Multiple rotation averaging plays a crucial role in computer vision and robotics domains. The conventional optimization-based methods optimize a nonlinear cost function based on certain noise assumptions, while most previous learning-based methods require ground truth labels in the supervised training process. Recognizing the handcrafted noise assumption may not be reasonable in all real-world scenarios, this paper proposes an effective rotation averaging method for mining data patterns in a learning manner while avoiding the requirement of labels. Specifically, we apply deep matrix factorization to directly solve the multiple rotation averaging problem in free linear space. For deep matrix factorization, we design a neural network model, which is explicitly low-rank and symmetric to better suit the background of multiple rotation averaging. Meanwhile, we utilize a spanning tree-based edge filtering to suppress the influence of rotation outliers. What's more, we also adopt a reweighting scheme and dynamic depth selection strategy to further improve the robustness. Our method synthesizes the merit of both optimization-based and learning-based methods. Experimental results on various datasets validate the effectiveness of our proposed method.

Semantic segmentation of large-scale outdoor point clouds is of significant importance in environment perception and scene understanding. However, this task continues to present a significant research challenge, due to the inherent complexity of outdoor objects and their diverse distributions in real-world environments. In this study, we propose the multilateral cascading network (MCNet) designed to address this challenge. The model comprises two key components: a multilateral cascading attention enhancement (MCAE) module, which facilitates the learning of complex local features through multilateral cascading operations; and a point cross-stage partial (P-CSP) module, which fuses global and local features, thereby optimizing the integration of valuable feature information across multiple scales. Our proposed method demonstrates superior performance relative to state-of-the-art approaches across two widely recognized benchmark datasets: Toronto3D and SensatUrban. Especially on the city-scale SensatUrban dataset, our results surpassed the current best result by 2.1% in overall mean intersection over union (mIoU) and yielded an improvement of 15.9% on average for small-sample object categories comprising less than 2% of the total samples, in comparison to the baseline method. Our code is available athttps://github.com/ranhaogong/MCNet.

Quantitatively reconstructing the 3D structure of individual leaves within tree canopies is critical for understanding forest function and environmental responses to climate change. While quantitative structure models (QSMs) using terrestrial laser scanning (TLS) effectively capture woody structures, they lack the capability to accurately reconstruct non-woody leaf components. This study proposes AdLeaf (Accurate and Detailed Leaf), a novel approach for fine-scale reconstruction of individual leaves using TLS point clouds. AdLeaf combines wood-leaf separation, individual leaf segmentation, detection and repair of incomplete leaves, explicit reconstruction, and parameter extraction. It automates semantic segmentation at the tree scale to separate woody and leafy components. Instance segmentation is refined through similarity graphs. Incomplete leaves are detected and repaired using shape concavity analysis and symmetry-based mirroring. AdLeaf enables direct measurement of leaf attributes, including count, area, inclination, volume, and azimuth. Validation using field scans, synthetic data, and both in-situ and destructive measurements shows high accuracy: leaf counting errors ranged from 0.58% to 8.23% for trees with 201-4,000 leaves. Reconstructed leaf geometries had mean and standard deviations below 0.83 cm and 0.70 cm, respectively. Leaf area measurements (10–180 cm2) achieved a coefficient of determination (R²) of 0.95, bias of -0.20 cm², and root mean square error of 5.63 cm2. Incomplete leaf detection errors were below 28%, with the repaired area relative RMSE reduced by 9.4%. By addressing QSM limitations, AdLeaf enables explicit 3D leaf reconstructions that support detailed analysis of canopy light interception, spatial heterogeneity, and photosynthesis. It provides a robust framework for linking leaf structure to function at the tree level, advancing forest structure and radiative transfer research.

The accurate separation of leaves from woody material in individual-tree point clouds is crucial for the precise estimation of tree structural parameters. While supervised deep learning methods have demonstrated state-of-the-art performance in this domain, they rely extensively on large volumes of labeled data. However, the process of collecting and annotating tree point cloud data presents significant challenges due to the complexity of the intricate structures of trees, which necessitate substantial human resources and expertise. These constraints highlight the critical need to reduce labeling requirements, a challenge that remains largely unexplored. To address this, the present study first systematically analyzes the model performance under limited data annotation. This analysis is divided into two scenarios, with limited trees and limited point annotations per tree. In addition, based on the aforementioned analysis, we propose a specified weakly supervised framework that integrates consistency regularization, contrastive learning, and prototype learning to further improve performance under limited labeling. A series of experiments conducted on a variety of tree species have indicated that the diversity of tree samples is preferable to the use of more labeled points in the context of limited data annotations. The proposed weakly supervised framework demonstrated a mean intersection over union of 82.0% under the extreme scenario ofone point per class per tree(i.e., one leaf point and one wood point per tree) annotation. This result is nearly on par with the 84.3% mIoU achieved by a fully supervised model. This study offers significant insights into the improvement of label efficiency in the context of learning-based tree leaf-wood separation, paving the way for the development of efficient and scalable methodologies for 3D structural analyses in forestry and subsequent practical applications. The implementation code is available on [will be released if accepted].

