###### Abstract  
It is critical to take the variability of leaf angle distribution into account in a remote sensing analysis of a canopy system. Due to the physical limitations of field measurements, it is difficult to obtain leaf angles quickly and accurately, especially with a complicated canopy structure. An application of terrestrial LiDAR (Light Detection and Ranging) is a common solution for the purposes of leaf angle estimation, and it allows for the measurement and reconstruction of 3D canopy models with an arbitrary volume of leaves. However, in most cases, the leaf angle is estimated incorrectly due to inaccurate leaf segmentation. Therefore, the objective of this study was an emphasis on the development of efficient segmentation algorithms for accurate leaf angle estimation. Our study demonstrates a leaf segmentation approach based on a \(k\)-means algorithm coupled with an octree structure and the subsequent application of plane-fitting to estimate the leaf angle. Furthermore, the accuracy of the segmentation and leaf angle estimation was verified. The results showed average segmentation accuracies of 95% and 90% and absolute angular errors of 3\({}^{\circ}\) and 6\({}^{\circ}\) in the leaves sampled from mochi and Japanese camellia trees, respectively. It is our conclusion that our method of leaf angle estimation has high potential and is expected to make a significant contribution to future plant and forest research. \(k\)-means; leaf angle distribution; leaf angle estimation; LiDAR; octree structure; plane-fitting 1  
K. K. K.  
Such model-based approaches have greatly minimized the requirement of field measurements; however, the models were based on unclear reasoning, and there was insufficient field experimental verification. On the other hand, LAD measurement simulated by leveled digital photograph techniques has shown great potential, but it is susceptible to the direction in which the camera is facing the target [14; 15]. Recently, there has been attention on using terrestrial LiDAR (Light Detection and Ranging) to capture canopy structural details down to millimeter-level resolutions [16]. Terrestrial LiDAR achieves a high resolution of distance measurements or object structures by illuminating the target with a laser and measuring the reflected pulse phase difference or the round-trip time of the pulse (time of flight). Terrestrial LiDAR has great potential for accurately obtaining canopy structure details, which are widely used to estimate vegetation structure parameters such as tree height [17], leaf area index [17; 18; 19; 20], leaf area density [10; 21; 22], and leaf angle distribution [10; 16]. In mathematical parlance, the leaf angle is typically described by the normal vector of the leaf surface. In short, it seems likely that the calculation of the normal vector should be an important task for obtaining accurate leaf angle estimates. Point cloud data (PCDs), a form of LiDAR-derived data, can reconstruct a 3D model of a leaf. Through 3D leaf models, the structure of leaf PCDs has been recognized and the leaf angle calculated by employing the plane-fitting method, which follows the same pattern as the least-squares method [16; 19; 22; 23]. As a necessary process for obtaining appropriate leaf segments to fit the surface, leaf angles estimated from the fitted plane of the leaf PCDs have been manually extracted from entire LiDAR-derived PCDs [22; 23]. Yet, the process of manual segmentation of leaf PCD is time-consuming. In most cases, manual segmentation is not recommended for complicated canopy structures, while automatic segmentation still presents challenges. An algorithm that automatically separates LiDAR-derived PCDs into acceptable clusters has been reported. In the reported method, the LiDAR-derived PCDs were regularly segmented into clusters using sequence cubic grids [24]. Moreover, neighboring points of center were repetitively selected to group the clusters within a certain Chebyshev distance (e.g., 1 cm) [25] as well as triangular intersect regions [10].