# Structured Pointcloud Segmentation for Individual Mangrove Tree Modeling

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## Abstract

Tree structure parameters of mangrove forests are hard to measure in the field and therefore inventories of this type of forests are impossible to keep up to date. In this article, we tested a structured pointcloud segmentation method for extracting individual mangrove trees. Structure parameters of individual trees were estimated from the segmented pointcloud and its 3d geometry was generated using revolution surfaces. Estimated parameters were then assessed at both plot and tree levels using field data. It was observed that the number of segments in each test plot agreed well with the number of trees observed in the field. Nonetheless, the estimated parameters exhibited mixed accuracy with top height being the most accurate.

## Keywords

LiDAR Mangrove Tree crown segmentation Connected components## 1 Introduction

The study and monitoring of fragile ecosystems such as mangrove forests is of vital importance worldwide as they are among the most productive and most Carbon-rich forest in the tropic; they provide habitats to over 1300 species of animals and act as protection of shorelines, hurricanes and tidal surges. It is estimated that between 35–50% of mangrove coverage have been lost in the past 60 years due mainly to human activities and, despite it accounts for only the 0.7% of tropical forest areas, it amounts as much as around 10% of emissions from deforestation globally [3]. Their assessment have been largely carried out through forest inventories that are time consuming, costly and, consequently, not frequently updated. More recently, efforts have been made to streamline inventorying processes through remote sensing and computational technologies, including pointcloud analysis, which is still limited due to the lack of efficient automation processes.

Among the many alternatives found in the literature, the voxel method is one of the most widely used method for three-dimensional models of trees due to its relative easy structure [14]. Other approaches use simple geometric models such as paraboloids or spheres to approximate the tree crown [7, 9, 12]. More realistic models have been also investigated, but tend to be computationally costly. For instance, radial basis functions and isosurfaces have been shown to achieve more natural forms of tree crowns [4], while others have focused on the reconstruction of the skeleton [1] or adjust free shapes to pointclouds [2]. From an inventorying viewpoint, the most useful models are those that can encode the most relevant structure parameters with the lowest complexity. One fundamental processing step is the extraction of individual trees pointclouds through a segmentation method. Major pointcloud segmentation strategies have been revised by [13], but all of them can be grouped in one of three types depending on the format of the input: 1) based on unstructured pointclouds, such as unsupervised clustering or primitives fitting [5, 15], 2) raster-based methods, which impose a regular spatial structure, either in 2-d (pixels) or in 3-d (voxels) on the pointcloud [6, 11], and 3) based on structured pointclouds, where the neighbourhood relationship is imposed using a directed graph. Although the latter approach can be the most accurate, it is also the most difficult to implement and thus the least researched approach. One of the few studies is that of [10] who used graph partition and connected components labelling (CCL) to delineate tree crown over a pine-dominated site. Nonetheless, they used a raster-based segmentation for building a hierarchical structuring prior to graph partitioning.

In order to fill this gap, we propose a novel structured pointcloud-based segmentation method that integrates *a priori* knowledge about the shape of target objects for the neighbourhood definition. The general strategy consists in creating an initial neighborhood connectivity matrix used with the CCL algorithm that is then progressively pruned and re-labelled. In the following sections we present 1) a brief description of the study site and data used, 2) the segmentation method, 3) the 3-d modelling approach, 4) the accuracy assessment and 5) the major conclusions.

## 2 Study Site and Data Used

*Rhizophora mangle*), a threatened species (SEMARNAT, 2010) that mixes with medium sub evergreen tropical forest of pucté (

*Bucida buceras*L.). There is also a low population of white mangrove (

*Laguncularia racemosa*) around the lagoon and channels.

