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Aug 3, 2024, 1:13:50 PM8/3/24

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Abstract: This paper presents a new method for constructing quickly and automatically precision tree models from point clouds of the trunk and branches obtained by terrestrial laser scanning. The input of the method is a point cloud of a single tree scanned from multiple positions. The surface of the visible parts of the tree is robustly reconstructed by making a flexible cylinder model of the tree. The thorough quantitative model records also the topological branching structure. In this paper, every major step of the whole model reconstruction process, from the input to the finished model, is presented in detail. The model is constructed by a local approach in which the point cloud is covered with small sets corresponding to connected surface patches in the tree surface. The neighbor-relations and geometrical properties of these cover sets are used to reconstruct the details of the tree and, step by step, the whole tree. The point cloud and the sets are segmented into branches, after which the branches are modeled as collections of cylinders. From the model, the branching structure and size properties, such as volume and branch size distributions, for the whole tree or some of its parts, can be approximated. The approach is validated using both measured and modeled terrestrial laser scanner data from real trees and detailed 3D models. The results show that the method allows an easy extraction of various tree attributes from terrestrial or mobile laser scanning point clouds. Keywords: terrestrial laser scanning; automatic tree modeling; precision tree models; segmentation; forest inventory; branch size distribution; carbon cycle estimation

The determination and prediction of tree characteristics and quality attributes is important in forest management, especially in pre-harvest measurements [1]. These attributes are geometric and statistical characteristics of trees such as the crown-base height, total above-ground volume, the branch size distribution, and the branching structure. In particular, timber assortments, tree quality, branch decay times and carbon cycle estimations, etc. require accurate estimates on branch sizes and other tree attributes. However, many of these characteristics have been difficult or even impossible to measure operationally, often requiring cutting and laborious manual measurements.

With accurate and fast-to-use laser scanners, tree parameters can be determined with fewer practical difficulties [3]. 3D mapping of smaller areas with high detail is possible with terrestrial laser scanning (TLS) which can produce dense 3D point clouds of the tree surfaces [4]. However, often the laser scanner data are only used together with statistical models to give statistical estimates of tree properties. For example, standing tree biomass and its changes can be measured with TLS because they are highly correlated with the number of hits in the TLS point cloud [5,6].

Many problems in forestry, biomass estimation, forest research, and forest remote sensing could be more readily tackled if it were routinely possible to fit tree models to TLS measurements, such that a model is:

Comprehensive: it (i) covers all parts of the tree that are resolved in the data; and; (ii) interpolates to obtain credible reconstructions of the unseen parts that are not represented in the dataset but are located between some seen parts.

Precise: its parts are best-fit solutions describing the corresponding parts of the tree accurately and in detail, giving their location, size, orientation, relation to other parts of tree, or many other desired topological and metric attributes.

Compact: it is easily stored and manageable, and any attributes can be readily extracted from it anytime after its construction without having to use the actual data. Most of the relevant information of the original data is retained for future use in a compact form, even if one does not yet know what that information is.

Our scheme is based on the principle of building the global model step by step by an advancing collection of small connected surface patches. These patches are small local subsets of the point cloud and their geometric properties and neighbors are easily defined. This building-brick approach makes the method robust as the procedure does not need to know what a tree is supposed to look like and the point density can be quite varying. An ordered collection of local connected surface patches automatically yields the global structure both qualitatively and quantitatively.

A key part of any modeling method is the segmentation of the point cloud into branches. The segmentation gives the topological tree structure and the resulting segments (branches) can be then geometrically reconstructed. Our segmentation procedure uses the surface patches and recognizes bifurcations along the tree surface by checking local connectivity of a moving surface region. Other methods for segmenting have been presented: one way is to use voxels and mathematical morphology [21]. Another is to use octree based skeletonization approach [22,23]. Skeletons can be defined also using a neighborhood graph and checking the connected components of the level sets of the graph [17,24].

We have published two short conference papers [25,26] describing some of the ideas of our method. In this paper, however, we develop the method further and present many more details, tests, and validations. The primary novel features of our method are: (i) the partition of the point cloud into patchlike sets that allow a fast automatic procedure; (ii) efficient segmentation rules that retain the topological and hierarchical information; and (iii) a tool-like interface with direct handles for any geometric and topological attributes of the tree. We render the processed point cloud of a tree in a readily accessible geometric mode that can be utilized by a wide variety of applications and end-users.

All the desired external characteristics of the tree can be readily approximated from the cylinder data. Moreover, the method is scale-independent because it uses only topological properties and relative sizes. Absolute size restrictions are related to cover set size (building brick size) and the accuracy and density of measurements. Thus, if the cover set size is small enough, the method can be used to reconstruct the model accurately down to the measurement accuracy of the laser scanning. From the point of view of information compression, the cylinder model retains most of the information of the original point cloud in a format that is hundreds to thousand times more compressed in size.

Constructing the tree model requires some assumptions and a priori knowledge about the data and trees. First, we assume that the point cloud is a locally uniform and extensive enough sample of the surface in a 3D Euclidean space modeling of the real tree. Second, it must be possible to cover the point cloud sample with small sets that correspond to connected patches along the surface. Third, some other features of the tree, such as the order of magnitude of the branch and trunk size and the approximate trunk direction, are assumed to be known. Finally, we assume the tree to be locally approximately cylindrical. In the future versions of the algorithm, we will include the option of deformable cylindrical surfaces whenever this approximation is significantly violated.

The main steps of the method are the following (see Figure 4). At first, the point cloud is filtered to remove noise or isolated points (see Section 2.3). Then the filtered point cloud is covered with small sets conforming to the surface of the tree (Section 2.4). Next the neighbor-relation of the cover sets is defined (Section 2.5) and the sets are geometrically characterized (Section 2.6). The neighbor-relation determines the connectivity properties, and the geometric characterizations are used, e.g., for the classification of trunk points. Next, the sets that are not part of the tree, such as the ground sets, are removed, and the tree components and their bases are defined (Section 2.7). Here, and throughout the paper, by a tree component we mean an essentially separate part or cluster of the point cloud that can be, e.g., a single branch, a collection of branches, or even the whole tree. Following this, the tree components are segmented (Section 2.8). Throughout the paper, by segment we mean a connected non-bifurcated part of the tree, such as a branch or part of a branch or the trunk. The segmentation also gives the ordered information of the tree structure. In the segmentation process, we use surface growing, and bifurcations are recognized by checking local connectivity. The next step is to approximate each segment as a sequence of cylinders of possibly varying radius, length, and orientation (Section 2.9). To complete the cylinder model of the whole tree, gaps between cylinders are sought and filled with additional cylinders (Section 2.10). Finally, statistical and other characteristics of the tree can be computed from the completed cylinder model (Section 3.1).

The point cloud sample may contain outliers and noisy points caused by various reasons such as interference effects. Such points are not regarded as samples of the actual surface we want to reconstruct, and the first step in our method is to filter some noise from the point cloud. Our approach to filtering is based on the covers of the point cloud that are defined in the next section.