114	0.002	0.194	0.152	0.002	0.249
BEVPlace++	0.207	0.009	0.302	0.279	0.002	0.408	0.224	0.078	0.268	0.252	0.054	0.298
Ours	0.328	0.223	0.494	0.404	0.060	0.580	0.319	0.218	0.485	0.349	0.215	0.519

The Sejong02–Sejong03 sequences from the MulRan dataset were recorded as opposite-direction traversals on a long highway, which produces sparse structural geometry throughout the sequences. The restricted FoV of the dataset’s LiDAR further increases the difficulty of inter-session loop closure detection. As shown in Table 3a, all baselines perform substantially worse on this pair of sequences, especially when we compare their results to those on the KAIST01–KAIST03 sequences from the same dataset, recorded with the same setup but in a dense urban environment.

The Bridge sequences from the HeLiPR dataset underscore the benefit of our self-similarity pruning strategy. Strong perceptual aliasing causes most baselines to either miss 100% precision entirely or reach it only at negligible recall. Even BTC, which performs comparably to our method in most other scenarios, fails to maintain its high precision on the Bridge sequences because it lacks an explicit mechanism to handle perceptual aliasing. In contrast, our approach detects accurate loop closures at comparatively higher recall, as reflected in the clear separation of our precision-recall curves from the baselines.

Additionally, we achieve better performance across different LiDAR sensors on the same sequences without changing any parameters in our pipeline. As shown in Table 3b, the Aeva Aeries II LiDAR experiences a sharp drop in maximum recall at 100% precision on the Bridge02–Bridge03 sequences. This drop arises from the overlap threshold used to define ground-truth loop closures: a few valid closures fall below the threshold and are therefore marked as false positives in ground-truth local maps, which lowers the maximum recall at 100% precision. Nevertheless, the average precision and the corresponding precision-recall curve in Figure 10 demonstrate that our method still performs strongly, maintaining near-100% precision across a substantially larger recall range.

On the NCLT dataset, which includes a revisit after about 1 year with a low-resolution Velodyne HDL-32E LiDAR, our approach again achieves the best recall at 100% precision and maximum F1 score. Only STD and BTC are the baselines that perform comparably in this scenario. This emphasizes the importance of having explicit knowledge about the ground plane under non-planar LiDAR motion.

These results also highlight the challenges that scan-based global descriptor methods such as Scan Context, SOLiD, and LoGG3D face in long-term revisit scenarios. In such scenarios, significant lateral shifts, viewpoint changes during revisits, and scene changes can all alter the global descriptor substantially. In contrast, local map-based local descriptor methods like ours, STD, and BTC avoid these issues by aggregating multiple scans to reduce viewpoint dependence and by focusing on local regions of the scene that remain similar across revisits, rather than compressing the local context into a single global descriptor.

The results on the HeLiPR sequences further highlight the impact of the LiDAR type on long-term place recognition. Even among the stronger baselines, we observe a noticeable drop in performance when switching from a 360°-horizontal-FoV Ouster OS2-128 LiDAR to the limited-horizontal-FoV LiDAR sensors such as Aeva Aeries II and Livox Avia, even when evaluating the same pair of sequences.

We next evaluate inter-LiDAR loop closure detection across multiple sessions. As shown in Table 4, our approach ranks second overall to BTC but achieves the best recall at 100% precision on 5 of 10 sequences. The precision-recall curves in Figure 11 highlight the same trend: our method often detects fewer closures but preserves high precision, ensuring reliable results without extensive parameter tuning.

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Table 4.

Average precision (AP), maximum recall at 100% precision (R@1), and maximum F1 scores (F1 _m ) of state-of-the-art baselines and our approach for inter-session loop closure detection between sequences recorded with different LiDAR sensors. Larger values indicate better performance. The best values are in bold, and the second-best values are in italics. The R@1 field is marked with “-” when the baseline cannot achieve a 100% precision upon varying its corresponding thresholding parameter.

