Accurate measurement of stem diameter is essential to forest inventory. As a millimeter-level measuring tool, terrestrial laser scanning (TLS) has not yet reached millimeter-level accuracy in stem diameter measurements. The objective of this study is to develop an accurate method for deriving the stem diameter from TLS data. The methodology of stem diameter measurement by diameter tape was adopted. The stem cross-section at a given height along the stem was determined. Stem points for stem diameter retrieval were extracted according to the stem cross-section. Convex hull points of the extracted stem points were calculated in a projection plane. Then, a closed smooth curve was interpolated onto the convex hull points to simulate the path of the diameter tape, and stem diameter was calculated based on the length of the simulated path. The stems of different tree species with different properties were selected to verify the presented method. Compared with the field-measured diameter, the RMSE of the method was 0.0909 cm, which satisfies the accuracy requirement for forest inventory. This study provided a method for determining the stem cross-section and an efficient and precise curve fitting method for deriving stem diameter from TLS data. The importance of the stem cross-section and convex hull points in stem diameter retrieval was demonstrated.

Terrestrial laser scanning (TLS) can be used as a millimeter-level measurement tool for forest inventories. However, the stem diameter retrieval accuracy in sample plot scanning is not yet convincing. The errors in each step of stem diameter retrieval algorithms must be evaluated. In this study, six numerical calculation methods for the numerical calculation step, i.e., cylinder fitting (CYF), circle fitting (CF), convex hull line fitting (CLF), the proposed caliper simulation method (CSM), closure B-spline curve fitting (SP) and closure Bézier curve fitting with global convexity (SPC), were applied to stem diameter retrieval, and the similarities and differences were evaluated. The ovality, completeness and roughness were used to evaluate the stem slice point cloud quality. A total of 165 stem slice point clouds at breast height collected from three Larix kaempferi plots were used. Compared with the field-measured stem diameters at breast height (DBHs), the root mean square errors (RMSEs) of the CYF, CF, CLF, CSM, SP and SPC methods were 0.30 cm, 0.30 cm, 0.51 cm, 0.51 cm, 0.56 cm and 0.54 cm, respectively. Compared with the SPC method results, the RMSE of the CSM results was 0.05 cm. The results illustrated that the CYF and CF methods performed the same, as did the CLF and CSM methods. Most DBHs retrieved by the CYF and CF methods were smaller than the field-measured DBHs, and most DBHs retrieved by the CLF, CSM, SP and SPC methods were larger than the field-measured DBHs. This study demonstrated that the CYF and CF methods perform the best and are the most robust, and the measurements by a diameter tape and a caliper are similar enough for forestry inventories. Evaluating and preprocessing stem slice point clouds is a potential way to improve stem diameter retrieval accuracy.

A tree skeleton reflects the geometric and structural characteristics of a tree. Terrestrial laser scanning (TLS) provides an effective means to construct tree skeletons that can capture the surface and topological features of trees. However, it is difficult to construct a tree skeleton located at the geometric centre of the tree with a detailed hierarchy of branches because of the natural intricate topology of the tree and the defects of the tree point cloud scanned by TLS. In this study, we presented a tree-skeletonization method based on density-based spatial clustering of applications with noise (DBSCAN) using TLS data. First, outliers were removed using DBSCAN, and the point-traversal order of each point was recorded. Next, a tree point cloud was divided into several tree slices using contour planes, and several tree segments were obtained by applying DBSCAN to each tree slice. Tree skeleton points were retrieved from each tree segment after the point-inversion transformation. Then, the adjacent relationship between skeleton points and the flow weight of each skeleton point was calculated based on the point-traversal order. After that, the skeleton points were classified into stems and different levels of branch points using the flow weights of the skeleton points, and the branch hierarchies were identified. Finally, the tree skeleton was optimized using the angle consistency. The positional deviation $d_p$ and directivity deviation $d_d$ were presented in this study to verify the validity of the constructed tree skeleton. From the visualization results, the constructed tree skeleton effectively reflected the geometrical structure and branch hierarchies of the tree. The averages of $d_p$ and $d_d$ were 0.418 cm and 8.474 degrees, respectively. The results demonstrated the validity of the presented method. It will help improve the visualization and accurate measurement of trees.

The traditional stem model is inconsistent with the real geometry of the stem. Terrestrial laser scanning (TLS) provides a possibility of constructing a realistic stem model. In this study, we present a 3D stem model, which includes the stem axis curve and stem cross-sectional profile curve, with geometrical consistency and stem parameter retrieval methods using TLS data. The 3D stem axis curve is interpolated based on the geometric central points, which are calculated from stem slices formed by stem cross-sections. From the 3D stem axis curve, the stem shape characteristic is clearly depicted in 3D space. Stem parameters, such as the location of a stem cross-section, stem diameter, height, length, curvature and torsion at any position along the stem, are calculated. The stem cross-sectional profile curve is interpolated based on the stem cross-sectional profile points, which are calculated from stem cross-sectional points by angle simplification. Then, the convex-concave characteristic of the stem cross-section is represented by the stem cross-sectional profile curve, and from this, the integral method for basal area calculation is presented. The presented methods were tested on stem points from different tree species with different shape properties. The feasibility and validity of the 3D stem model was demonstrated by 3D stem model visualization. The root mean square error (RMSE) of the presented stem diameter method was 0.129 cm. Compared with the basal area calculated from the cross-sectional profile curve, the mean absolute percentage error (MAPE) and RMSE values of the traditional method were 8.921% and 49.926 cm², respectively. The stem parameter retrieval experiment demonstrated the accuracy and practicability of the 3D stem model. Compared with the traditional stem model, the 3D stem model can accurately represent the geometric structure of the stem and provide accurate calculations of stem parameters. It will help improve the applications of TLS in forestry inventories.

Searchable public key encryption supporting conjunctive keyword search is an important technique in today’s cloud environment. Nowadays, previous schemes usually take advantage of forward index structure, which leads to a linear search complexity. In order to obtain better search efficiency, in this paper, we utilize a tree index structure instead of forward index to realize such schemes. To achieve the goal, we first give a set of keyword conversion methods that can convert the index and query keywords into a group of vectors and then present a novel algorithm for building index tree based on these vectors. Finally, by combining an efficient predicate encryption scheme to encrypt the index tree, a tree-based public key encryption with conjunctive keyword search scheme is proposed. The proposed scheme is proven to be secure against chosen plaintext attacks and achieves a sublinear search complexity. Moreover, both theoretical analysis and experimental result show that the proposed scheme is efficient and feasible for practical applications.