The Apple-Trees dataset was collected from a commercial orchard in Shunyi District, Beijing, China (40.21°N, 116.54°E). The orchard features Aztec Fuji apple trees, a tall-spindle variety commonly grown in northern orchards. The 5–7 years-old trees, averaging 300–350 cm in height, were planted in rows with 1 m spacing between trees and 3 m between rows. Drip irrigation tapes were installed at 0.5 m above the ground to facilitate precise irrigation, as shown in Figure 1 .

Data acquisition was conducted in March 2024 during the dormancy period to avoid interference from fruits and dense foliage ( Figure 1A ). The Trimble TX8 terrestrial LiDAR was selected as the data acquisition device for the experiment, as similar terrestrial LiDAR systems are widely recognized as effective and precise tools for acquiring point cloud data during high-precision 3D reconstruction (Guan et al., 2020; Sun et al., 2021). The device has a 360° × 317°field of view, a measurement range of 0.6–120 m, and an accuracy of up to 2 mm. Double leveling was achieved using both external and built-in electronic leveling bubbles.

To compile the dataset, 10 apple trees were randomly selected from three rows using interval selection ( Figure 1B ). For each selected tree, data were collected from four stations positioned in a rectangular arrangement around the tree. Stations were positioned approximately 2 m from the tree rows and 2.3 m from the selected trees, considering the orchard layout. Station pairs S1-S4 and S2-S3 provided low-overlap 180° viewpoints, while S1-S2 and S1-S3 offered high-overlap viewpoints for algorithm evaluation.

The raw data collected by the instrument was processed using Trimble RealWorks software, where point clouds were extracted via spatial sampling at a 2 mm resolution. Since the collected raw data included multiple trees, extensive ground areas, and other environmental features, it was necessary to manually extract the regional point cloud of each target tree to enable a fair and independent evaluation of the algorithm’s performance on the tree structure itself. To minimize the impact on the practical application process, this manual step was limited to a simple regional segmentation to obtain all points within the single fruit tree’s area (including the ground points). Additionally, to ensure the evaluation focused solely on the tree’s complex geometry and to enhance the method’s generalizability, the geometrically simple and distinct drip tape point clouds were also manually removed.

Following obtaining the point cloud of the experimental region ( Figure 2A ), a series of automated preprocessing steps are sequentially applied to prepare the data for the core matching algorithm, as illustrated in Figure 2 . The first and most critical step is to establish a consistent spatial reference by fitting a ground plane using the RANSAC method (Fischler and Bolles, 1981). This plane serves as the basis for all subsequent height-dependent feature calculations.

Once this coordinate system is established, the ground points are removed to reduce computational load and focus the analysis on the tree’s structure ( Figure 2B ). Subsequently, a statistical outlier removal filter is applied to eliminate sparse noise points that may have resulted from sensor errors or environmental factors. The filter was configured with a number of neighbors k = 5 and a standard deviation multiplier of 0.1 ( Figure 2C ). Finally, to enhance computational efficiency for the subsequent registration steps, the point cloud is downsampled using a voxel grid filter with a voxel size of 8 mm, which standardizes the point density while preserving the essential geometric details of the trunk and branches ( Figure 2D ).

To establish baseline alignment data, spherical markers were additionally deployed as a ground truth method for point cloud registration (Liang et al., 2018). Specifically, markers were arranged to cover the region of interest ( Figure 1A ), and precisely leveled LiDAR scans captured all scene elements, including the markers. The collected point clouds were imported into Trimble RealWorks, where spherical markers were automatically identified, and their centers were fitted to establish correspondences. The software calculated an optimal transformation matrix (rotation and translation) by minimizing alignment errors, producing a ground truth dataset with an average distance error of 0.59 mm. This accuracy serves as the benchmark for subsequent experimental evaluations.

What’s more, the complete point clouds, registered from all four stations using this ground truth method, also serve as the baseline reference for deriving the structural parameters of each sample tree. Table 1 provides detailed information for each tree in the Apple-Trees dataset, including statistics on the point clouds and these key structural parameters.

Point cloud registration typically relies on identifying correspondences within overlapping regions (Liu et al., 2017). However, in diametrically opposed 180° scans, these regions are confined to sparse transitional boundaries—narrow zones where front and rear projections partially intersect. These sparse common points in such boundaries exhibit feature ambiguity due to occlusion and geometric complexity, limiting the effectiveness of both conventional methods (e.g., FPFH) and learning-based approaches (Fu et al., 2023).