(a)
Datasets	HeLiPR
Revisit interval	2 weeks			4 weeks			≈2 weeks						2 weeks
Reference seq.	Bridge02			Bridge01			Roundabout01						Town02
Query seq.	Bridge03			Bridge03			Roundabout02						Town03
Reference LiDAR	Ouster OS2-128			Ouster OS2-128			Ouster OS2-128			Aeva Aeries II			Ouster OS2-128
Query LiDAR	Aeva Aeries II			Aeva Aeries II			Aeva Aeries II			Livox Avia			Aeva Aeries II
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.086	0.003	0.208	0.061	-	0.188	0.109	0.003	0.229	0.019	-	0.134	0.165	0.017	0.250
BTC	0.398	0.033	0.592	0.352	0.004	0.520	0.499	0.152	0.620	0.361	0.002	0.504	0.478	0.243	0.612
SOLiD	0.048	-	0.097	0.028	-	0.072	0.102	-	0.228	0.099	0.004	0.198	0.105	-	0.251
LoGG3D	0.010	-	0.084	0.006	-	0.061	0.086	-	0.232	0.043	-	0.169	0.063	-	0.204
BEVPlace++	0.079	0.003	0.215	0.016	0.002	0.108	0.010	0.001	0.065	0.058	-	0.188	0.055	-	0.221
Ours	0.156	0.032	0.280	0.082	-	0.176	0.332	0.176	0.502	0.067	0.039	0.130	0.141	0.093	0.251

(b)
Datasets	HeLiPR						MulRan × HeLiPR						Self-recorded
Revisit interval	2 weeks			4 weeks			> 4 years						2 weeks
Reference seq.	Town02			Town01			MulRan KAIST01						IPB-Car
Query seq.	Town03			Town03			HeLiPR KAIST05						IPB-Backpack
Reference LiDAR	Livox Avia			Livox Avia			Ouster OS1-64			Ouster OS1-64			Ouster OS1-128
Query LiDAR	Aeva Aeries II			Aeva Aeries II			Ouster OS2-128			Aeva Aeries II			Hesai Pandar-128
Metrics	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m	AP	R@1	F1 m
STD	0.159	0.045	0.229	0.159	0.034	0.226	0.124	0.014	0.278	0.108	-	0.271	0.012	0.012	0.052
BTC	0.325	0.002	0.468	0.297	0.004	0.437	0.585	0.100	0.713	0.410	0.087	0.579	0.156	0.167	0.286
SOLiD	0.163	-	0.242	0.171	0.002	0.250	0.171	0.002	0.266	0.156	-	0.252	0.005	-	0.025
LoGG3D	0.073	-	0.187	0.113	0.002	0.186	0.027	-	0.162	0.051	-	0.194	0.013	-	0.050
BEVPlace++	0.083	0.003	0.215	0.105	-	0.236	0.151	0.002	0.359	0.140	-	0.303	0.054	0.012	0.192
SC	N/A	N/A	N/A	N/A	N/A	N/A	0.251	0.202	0.432	N/A	N/A	N/A	0.031	-	0.107
Ours	0.145	0.098	0.259	0.143	0.044	0.256	0.229	0.106	0.377	0.091	0.054	0.200	0.149	0.167	0.362

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Figure 11.

The precision-recall curves of state-of-the-art baselines and our approach for inter-LiDAR loop closure detection.

The performance of scan-based methods like Scan Context, SOLiD, LoGG3D, and BEVPlace++ is adversely affected by the difference in the scanning patterns, FoVs, and resolutions across LiDAR sensors. The local map-based methods achieve better results in such cross-LiDAR scenarios.

On the Roundabout01–Roundabout02, Town01–Town03, and Town02–Town03 sequences, our pipeline achieves the best recall at 100% precision among all baselines, demonstrating robustness to opposite traversals and constrained sensor views. However, on Bridge01–Bridge03 and Bridge02–Bridge03 sequences, the feature-pruning strategy limits recall to very low values, leaving room for improvement.

Cross-dataset evaluations between MulRan and HeLiPR push this further, with revisit intervals of over 4 years and different LiDAR sensors. These scenarios introduce structural changes in addition to sensor differences, making them highly challenging. Even so, our method achieves the second-best recall at 100% precision, while all baselines, including ours, achieve lower recall overall.

Finally, in self-recorded datasets collected 2 weeks apart with platforms having different motion profiles and LiDARs, our method performs comparably to BTC across all metrics, confirming its ability to generalize across diverse sensor setups.

Overall, these evaluations demonstrate that our approach effectively detects loop closures across multiple sessions for different LiDAR sensors and revisit intervals, thereby supporting our second key claim. At the same time, they highlight opportunities for further research on the highly challenging problem of inter-LiDAR loop closure detection.