Tree structure data was collected from 10 plots of 50 m by 50 m in 2014 (plots 1–10), 20 plots of 25 m by 50 m in 2016 (plots 1–20) and 7 plots of 25 m by 50 m in 2017 (plots 21–27). Plot center and orientation were measured with sub-meter precision GPS system. Tree individuals data included species name, *xy*-location (measured with respect to plot center), total height, diameter at breast height (DBH), diameter above and bellow highest root (mangrove trees only), crown diameters along E-W and S-N orientations, root diameters along E-W and S-N orientations, roots total height, and time and date of measurement. Individuals with lower DBH than 10 cm were not sampled. Only data from 25 plots were used as some were either not fully covered by LiDAR data or repeated in two different years.

The LiDAR sensor was flown in March 26, 2014 over an area of 2.5 km by 3.6 km (Fig. 1b) with an average point density of 20 pts/m\(^2\) and vertical accuracy of \(\pm 0.15\) m. Data was delivered with ground points identified, from which a terrain surface was generated. Subsets for each sampling plot with a buffer of 20% where extracted and normalized by subtracting the terrain surface. These data were the main input to the individual tree point extraction method described next.

## 3 Segmentation Method

Segmentation parameters used. \(z_{max}\) is the maximum *z*-coordinate of segment.

Symbol | Description | Value |
---|---|---|

\(z_{grmax}\) | Maximum | 0.15 [m] |

\(r_{max}\) | Maximum edge horiz. distance | 5 [m] |

\(d_{max}\) | Maximum segment diameter | 5 [m] |

\(w_{min}\) | Minimum points per segment | 10 [pts] |

\(E_{min}\) | Minimum break energy | 20 [m*pts] |

\(n_{iter}\) | Maximum splitting iterations | 10 |

\(d_{min}\) | Minimum crown diameter | 2 [m] |

\(h_{min}\) | Minimum tree height | 2 [m] |

\(z_{himin}\) | Minimum | \(0.3z_{max}\) [m] |

\(z_{lomax}\) | Maximum | \(0.15z_{max}\) [m] |

### 3.1 Point Connectivity and Pruning

Pointcloud neighbourhood is represented through an adjacency or connectivity matrix \(C=[C_{i,j}]_{i,j=0,\ldots ,n}\), so that a point *j* is said to be in the neighbourhood of point *i* if \(C_{i,j}\) is one, otherwise it is zero. The connectivity matrix of any order, including the zeroth, shall be denoted by \(C^*\). Recall that the *k*-th order neighbours are given by the power matrix \(C^k\).

*k*-nearest neighbours, and Delaunay tessellation, among others. Here we used the latter option as its computation is efficient yielding a relatively high sparsity, i.e., high fraction of zeroes in

*C*. Hence, the initial connectivity matrix is given by:

- 1.
All the neighbors must be lower than the point, i.e., \(C_{i,j} = 0, \text { if } z_i \le z_j\)

- 2.
All points must be non-terrain points, i.e., \(C_{i,j} = 0, \text { if } z_i \le z_{grmax}\)

- 3.
Every point is at most in the neighborhood of the nearest option, i.e., \(C_{i,j} = 0, \text { if } d_{i,j} > \min _k\{d_{k,j}\}\)

- 4.
Horizontal distance between a pair of neighbors is within a maximum distance, i.e., \(C_{i,j} = 0, \text { if } r_{i,j} > r_{max}\)

The first criterion ensure that the graph defined by the connectivity matrix is top-down directed, the second criterion discard terrain points, and the third one ensures no loops are present in the directed graph, thus defining a tree-like structure. The threshold distance \(r_{max}\) in the fourth criterion controls the size and number of segments. A large threshold value favors the inclusion of points from distinct nearby trees into a single segment (under segmentation), whereas a small value will tend to separate points from a single tree into several segments (over segmentation). Because of the high density of mangrove forests, no optimal value for \(r_{max}\) can be satisfactory and one always needs to undertake further steps to either merge or split segments. The favored option here is to select a relative large threshold value and to apply a progressive splitting strategy. This decision is mainly driven by the difficulty of searching points to reconnect over the option of searching edges to eliminate.