To address this, the proposed method eliminates dependency on explicit overlap by leveraging the structural consistency of trees. By focusing on these anatomically consistent components, such as trunks and primary branches, which are typically observable from both views despite low overlap, the algorithm locates corresponding structural parts in each point cloud and constructs robust initial alignments under challenging low-overlap conditions.

For the trunk, the same parts across viewpoints can be identified using height above ground. However, relying solely on the trunk often fails to meet 3D registration requirements. Therefore, branch morphological and spatial distribution characteristics are utilized to assist registration. Branches exhibit significant morphological differences and distinctive spatial distributions, providing a critical basis for matching point clouds from different perspectives.

Describing trunks and branches typically requires referencing the ground as a baseline and employing 2D circular or 3D cylindrical fitting to extract structural information (Pfeifer et al., 2004; Xu et al., 2022). However, trunks and branches often appear as ellipses or irregular shapes in thin cross-sections, and noise complicates precise differentiation. While 2D circle fitting is computationally intensive and error-prone, cylindrical fitting, which incorporates multi-layer information, improves stability and accuracy, outperforming single-layer fitting (Raumonen et al., 2013; Li et al., 2022). Thus, this paper adopts cylindrical fitting for better localization.

Here we detail the branch matching process, covering the segmentation of key branch segments, the filtering of potential pairing branches, and the final selection of the best match.

Firstly, branch segments in the same key region of both point clouds are segmented. This initial step is designed to simplify the complex matching problem by focusing on short, geometrically simple segments rather than the entire intricate branching structure. Specifically, we isolate the tree’s middle-lower sections based on height above the ground ( Figure 4A ), where the trunk and branches are thicker and less affected by wind, and the trunk reflects the tree’s overall growth trend. Given the trunk’s larger radius, we can use RANSAC to fit a cylinder (Fischler and Bolles, 1981) and identify the trunk, obtaining its axis. This axis then serves as a reference to segment the branch segments within a specific distance ( Figure 4B ).

To define the area of branch segments suitable for robust matching, we conducted field measurements and statistical analysis on the 5–7-year-old tall-spindle apple trees used in our study. Our analysis indicated that while branch-trunk junction shapes vary significantly in the region up to 0.07 m from the trunk, the zone between 0.07 m and 0.14 m is optimal. Within this region, branches consistently display more pronounced cylindrical characteristics with fewer secondary branches, which reduces geometric ambiguity for our matching algorithm. In addition, as these segments are located closer to the trunk, they are less susceptible to wind-induced motion, further improving their geometric stability. This region is also more likely to contain branches segments that are both visible from both opposing viewpoints, thereby reducing mismatches due to single-view visibility in the 180° setup. Meanwhile, the standardized tall-spindle horticultural system, through continuous pruning, ensures that this key structural geometry remains highly consistent across the representative age range of our subjects and is less influenced by species-specific variations. Consequently, this region is identified as the key branch area for registration.

Secondly, potential pairing branches are filtered among the key branch segments obtained earlier. For the initial screening, the Euclidean clustering method (Miao et al., 2023) was employed to filter clusters based on point count. Larger clusters, which likely contain curved branch segments or secondary branch junctions, and smaller clusters, typically representing thinner branches or incomplete point clouds, were both excluded due to their poor conformity to cylindrical shapes. Next, cylindrical fitting was performed on clusters of moderate size, and the quality of the fit was evaluated by the proportion of inliers (Salehi et al., 2022; Martínez-Otzeta et al., 2023). Clusters with an inlier ratio below 30% were discarded, while those exceeding the threshold were labeled as “potential pairing branches.” Thus, we filtered potential pairing branches S = { s 1 , s 2 , … , s n } from the source point cloud and T = { t 1 , t 2 , … , t m } from the target point cloud, as illustrated in Figure 4C . At this stage, there are m × n possible pairing combinations between S and T .

Finally, the best match is selected from the possible pairing combinations. To identify structural correspondences under low-overlap conditions, we introduce a branch matching strategy based on local geometric attributes. Specifically, three key features are extracted and quantified for each candidate branch segment: the radius r of the fitted branch cylinder, the angle θ between its axis and the trunk cylinder axis, and the height h of its centroid above the ground, as shown in Figure 5 . These features jointly characterize the spatial and morphological properties of each branch, offering sufficient distinctiveness and consistency across viewpoints.