5.3. Analysis and evaluation of the ground alignment module

In this section, we present both qualitative and quantitative evaluations of the ground alignment stage, which enhances the detection and alignment of loop closures. As we describe in Section 3.2, we need this stage in scenarios where the LiDAR experiences non-planar motion, allowing us to maintain a consistent reference plane for the BEV projection across revisits.

When we turn off the ground alignment module, our approach projects local maps onto the xy-plane, assuming planar motion. Consequently, using the RANSAC-based validation, it can align the local maps only along the xy-plane. We illustrate such a 2D alignment in the top-left image of Figure 12, where two local maps appear well-aligned from a top-down view. However, this alignment can be misleading. In the top-right image of Figure 12, a different perspective reveals an apparent misalignment in height and tilt between the two local maps, caused by non-planar LiDAR motion.OPEN IN VIEWER

By applying explicit ground alignment, we ensure that the local maps involved in a loop closure align correctly in 3D. This improvement enables our method to perform complete 3D global alignment rather than relying solely on a 2D assumption. The second row of Figure 12 shows a more accurate initial alignment between the local map pairs, even before any point cloud registration takes place.

We further validate this improvement through quantitative analysis. For each detected loop closure, we compute the overlap between the corresponding local maps after applying our initial transformation estimate T r m . We evaluate this on two sequences with non-planar LiDAR motion: the 2013-04-05 sequence from the NCLT dataset (Carlevaris-Bianco et al., 2016) and the IPB-Backpack sequence recorded using our in-house setup. In Table 5, we report the number of true positive loop closures with at least five inliers and the root mean square error of the overlap between aligned local maps, compared to the overlap between their reference counterparts generated with ground-truth poses.

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Table 5.

Evaluation of the ground alignment strategy for loop closure detection and local map alignment. We report the number of correctly identified loop closures and the root mean square (RMS) error in the overlap between aligned local maps using our pose estimate T r m and the overlap between the reference local maps. We report results with and without the proposed ground alignment module.

Dataset	NCLT 2013-04-05		IPB-Backpack
Ground alignment	OFF	ON	OFF	On
Correct loop closures ↑	6	6	10	26
RMS error in overlap ↓	0.280	0.110	0.468	0.104
Recall ↑	0.500	0.500	0.139	0.361

As seen in Table 5, the ground alignment stage significantly reduces the overlap error between local maps. This improvement occurs without applying any local point cloud registration. This advantage becomes evident in datasets with strong non-planar motion, such as the IPB-Backpack setup, where roll and pitch angles vary approximately between −30° and 30°. In such cases, the proposed ground alignment module enables our system to detect substantially more loop closures. This is because the BEV density images remain consistent across revisits when we project them onto the actual ground plane in the environment rather than onto the xy-plane of the local map frame.

We next evaluate the ability of our ground alignment module to correct misalignments between the ground plane and the map’s local xy-plane. To test this, we manually apply rotations in the range (10°–80°) about 10 random axes lying in the xy-plane of each reference local map. Our method then estimates the transform T m g that realigns the ground plane with the map’s xy-plane. We perform this evaluation on the MulRan KAIST01 and Sejong01 sequences, as well as the HeLiPR Bridge01 sequence, using the Aeva Aeries II and Livox Avia LiDARs. These sequences feature near-planar LiDAR motion, so their reference local maps already have the ground plane aligned with the xy-plane.

In Figure 13, we report the mean and standard deviation of the absolute error in the predicted rotation magnitude, averaged across all 10 axes for each local map, as a function of the applied misalignment. The ground alignment module reliably corrects misalignments up to 60°, with a mean error below 1° and a standard deviation below 8°. Even at initial misalignments of around 80°, the mean absolute error typically remains below 10°, except in the Livox Avia sequence, where observed failures stem from the Livox Avia sensor’s unusual reflective artifacts. These artifacts produce misleading, consistently oriented below-ground points that disrupt low-lying points sampling and PCA filtering under artificially large rotations. We would like to highlight that this is a sensor-specific quirk and not a flaw in the alignment method. However, since real-world misalignments rarely approach such extreme values, this level of performance is sufficient for practical use.OPEN IN VIEWER

These results support our third claim that the proposed ground alignment module enables robust handling of handheld or non-planar LiDAR motion and also provides a strong initial pose estimate for the 3D alignment of loop-closed local maps.