### 3.2 Segment Splitting

Starting with the segmentation induced by labelling the connected components in *C*, the segment splitting procedure is applied to wide segments as follows. For each selected segment one of the connection in the connectivity matrix is eliminated and the process repeated until either no more wide segments are available or the maximum number of iterations has been reached.

Segments are considered to be wide if its diameter is greater than a maximum allowed diameter (\(d_{max}\)), whereas segment diameter is computed by averaging the ranges of projections \(u_i = x_i\cos \theta +y_i\sin \theta \) along four directions: \(\theta = 0\), 45, 90 and 135\(^\circ \). Such diameter computation must be based on high points, i.e., the points with *z*-coordinates greater than threshold (\(z_{himin}\)). In addition, segments with lower number of points than a threshold (\(2w_{min}\)) are not considered candidates for splitting.

- 1.
Large horizontal distance

- 2.
Similar number of points in generated sub-graphs

- 3.
Low points available in generated sub-graphs

*i*,

*j*), \(w_j\) is the size of sub-graph at

*j*, \(w_j^c\) the size of complement sub-graph at

*j*, so that \(w_j+w_j^c\) is the size of original graph, i.e., the total number of points in the segment, and \(b_j\) and \(b_j^c\) are

*z*-coordinates of lowest point of each sub-graph. Equation (2) can be interpreted through a physical system analogy where points represent particles of unit weight connected trough rigid links, which are defined by the connectivity matrix

*C*. Each link is subject to a pair of forces or weights that excerpt torques with respect to middle point of the link, which is supposed fix. Hence, maximizing of the energy acting on the rigid link while minimizing the tendency to motion yields an expression like Eq. (2). Such energy is required to be over a threshold (\(E_{min}\)) to cause the link to break.

## 4 3-D Modelling

### 4.1 Tree Structure Estimation

Tree structure parameters as computed from segment points.

*z*can be further assumed for the roots, one can estimate crown diameter, crown bottom height, root diameter and root height using the ellipse in the

*rz*-plane

^{1}:

While high points and low points determined crown and root parameters, trunk diameter had to be computed through an empirical relation between the DBH and crown diameter of red mangrove, which was strongly linear and statistical significant (\(R^2=0.63\)). This was necessary, because trunk points are hard to determine and seldom accessible from airborne LiDAR. Moreover, trunk orientation was defined through the elevation and azimuth angles of a vector joining root top and crown base locations, and where no low points were available, crown location was used, the root height was defined as zero and the root diameter, same as the trunk diameter.

*a*is the top limit,

*b*the bottom limit and

*r*is the radius of the surface. The ± symbol indicates that there are two types of models: models with the plus sign are of hyperbolic type, whereas the negative are of parabolic type.

*xy*-coordinates as function of

*z*-coordinate. In this case,

*xy*-coordinates are given by:

## 5 Accuracy Assesment

The segmentation method was applied on the 25 plots from which tree models were generated. Figure 2 shows the top and lateral views of the segmented pointcloud and the corresponding surface model for a couple of plots. It can be seen that the object level representation captures the coarse shape of the pointcloud, yet whether such a representation match the actual forest structure was subject to a quantitative assessment, both at the plot and individual levels.

Coefficient of determination (\(R^2\)) and root mean square error (RMSE) at the plot and individual levels. (Values in parenthesis were based on mangrove species only).

## 6 Conclusions

Most existing tree crown segmentation methods have focused on temperate forests, where intertwined branches and aerial roots do not represent an issue. In contrast, in this study we developed and tested a segmentation method that incorporates information about the structure of objects embedded in the pointcloud, namely, the mangrove trees. The method used a sparse matrix that defines the neighbourhood relation among points, from which the connected-component labelling method is repeatedly applied together with a segment splitting strategy. The accuracy assessment showed a good promise for automated mangrove forest inventories. Nonetheless, methods for parameters estimation must be further improved, specially root structural parameters, specially because they are critical for quantifying blue Carbon storage by mangrove forests.

## Footnotes

- 1.
Root points are in the upper hemisphere of an ellipse.

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