Due to inherent fitting errors arising from occlusions, noise, and viewpoint differences, residual discrepancies frequently exist between the feature values of truly corresponding branches. To account for this, we first compute the differences in radius, angle, and height for all m × n possible pairing combinations, and compare them against empirically determined thresholds ( t o l r = 5 mm, t o l θ = 15°, t o l h = 50 mm). These thresholds were established through data-informed tuning on a representative subset of manually annotated branch pairs. They are conservatively chosen to accommodate noise and fitting uncertainty while effectively eliminating structurally implausible matches. Only pairs satisfying all three threshold conditions are retained for further evaluation.

Although threshold-based filtering eliminates most implausible matches, finer ambiguities may still arise when multiple source branches fall within the threshold bounds of the same target branch. To resolve such cases, enforce one-to-one correspondence, and account for the differing sensitivities of the three features, we introduce a feature discriminant function with dynamic weights to compute a fused residual (Equation 1):

where Δ r , Δ θ and Δ h represent the residuals of the radius, angle, and height, respectively, such as Δ r = | r s − r t | for radius residual. The corresponding weighting factors are w e i g h t r , w e i g h t θ and w e i g h t h , calculated as follows Equation 2:

The core idea of this dynamic weighting strategy is to assign higher weights to features with smaller residual, thereby emphasizing the contribution of geometrically consistent features to similarity assessment. Unlike static weighting, this adaptive strategy adjusts feature importance based on different structural configurations, enabling more effective differentiation between correct and false matches. Specifically, a normalized dynamic weighting strategy is employed using a negative logarithmic function. Each feature’s residual is normalized by dividing by its predefined threshold, and the negative logarithm of the normalized residual is applied to compute dynamic weights. The final score, which indicates fused residual of multiple features, is calculated using these weights, where lower scores correspond to smaller residual and higher similarity. Ultimately, for each branch in the target point cloud, only the source point cloud pairing with the smallest score is retained, ensuring a high-confidence one-to-one match.

As a final validation step, the quality of the cylindrical fit is used as a global confidence measure. Among all candidate pairs retained after scoring, the pair with the highest number of inlier points in its fitted cylinder is selected. This tie-breaking criterion ensures that the final correspondence used for transformation estimation is based on structurally robust and reliably measurable segments, adding an additional layer of stability to the matching process.

The essence of point cloud registration is solving the transformation matrix T that aligns the source point cloud 𝒫 = { p i * , 1 ≤ i ≤ N P * } with the target point cloud 𝒬 = { q i * , 1 ≤ i ≤ N q * } . This process can be expressed by Equation 3:

where p i * and q i * represent the coordinates of the i-th point in the source and target point clouds, respectively. T , as a rigid-body transformation in space, is typically considered 6 degrees of freedom (DoF) transformation, consisting of 3-DoF for rotation and 3-DoF for translation.

Since most TLS devices, including the TLS used in this study, provide high accuracy in the horizontal direction (Cai et al., 2019; Zang et al., 2021), rotations around the X and Y axes can be neglected during the matrix solution, and the matrix T simplifies to T ˙ (Equation 5):

The simplified matrix T ˙ is a 4-DoF problem, and Wang X. et al. (2023) have also compared 6-DoF and 4-DoF estimation methods for TLS point cloud registration, with the latter demonstrating significantly higher accuracy. The transformation matrix T ˙ can be further decomposed into a 1-DoF rotation around the vertical axis and a 3-DoF translation in space. Specifically, rotational alignment in the XOY plane is achieved using the best matching branch, followed by translational alignment in 3D space using trunk information.

The first step is rotation in the XOY plane, i.e., around the vertical axis. In low-overlap viewpoints, the structural information of matched branches and trunks exhibits higher consistency. To leverage this, cylinders are fitted to the best matching branch, and their axes are extracted. These axes are then projected onto the XOY plane, with their intersection point denoted as O ( x o , y o , 0 ) . The angle between the projected axes determines the required rotation angle α . Specifically, the center of rotation is first shifted from the origin to O . The source point cloud is then rotated around O , after which the rotated point cloud is translated back to the origin. Through this series of combined transformations, the transformation matrix can be calculated (Equation 6). As shown in Figure 6 , this step aligns the two point clouds by rotation.