5.4. Analysis and evaluation of the self-similarity pruning strategy

In this section, we evaluate the effectiveness of the self-similarity pruning strategy in detecting loop closures within environments characterized by highly repetitive structures. Specifically, we focus on the Bridge sequences from the HeLiPR dataset, which feature long bridges composed of repeating mechanical elements. These conditions present significant challenges due to perceptual aliasing, which can lead to false loop closures.

Figure 14 shows a zoomed-in precision-recall curve for different self-similarity pruning thresholds based on the Hamming distance between ORB descriptors. The mark X on the curve represents the performance at an inlier threshold of 5, the default setting in our pipeline. Lower threshold values prune only strictly similar features, leading to higher recall values but a drop in precision, similar to the performance without pruning. Conversely, higher thresholds prune more features, leading to a drop in recall but maintaining high precision. The threshold value of 35 provides a desirable trade-off, maintaining a recall of around 0.6 with minimal loss in precision.OPEN IN VIEWER

Without the pruning strategy, our method detects false loop closures in these Bridge sequences. We show one example at the bottom-left of Figure 15, where a false match occurs with a near-perfect alignment between local maps. This alignment is supported by a sufficient number of inlier correspondences after a 2D RANSAC alignment of their BEV features (right-hand side of Figure 15), primarily caused by repetitive structures on the bridge. We successfully eliminate these matches between similar structures by applying the feature pruning strategy described in Section 3.4, thereby preventing the false loop closure.OPEN IN VIEWER

We further compare the performance of our pipeline with and without feature pruning in Figure 16. The precision-recall curves for both configurations, across the two Bridge sequences and three different LiDAR sensors, show that our approach with pruning maintains high precision throughout rather than compromising on precision to achieve a better recall. In contrast, our approach without pruning achieves slightly higher recall but significantly drops precision.OPEN IN VIEWER

To underscore the importance of precision, we conduct a pose-graph optimization experiment using the loop closures detected under both settings. As shown in Table 6, loop closures obtained with pruning lead to markedly better absolute trajectory estimates despite detecting fewer closures. In contrast, disabling pruning results in more false positives, which degrade the final trajectory estimate, even surpassing the error of odometry-only results.

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Table 6.

The effect of feature pruning on loop closure accuracy, measured by RMS APE w.r.t. translation after pose-graph optimization. We report the results for three LiDAR sensors across two sequences from the HeLiPR dataset.

Metric	RMS APE w.r.t. translation (m) ↓
Sequence	HeLiPR Bridge01			HeLiPR Bridge02
LiDAR	Ouster	Aeva	Livox	Ouster	Aeva	Livox
Odometry	178.8	124.4	223.0	52.4	149.3	114.9
w/o pruning	331.1	282.7	695.9	572.6	314.1	457.7
w /pruning	23.9	28.7	51.0	16.6	23.5	56.4

Overall, this study supports our fourth claim that the self-similarity feature pruning strategy introduced in Section 3.4 is essential for maintaining robustness in loop closure detection under high structural repetition. By prioritizing precision, our method avoids catastrophic failures in pose estimation, ultimately leading to more reliable mapping and localization.

5.5. Evaluation of the 3D alignment estimates

In this section, we evaluate the accuracy of the initial alignment ( T r m ) for the loop closures detected by our approach across the HeLiPR, NCLT, and IPB-Car datasets. To obtain a reliable reference for evaluation, we refine the local map alignments using Open3D’s (Zhou et al., 2018) point-to-point ICP registration, initialized with the dataset ground-truth pose. We use these refined results strictly as a proxy ground-truth alignment, since directly comparing against the dataset poses would conflate alignment error with odometry drift accumulated within the local maps that we generate using LiDAR odometry.

In Table 7a, we report the number of correctly identified loop closures and the RMS APE in translation and rotation for the pose estimates ( T r m ) produced by our method. Our loop closure identification approach consistently yields initial alignments within a couple of meters of translation and a few degrees of rotation relative to the reference alignment. This performance holds across all evaluated LiDARs, despite their differing scanning patterns, resolutions, and FoVs. It can thus be used with ICP for fine alignment.

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Table 7.