The normal distributions transform (NDT) is an effective paradigm for point set registration. This method was initially designed for pair-wise registration and suffers from the accumulated error problem when directly applied to multi-view registration. Under the framework of point-to-cluster correspondence, this paper proposes a novel multi-view registration method named 3D multi-view registration based on the normal distributions transform (3DMNDT), which integrates the k-means clustering and Lie algebra optimizer to achieve multi-view registration. More specifically, the multi-view registration is cast into the maximum likelihood estimation problem. Firstly, k-means clustering is utilized to divide all data points into different clusters, where one normal distribution is computed to locally model the probability of measuring a data point in each cluster. Subsequently, the multi-view registration problem is formulated by the NDT-based likelihood function. To maximize this likelihood function, the Lie algebra optimizer is introduced and developed to optimize each rigid transformation sequentially. 3DMNDT implements data point clustering, NDT computing, and rigid transformation optimization alternately until the desired registration results are obtained. Experimental results tested on benchmark data sets illustrate that 3DMNDT can achieve state-of-the-art performance for multi-view registration. Note to Practitioners—This paper is motivated by solving the problem of registering multiple point sets. The normal distributions transform (NDT) is a well-known pair-wise registration method widely applied in the robotic domain. This paper extends the original NDT and proposes a novel registration method to simultaneously align more than two point sets. The multi-view registration is cast into the maximum likelihood estimation problem. Subsequently, the k-means clustering and Lie algebra optimizer are integrated to estimate registration parameters. Experimental results demonstrate its superior performance on the accuracy, efficiency, and robustness for multi-view registration of point sets.

Light detection and ranging (LiDAR) technology has revolutionized forest analysis in past two decades. The increase of available LiDAR data volume is accelerating in recent years. However, the dense and large-volume point clouds may constitute challenges for proper data storage and processing. Point subsampling is often a prerequisite in this circumstance. Nonetheless, the commonly used uniform and random subsampling methods fail to preserve the topological details of branching structures, as they essentially drop points globally. This generates problems for studies on detailed branching structures, and currently there are no point subsampling methods designed for trees. In this letter, a structure-aware subsampling (SAS) method is proposed to tackle this issue. SAS relies on skeleton-adaptive clustering to subsample points locally and maintains the global integrity simultaneously. The proposed method was tested and compared with uniform and random subsampling for retrieving key tree parameters including height, diameter at breast height (DBH), crown area, and wood volume based on geometrical reconstructions. Three datasets from terrestrial, mobile, and unmanned aerial vehicles (UAV) LiDAR platforms were tested. Results showed that SAS was able to achieve similar accuracies of structural parameters compared to the full-resolution data, even with a subsampling rate (SR) of over 90%. More importantly, at the same sampling rate, SAS faithfully preserved more points of thin branches compared to uniform and random subsampling. These results imply that the proposed method maintains the complex tree topology while significantly reduces the data size. This study provides a crucial advancement in LiDAR and forest applications, where data reduction still remains widely unexplored.

Most conventional Leaf Area Index (LAI) retrieval methods using Terrestrial Laser Scanning (TLS) data are based on Beer’s law and are severely affected by the effects of leaf occlusion and aggregation. Moreover, the correction of LAI using the Clumping Index (CI) relies on assumptions and is generally not robust. This paper exploits the high spatial resolution and penetration capability of TLS to explore the physical meaning of point cloud data sampling and then model the leaf cluster envelope by the Alpha-shape algorithm. Subsequently, canopy LAI is obtained by counting the surface area of the envelope of each leaf cluster within the canopy and combining it with the projected area of the canopy. The entire process is physically based and introduces a new LAI inversion approach based on TLS. We tested the approach by simulating the TLS data of 25 synthetic trees with different leaf areas and morphologies to evaluate its robustness. Four strategies were adopted for parameter selection in the envelope modeling step to automate the process of finding the optimal envelope radius and improve the inversion accuracy of LAI. In comparison with the traditional LAI retrieval method based on Beer’s law (RMSE% is 47.3%), we found that the method proposed in this letter has a higher inversion accuracy with a minimum RMSE% of 27.7%. Our method also is significantly more robust for high LAI scenes and performs well in scenes with high occlusion and aggregation.

Terrestrial laser scanning (TLS) is an effective tool for retrieving forest attributes. For example, stem diameters can be estimated from the TLS point cloud by applying automatic algorithms, which often approximate the stem cross section by using a circle or a cylinder. However, the cross section of a tree stem is never exactly a circle. Moreover, the cross section provides other economically important attributes related to, for example, the wood quality and growth environment. Thus, advanced curve fitting and other geometric fitting methods should be explored further. In this letter, a Fourier series curve approximation approach is proposed for modeling stem cross section shapes. The routine uses iterative Fourier series approximation in polar coordinates to remove gross errors. Three different diameter approximations are tested: circle fitting, Fourier series fitting, and combined Fourier series and circle fitting. The proposed approach is tested for approximating the diameter at breast height (DBH) with the use of two data sets: the first from an Alpine mixed and landslide-affected forest with multiscan TLS, and the second from a mature Scots pine forest in Finland with single-scan TLS. The results showed that for the multiscan data, the use of the combined Fourier series and circle fitting improved the root mean square error of DBH by 12.4% compared with direct circle fitting. The DBH accuracy for the single-scan data resulted in similar accuracy compared with that of the circle fitting. The results imply that the new approach is able to accurately reconstruct stem cross sections, especially for multiscan data.

Despite the fact that original Iterative Closest Point(ICP) algorithm has been widely used for registration, itcannot tackle the problem when two point clouds are par-tially overlapping. Accordingly, this paper proposes a ro-bust approach for the registration of partially overlappingpoint clouds. Given two initially posed clouds, it firstlybuilds up bilateral correspondence and computes bidirec-tional distances for each point in the data shape. Based onthe ratio of bidirectional distances, the exponential functionis selected and utilized to calculate the probability value,which can indicate whether the point pair belongs to theoverlapping part or not. Subsequently, the probability val-ue can be embedded into the least square function for reg-istration of partially overlapping point clouds and a novelvariant of ICP algorithm is presented to obtain the optimalrigid transformation. The proposed approach can achievegood registration of point clouds, even when their overlappercentage is low. Experimental results tested on public da-ta sets illustrate its superiority over previous approaches onrobustness.