The next step is a straightforward translation operation, aligning corresponding points after rotational alignment. Given that the basal trunk generally lacks lateral branches, has a larger diameter, retains more complete point clouds, and approximates a cylinder, its structural center is selected as the reference for translation. Specifically, a trunk section at the same height is extracted from both viewpoints—at a height between 0.20 m and 0.30 m above the ground plane, a range chosen to avoid irregularities near the root collar while remaining below the first major branches—approximating different observations of the same bottom trunk. And then a cylindrical model is fitted to this section by RANSAC, and from its resulting axis, the geometric center of this trunk segment is computed, denoted as G s r c ( x s , y s , z s ) in the source point cloud and G t g t ( x t , y t , z t ) in the target point cloud ( Figure 7 ). These centers serve as the corresponding points for translation. At this stage, the coordinate difference between the corresponding points represents the translation component of the transformation matrix, which can then be obtained (Equation 7):

With this, the complete rotation translation matrix for coarse registration can be constructed as T c = T 2 T 1 .

To further improve the registration accuracy and quality, fine registration is performed using the point-to-point iterative closest point (ICP) algorithm (Besl and McKay, 1992), which minimizes the Euclidean distance between corresponding points to iteratively achieve optimal alignment. However, we observed that in practice, excessive pursuit of local minimization can lead to overfitting, a phenomenon we term “over-registration.” This issue may cause the final alignment deviating from the true geometric structure (Kelbe et al., 2016), as illustrated in Figure 8 .

To address this issue and ensure the alignment is focused on the key structural features, our primary strategy is to exclude the ground and trunk point clouds from the ICP process, which are more prone to causing local minima convergence, and use only the remaining branch point clouds for registration. This is because these geometrically simple structures constitute a dominant portion of the total point cloud, and their high consistency between scans can dominate the registration’s error metric, masking misalignments in the more complex branching architecture. In contrast, the morphology of branches is more complex and diverse, making them better representations of local features from different viewpoints of the same tree. These features provide independent constraints, helping to prevent convergence to local minima, while enhancing registration stability and accuracy in low-overlap scenarios.

Additionally, to further refine this process and improve stability, we introduce the “theoretical overlap ratio” parameter from the CloudCompare core library. In our branch-only ICP process, we empirically set this value to 90%. This directs the algorithm to, in each iteration, effectively filter out the 10% of point-pair correspondences with the largest Euclidean distances. This supplementary measure further reduces the influence of potentially unreliable correspondences, ensuring the registration is robust against residual noise or minor misalignments. This two-step process ensures that the final alignment is determined by the most reliable correspondences on the tree’s branching structure, yielding a high-fidelity result. By using this ICP algorithm optimized for low-overlap cases, we obtain the transformation matrix T f for fine registration. This allows us to compute the overall rotation-translation matrix for point cloud registration as T = T f T c . And then ultimately align the source and target point clouds according to Equation 3, completing the 3D reconstruction of the apple tree point cloud.

In summary, by optimizing the processing flow and strategies, the proposed method achieves marker-free, automated registration of low-overlap point clouds for individual apple trees. Designed specifically for low-overlap scenarios, this method utilizes local matching of the trunk and branches to effectively address the challenges of feature extraction and registration from different viewpoints, thereby completing the 3D reconstruction of point clouds.

We tested our proposed registration algorithm on the Apple-Trees dataset and quantitatively evaluated the registration results using the ground truth. Based on the overall workflow and the intermediate values and results that may arise during the process, we use the following three evaluation metrics:

where tr ( R ) is the trace of matrix R .

where N p * is the number of points in the source point cloud, and p i * is the i-th point.

This study aims to register two 180°-separated, low-overlap point clouds. The algorithm is tested on the Apple-Trees dataset under these conditions. Due to its symmetry in source-target selection, registration results are analyzed in two configurations: S1 (target) with S4 (source) and S2 (target) with S3 (source).

To comprehensively validate the effectiveness of low-overlap point cloud registration for two stations 180° apart, we compare its results with those of high-overlap multi-station registration and other registration algorithms.

A potential limitation, common to registration methods that rely on fitting geometric primitives to real-world data, is their theoretical susceptibility to error propagation. In our approach, for instance, minor viewpoint-dependent variations—such as those introduced by topographic inconsistencies—may result in small discrepancies in the estimated ground plane across scans. These initial deviations can propagate through subsequent steps, potentially affecting the localization of trunks and key branches. Such propagation may influence feature-based thresholding, thereby increasing the risk of branch matching failures under certain conditions.

Additionally, the BranchMatch method employs several empirical thresholds (e.g., for cylindrical fitting and branch features) tailored to the standardized architectural properties of tall-spindle apple trees. Although these values were determined through data-informed tuning and conservatively selected to accommodate noise and natural variation, their optimality may still vary with different data quality or sensor characteristics. This represents a common limitation of parameter-dependent methods, and future work could thus explore adaptive thresholding strategies to enhance the method’s robustness and generalizability across diverse scenarios.