Evaluation of the loop closure alignment accuracy. We report accuracy in terms of RMS APE in translation (m) and rotation (°) compared to the proxy ground-truth alignment obtained via Open3D point-to-point ICP. Best results are in bold.

(a) We report the number of true loop closures and the accuracy of the initial pose estimates ( T r m ) produced by our method. Results from KISS-Matcher (KM) are also shown to contextualize the quality of our estimates; KISS-Matcher’s values correspond to only successful alignments.
Sequence	LiDAR	# Closures		RMS APE (translation) (m)		RMS APE (rotation) [°]
		KM	Ours	KM	Ours	KM	Ours
HeLiPR Bridge01	Ouster OS2-128	215	216	5.38 ± 5.34	5.57 ± 5.40	0.87 ± 0.83	1.80 ± 1.47
	Livox Avia	122	122	15.68 ± 14.95	2.07 ± 1.24	2.09 ± 1.87	2.74 ± 1.91
	Aeva Aeries II	213	214	1.65 ± 1.43	2.17 ± 1.50	1.06 ± 0.87	1.90 ± 1.44
HeLiPR Town02	Ouster OS2-128	42	42	0.30 ± 0.20	0.89 ± 0.44	0.31 ± 0.17	1.11 ± 0.84
	Livox Avia	5	5	1.07 ± 0.62	1.46 ± 0.73	0.65 ± 0.26	0.82 ± 0.44
	Aeva Aeries II	9	9	0.55 ± 0.23	1.31 ± 0.60	1.32 ± 0.96	1.62 ± 0.90
HeLiPR Roundabout01	Ouster OS2-128	125	139	0.33 ± 0.22	0.72 ± 0.33	0.33 ± 0.23	0.56 ± 0.33
	Livox Avia	12	13	0.44 ± 0.27	2.52 ± 1.88	0.56 ± 0.40	2.04 ± 1.45
	Aeva Aeries II	44	51	1.02 ± 0.74	1.63 ± 0.90	1.14 ± 0.83	1.14 ± 0.61
IPB-Car	Ouster OS1-128	216	230	0.49 ± 0.40	0.84 ± 0.49	0.50 ± 0.36	1.15 ± 0.80
NCLT 2012-01-08	Velodyne HDL-32E	14	26	1.06 ± 0.87	1.23 ± 0.85	1.06 ± 0.86	1.28 ± 0.97

(b) We refine the pose estimates from both methods using Open3D point-to-point ICP, and report the RMS APE in translation and rotation relative to the reference alignment. Both methods converge to similarly accurate solutions, demonstrating that our initial pose estimates are sufficiently precise to serve as reliable initialization for ICP-style refinement within a SLAM pipeline.
Sequence	LiDAR	RMS APE (translation) (m)		RMS APE (rotation) [°]
		KM + ICP	Ours + ICP	KM + ICP	Ours + ICP
HeLiPR Bridge01	Ouster OS2-128	5.05 ± 5.03	5.05 ± 5.05	1.12 ± 1.11	0.73 ± 0.73
	Livox Avia	15.67 ± 14.98	0.47 ± 0.43	2.02 ± 1.90	0.70 ± 0.69
	Aeva Aeries II	1.51 ± 1.41	0.60 ± 0.56	0.72 ± 0.70	0.40 ± 0.39
HeLiPR Town02	Ouster OS2-128	0.02 ± 0.01	0.02 ± 0.01	0.03 ± 0.01	0.03 ± 0.01
	Livox Avia	0.04 ± 0.02	0.04 ± 0.02	0.02 ± 0.01	0.02 ± 0.01
	Aeva Aeries II	0.02 ± 0.01	0.02 ± 0.01	0.03 ± 0.01	0.03 ± 0.01
HeLiPR Roundabout01	Ouster OS2-128	0.02 ± 0.01	0.02 ± 0.01	0.02 ± 0.01	0.02 ± 0.01
	Livox Avia	0.23 ± 0.22	0.17 ± 0.16	0.45 ± 0.43	0.23 ± 0.22
	Aeva Aeries II	0.48 ± 0.47	0.26 ± 0.25	0.49 ± 0.48	0.25 ± 0.25
IPB-Car	Ouster OS1-128	0.30 ± 0.29	0.28 ± 0.28	0.17 ± 0.17	0.17 ± 0.16
NCLT 2012-01-08	Velodyne HDL-32E	0.63 ± 0.61	0.94 ± 0.89	0.65 ± 0.62	0.61 ± 0.57

We also compare our method to KISS-Matcher by Lim et al. (2025) (KM), a state-of-the-art global point cloud registration method based on 3D features. For KISS-Matcher, we report the number of loop closures it successfully aligns (i.e., more than five inliers) and compute the corresponding RMS error metrics with respect to the reference alignment. We include this comparison not as a competing baseline, but to contextualize the quality of our initial alignment, and demonstrate how close our pose estimates are to those produced by a dedicated global registration system.

