TreeSke: a structural-lossless skeleton extraction method for 1 point cloud data of canopy woody materials

5 Background: Skeletons extracted from point clouds of woody materials present 6 canopy structural features (e.g., the inclination angle of branches) for simulating canopy 7 interception and understory solar radiation distribution. However, existing methods 8 cannot easily capture structure-lossless skeletons of woody organs from tree point- 9 cloud data. To fulfill this goal, we proposed a distance-weighted method, named the 10 TreeSke method, to iteratively contract the point cloud of canopy woody materials to 11 their median-axis skeleton. After heuristically searching the local point set, we 12 pointwise-extracted the tightened weights to obtain the coarse skeleton. Then, we 13 thinned the skeleton of woody organs and optimized it by a noise filtering and re- 14 centering process. 15 Results: The proposed method was verified on six simulated tree models that have 16 reference skeletons and two field-collected datasets at the plot level. The results show 17 that the TreeSke-extracted skeletons were with higher location accuracy than using the 18 other two tested methods. The mean offset distance, the RMSE of the offset distance, 19 and the Hausdorff distance between the extracted and reference skeletons were less than 20 0.04 m, less than 0.06 m, and less than 0.11 m, respectively. Conclusions: The extracted skeletons by the TreeSke method could nearly integrally 22 depict the structural features of woody materials. The proposed method showed robust 23 for noisy points and outliers, while missing data would reduce the skeleton integrity 24 and cause deformation errors. From the extracted skeletons, users can extract the 25 inclination-angle features of canopy woody materials, which are useful for simulating 26 most eco-hydrological processes. 27


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The structural features and distribution trends of forest canopy components, such 45 as the canopy gap and leaf area distribution, evidently affect the canopy interception Previous studies mainly investigated the spatial distribution of leaves, while few 71 components can be precisely described as high-density discrete point cloud data using  for woody organs has the following advantages: (1) There is no need to segment single 92 woody organs from the original discrete point cloud with complex structural features. 93 The continuous median-axis skeleton can be beneficial to path-related analysis and

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The extracted skeleton can retain the local structural features of curves and holes.

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Although empirically setting the searching radius may reduce the skeleton extraction 125 accuracy, the Laplacian contraction-related method shows robustness to noise and 126 sample distribution. However, the skeleton extracted from the conjoined parts of woody 127 organs might be outside the organs' surface (Au, Tai et al. 2008). This issue also 128 appears in the results of some graph-based methods. After building the Reeb 129 analysis. The extracted results are always optimized by pruning the redundant branches 133 and by Laplacian smoothing. The main advantage of graph-based models is that they 134 are robust for data with low numbers of missing parts. Based on the prior knowledge 135 about point distributions, users can repair the missing data using topological skeletons.

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Unfortunately, it is an ill-posed method to build a graph and mesh for woody point 137 cloud data shown as overlapping and interlacing structural features (Song, Pang et al. 138 2016). For example, the mesh may contain an unreal network among points from 139 overlapping twigs. Therefore, it is difficult to obtain the structure-lossless skeletons for 140 canopy woody materials by using the above methods.  Most skeleton extraction methods were tested on watertight models, but rarely on 154 the discrete point cloud of canopy woody materials with interlacing distribution 155 features. The skeleton extraction requirements in this study are special to the above 156 methods in the following aspects: (1) Obtaining the structural lossless skeleton of 157 woody organs is necessary. It is the basis for assessing canopy phenotypic 158 thinned. Moreover, the extracted skeleton should maintain connectivity, especially at 161 the tree forks; (3) smoothing is not suitable for skeleton extraction from branches; (4) 162 The global setting parameters are not suitable to contract the tree point cloud data. 163 Otherwise, adjacent twigs may be over-contracted as a pseudo branch when setting the    Figure 1 shows the method's flow chart and two 180 running samples. The following four sections will introduce this method in detail. Coarse skeleton extraction 189 We iteratively contracted the coarse skeleton from the original discrete point cloud where dp is the Euclidean distance between the target point and its nearest point. The If a Pve has fewer than three points, we set LDM = 1 and SDM = 0 as the attributes for was relocated by the weighted median-based method as: Through several tests, setting M = 3 was shown to effectively extract the coarse For most skeleton points from linear-distributed twigs and slim branches with LDM 253 near 1, their Rop converged rapidly to 0 to avoid further being moved.