As shown in Table 7, KISS-Matcher, a technique designed to globally register point clouds, achieves better alignment accuracy across most sequences. This is expected as KISS-Matcher computes 3D features from the 3D point cloud and estimates the pose using a maximally consistent correspondence set. In contrast, our method combines 2D feature-based pose estimates with the approximate ground alignment estimates to get a complete 3D pose. Despite this fundamental difference, our RMS APE values remain within a few decimeters in translation and a couple of degrees in rotation compared to those of KISS-Matcher. Notably, KISS-Matcher performs worse than our method on the HeLiPR Bridge01 sequence because it lacks an explicit mechanism to handle perceptual aliasing during alignment.

To further demonstrate that our pose estimates are well-suited as initialization for a fine ICP-style alignment stage within a SLAM system, we explicitly run a point-to-point ICP refinement using Open3D, initialized with the pose estimates from our method as well as KISS-Matcher. The results in Table 7b show that both methods converge to solutions that are similarly accurate, and close to the reference alignment.

Our refined results also outperform KISS-Matcher on several sequences. The apparent performance inversion between KISS-Matcher and our pose estimation accuracy before and after ICP refinement may seem counterintuitive at first. A plausible explanation lies in the non-linear least-squares optimization underlying the ICP algorithm, which is sensitive to initialization and can converge to different local minima depending on the initial pose estimate.

Furthermore, two local maps generated from the same location using LiDAR odometry will generally not align perfectly, as they accumulate different amounts of drift and may contain artifacts due to imperfect scan deskewing. This could also lead to a different convergence for different initializations. It is also important to note that the discrepancy in performance between the two methods in Table 7b is, in most cases, on the order of only a few centimeters. The overall trend is that both methods converge to similarly accurate solutions after ICP refinement; therefore, we make no claims about the superiority of one method over the other in terms of final alignment accuracy.

Overall, these results support our fifth claim that the proposed approach yields accurate and complete 3D rigid-body transforms that align detected loop closures and are sufficiently precise to serve as initial guesses for fine-grained ICP-style registration within a SLAM back-end.

5.6. Multi-map alignment

This final experiment evaluates our pipeline’s ability to detect loop closures between the Riverside03 sequence and three KAIST sequences from the MulRan dataset. Although these trajectories share only minimal spatial overlap, it is sufficient to align the two scenes. These sequences also vary in temporal separation, with revisits ranging from the same day to a few months apart.

We first compare our method against baseline approaches using the precision-recall curves shown in Figure 17. Our approach consistently outperforms the baselines, achieving the highest recall while maintaining 100% precision across all three cases. Most other methods, except Scan Context, struggle in this challenging setting, with precision often falling below 50%.OPEN IN VIEWER

Next, we compute the optimized trajectory for each sequence using in-session loop closure constraints detected by our method, followed by an additional pose-graph optimization step to align these optimized sequences across sessions using the inter-session closures identified by our pipeline.

We show in Figure 18 the final aligned trajectories and corresponding local maps, illustrating the successful alignment in the overlapping region. We report the precision, recall, and F1 scores for the inter-session loop closures in Table 8, using the default parameters detailed in Section 4.2. Despite the limited overlap, our method achieves perfect precision in all cases.OPEN IN VIEWER

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Table 8.

Precision, recall, and F1 score for multi-session loop closures between the Riverside03 and KAIST sequences from the MulRan dataset. We report the RMS error in the overlap between aligned local maps using our pose estimate T r m and the overlap between the reference local maps.

Reference session	Riverside03
Query session	KAIST01	KAIST02	KAIST03
Revisit interval	2 months	Same day	1 week
Precision ↑	1.0	1.0	1.0
Recall ↑	0.120	0.108	0.150
F1 ↑	0.214	0.195	0.261
RMS error in overlap ↓	0.043	0.055	0.085

To assess the quality of the predicted alignment transformation T r m , we compute the RMS error of the overlap between aligned local maps, compared to the overlap between their reference counterparts generated with ground-truth poses. The last row of Table 8 demonstrates that our alignment closely matches ground-truth performance.

Additionally, we perform a similar cross-session multi-map alignment between the two self-recorded datasets, IPB-Car and IPB-Backpack, captured with different LiDAR sensors mounted on separate mobile platforms. These sequences exhibit varying motion dynamics and sensor configurations but still contain overlapping regions. We show the resulting aligned trajectories and detected loop closures in Figure 19.OPEN IN VIEWER

This experiment supports our final claim that our approach can successfully detect and align loop closures in challenging scenarios with little overlap. This capability is critical for tasks such as multi-robot map alignment, collaborative mapping, and long-term change detection.

5.7. Runtime evaluation of our approach

In this additional experiment, we evaluate the runtime of our approach. We run all the experiments on an Intel i9-10980XE @ 3.00 GHz CPU with 64 GB RAM. We implement our approach in C++ with a single-thread design. We report the runtime of different components of our pipeline in Table 9, including the mean and standard deviations for performing ground alignment for a local map, detecting loop closures using BEV density images, and validating detected loop closures through RANSAC. We also provide the average number of scans in each local map. The time required to generate each local map is not reported, as it directly corresponds to the LiDAR odometry algorithm used, that is, KISS-ICP.

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Table 9.

Runtime evaluation of our approach. We report the mean and standard deviation of the execution times for each key component of our pipeline.

Sequence	Avg. scans per local map	Execution time (mean ± standard deviation) (ms)
		Ground alignment	Loop closure detection	Loop closure validation
MulRan Sejong01	119	4.27 ± 1.59	17.74 ± 10.85	0.31 ± 0.11
HeLiPR Bridge01	96	7.44 ± 4.02	32.11 ± 21.21	0.34 ± 0.20
NCLT 2012-01-08	664	14.94 ± 7.21	63.79 ± 50.49	0.38 ± 0.31
IPB-Car	137	10.38 ± 6.04	50.96 ± 28.40	0.35 ± 0.33

Additionally, in Table 10, we compare the average runtimes of all baselines in terms of frames processed per second (FPS) across three sequences with dense, 360° FoV LiDARs. Scan Context achieves the highest processing speed on all sequences, followed by SOLiD and our method. Notably, the FPS values for STD, BTC, and our method include the runtime of KISS-ICP for scan registration, which generally makes them slower than scan-based methods such as SOLiD and Scan Context, which do not require registration. The learning-based methods, LoGG3D and BEVPlace++, are the slowest, often running below the typical LiDAR frame rate of 10 FPS.

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Table 10.

Average runtime evaluation of all the baselines. We report the average number of frames processed per second (FPS) for each baseline on three sequences with dense, 360° FoV LiDARs.

Sequence	MulRan KAIST01	HeLiPR Bridge01	NCLT 2012-01-08
LiDAR	Ouster OS1-64	Ouster OS2-128	Velodyne HDL-32E
STD	24	9	13
BTC	13	8	17
Scan Context	144	101	111
SOLiD	35	24	40
LoGG3D	12	7	15
BEVPlace++	7	5	5
Ours	27	15	29

Overall, our approach achieves a favorable balance between speed and effectiveness, outperforming most conventional baselines while remaining significantly faster than other local map-based and learning-based methods, consistently maintaining processing speeds above the sensor frame rate.

In summary, the experiments presented above support all our claims and showcase the applicability of our approach across various scenarios. The first experiment shows the robustness of our approach to various scanning patterns, FoVs, and resolutions of the LiDAR sensor. The second experiment illustrates the applicability of our approach to detect loop closures between multiple sessions with short-term and long-term revisits through the same environment. The two subsequent experimental evaluations support the newly proposed modules in our loop closure pipeline. We show that our approach can be used on LiDAR platforms with non-planar motion and is also robust toward perceptual aliasing. The fifth experiment confirms that our pipeline produces accurate and complete 3D pose estimates for aligning loop closures. We further demonstrate that our approach can align multiple trajectories with minimal physical scene overlap. Finally, we show that our pipeline can efficiently operate above sensor frame rates, even on dense 3D LiDAR sensors.