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(3) We used the distance-weighted average algorithm to relocate the points with Rop 255 higher than 0 and thin the coarse skeleton gradually. For a target point, its weight (Wthin) to the mean coordinate of nearby (n-1) points in a Pve during the Vth iteration was: In the thinned skeleton, we found that some points from stems with low Rop would 263 became outliers. Additionally, some skeleton points from tree forks or roots were shown 264 as lumped and redundant distribution trends. Thus, we needed to filter-out noisy points 265 from the skeleton extraction results.

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Noise filtering 267 We set the distance-based threshold to remove outliers and redundant points from 268 the thinned skeleton:

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(1) For point Po in the thinned skeleton, we searched its nearby k points; here, k was 270 set as 9. After summing the Euclidean distance from Po to its k neighboring points 271 (SUMd), we added the SUMd as an attribute to Po. Meanwhile, we removed the points 272 with LDM lower than 0.85, which were always shown to be the redundant points at the 273 tree forks.

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(2) According to the pointwise SUMd, we used the threshold filtering method to detect We also calculated the Hausdorff distance (HDF) between the extracted (E) and    Table 1.

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Owing to the noise and missing parts inevitably exist in the in-situ collected data,    Figure 2 The point cloud of woody materials converted from six simulated single tree 389 mesh models and those collected from MP and CA plots. 390 We embedded the extracted skeletons into the original point cloud data to 393 qualitatively evaluate their integrity and connectivity. As shown in the insets of Figure   394 3, the extracted skeletons can integrally present the structural features of interlacing to extract their local point sets. As the pointwise searching radius was heuristically set 405 according to Section 3.1, it is infeasible to subjectively adjust them. 406 We also performed a test by extracting the plot-level skeleton of woody materials   Table 2 The location accuracy comparison between those skeletons extracted from the 462 point cloud data with noise and free to noise. In this were over 28% of the number of points with the angle difference over 45゜. In addition, 473 the angle differences were higher for those points from trunks.

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Through visual assessment, we found these two methods had their own advantages 475 and disadvantages in evaluating the surface inclination angle of wood organs. As shown 476 in Figure 6, the SNV-based method could not correctly assess the pointwise inclination SNVs. We will discuss how to optimize the calculation methods of local surface 487 inclination angle for woody materials.  Table 3 Some statistical information about the pointwise absolute differences 496 between the SNV-and skeleton-based inclination angle. We compared the skeleton extraction accuracy of our proposed method with those The skeleton integrity and extraction accuracy obtained using the Laplacian 525 contraction method were significantly lower than those obtained using the TreeSke and 526 L1-median methods. Based on a visual comparison, we found that the skeleton 527 connectivity of tree forks exacted by the Laplacian contraction method was better than 528 that extracted by the other two tested methods (Figure 7). However, as shown in Table   529 4, the OFDRMSE, mean OFD, and HDF of the skeleton extraction results were generally 530 higher for the Laplacian contraction method than for the other two tested methods.

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Using the Laplacian method could not obtain the median-axis skeleton from woody 532 organs, which caused local distortion and evident missing parts, especially for the 533 trunks. Therefore, we conclude that the Laplacian contraction method is not suitable for 534 extracting skeletons from our tested data. limitations, which will be discussed in the following section.

Limitations and robustness 560
The TreeSke-extracted skeleton from the frustum-like root and junction parts of 561 woody materials hardly presented a smooth linear distribution, and the same was 562 observed for the L1-median extraction results. We found that the local geometrical To verify the robustness of our proposed method, we performed a test by extracting 573 a skeleton from the data with random and Gaussian noise, outliers, and missing parts.

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The results are shown in Figure 5. We found that the noise and outliers had limited 575 efforts on the skeleton extraction results. This is due to the fact that the pointwise 576 contraction weights were set according to two local geometrical metrics (LDM and 577 SDM) rather than the density-or distance-based weights. Although some outliers 578 remained in the thinned skeleton, they would be removed during the skeleton 579 optimization and re-centering steps.

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The TreeSke method can directly extract the skeleton of woody materials from a 644 discrete point cloud data. Before using this method, it is necessary to identify the woody 645 and foliage points from the whole tree point cloud data, which can be separated by Availability of data and materials 726 The datasets used and/or analysed during the current study are available from the 727 corresponding author on reasonable request. 728

Competing interests 729
The authors declare that they have no competing interests. 730