Canopy Segmentation of Overlapping Fruit Trees Based on Unmanned Aerial Vehicle LiDAR

Abstract

Utilizing LiDAR sensors mounted on unmanned aerial vehicles (UAVs) to acquire three-dimensional data of fruit orchards and extract precise information about individual trees can greatly facilitate unmanned management. To address the issue of low accuracy in traditional watershed segmentation methods based on canopy height models, this paper proposes an enhanced method to extract individual tree crowns in fruit orchards, enabling the improved detection of overlapping crown features. Firstly, a distribution curve of single-row or single-column treetops is fitted based on the detected treetops using variable window size. Subsequently, a cubic spatial region extending infinitely along the Z-axis is generated with equal width around this curve, and all crown points falling within this region are extracted and then projected onto the central plane. The projecting contour of the crowns on the plane is then fitted using Gaussian functions. Treetops are detected by identifying peak points on the curve fitted by Gaussian functions. Finally, the watershed algorithm is applied to segment fruit tree crowns. The results demonstrate that in citrus orchards with pronounced crown overlap, this novel method significantly reduces the number of undetected trees with a recall of 97.04%, and the F1 score representing the detection accuracy for fruit trees reaches 98.01%. Comparisons between the traditional method and the Gaussian fitting–watershed fusion algorithm across orchards exhibiting varying degrees of crown overlap reveal that the fusion algorithm achieves high segmentation accuracy when dealing with overlapping crowns characterized by significant height variations.

1. Introduction

In the agricultural scenario of fruit tree planting, the canopy structure information of fruit trees can be used to predict their growth and yield. In addition, canopy structure information is also an important basis for accurately managing orchards in terms of irrigation and fertilizer supplementation [1,2,3]. In modern agriculture, orchard management must be specific to each fruit tree, and the automatic picking process of the orchard also needs the information of individual trees. Especially in the context of automated orchard harvesting, the precise localization of individual fruit trees is crucial. Individual tree segmentation using LiDAR data allows for the extraction of crown metrics, including the tree’s crown width and spatial location. These attributes serve as a reliable foundation for accurately identifying target fruit trees during the harvesting process and are essential for the efficient path planning of unmanned vehicles within the orchard.

Traditional individual tree segmentation methods based on UAV LiDAR can be broadly categorized into two types. One is based on raster surface models for individual tree segmentation, where the canopy height model (CHM) is commonly used. Due to the complex geometric information and other noise presented in LiDAR data, detecting treetops solely based on local maxima inevitably leads to over-segmentation. Xu et al. (2021) [4] employed crown morphology to filter out LMs caused by surface irregularities to improve the tree detection accuracy, but it is difficult to automatically determine the optimal combination of parameter values. Ma et al. (2017) [5] interpolated a digital elevation model (DEM) from the ground returns and a digital surface model (DSM) from the first returns, and CHM was calculated as the difference between the DSM and DEM. Chen et al. (2006) [6] used the local maximum to detect the treetop based on CHM. After determining the positions of the treetops, they applied marker-controlled watershed segmentation to extract individual trees. Duncanson et al. (2014) [7] adopted CHM-based watershed to extract individual trees and then iteratively refine the results to enable the detection of multilayered forests. Lisiewicz et al. (2022) [8] refined the under-segmentation and over-segmentation errors using an automatic correction method after extracting individual segmentation errors based on CHM. Liu et al. (2019) [9] developed a multiscale local maxima algorithm to enhance the accuracy of local maxima obtained from CHMs at varying spatial resolutions. Wu et al. (2019) [10] combined individual tree segmentation-based methods, canopy height model-based approaches, and statistical model methods utilizing LiDAR metrics to estimate the canopy cover of pure Ginkgo (Ginkgo biloba L.) plantations in China. Liu et al. (2024) [11] introduced an approach that combines marker-controlled watershed segmentation with a spectral clustering algorithm to address the issues of over-segmentation and under-segmentation commonly encountered in traditional CHM-based methods.

The other method involves clustering based on spatial relationships between points after normalizing LiDAR point cloud data. The point-based individual tree segmentation can reduce the loss of tree information. Voxel clustering and k-means clustering are typically used to segment individual trees from LiDAR data directly. Wang et al. (2017) [12] resampled the normalized points into the local voxel space and then extracted the tree crown from the 2D projection images generated from the voxel space. Morsdorf et al. (2004) [13] used k-means clustering to segment individual trees without altering the original point cloud data. Yang et al. (2020) [14] applied a multidirectional 3D spatial profile analysis to refine the potential treetop positions based on the result of watershed segmentation and then adopted k-means clustering to achieve individual tree segmentation. It is able to improve the accuracy of treetop detection but cannot be applied to multilayer forest structures. Liu et al. (2021) [15] utilized the cluster center of higher points algorithm (CCHP) to detect tree positions with LiDAR data, which is less effective when dealing with overlapping crowns with significant height differences. Pang et al. (2021) [16] utilized spectral clustering to isolate individual trees using mean shift voxelization and Nyström approximation. Ma et al. (2022) [17] conducted a comparative analysis of the performance of the watershed segmentation and clustering segmentation on various types of forest ALS data, while also investigating the sensitivity of key parameters associated with different segmentation methods. Liu et al. (2023) [18] examined the effects of data sources and tree species on segmentation accuracy in the context of individual tree crown segmentation utilizing ALS data and image-derived 3D data. Chen et al. (2020) [19] combined the DBSCAN and K-means to segment individual trees from ALS data collected in coal mining areas, providing effective technical support and data reference for forest research in mining regions. Fu et al. (2024) [20] introduced the Dalponte region-growing method for crown delineation, and based on the delineation results, they employed mean-shift voxelization and supervoxel-weighted fuzzy C-means clustering to accurately segment the boundaries of the tree crowns. Zhang et al. (2024) [21] proposed a hierarchical filtering and clustering (HFC) algorithm specifically designed to enhance robustness when processing data with mixed tree species and different leaf conditions.

Different from airborne laser scanning (ALS), the terrestrial laser scanner (TLS) provides more accurate structural information about the understory. Fu et al. (2022) [22] detected the trunks using improved DBSCAN in TLS data and used Hough circle fitting to modify the detection results. Xu et al. (2023) [23] used Topology-based Tree Segmentation (TTS) to segment individual trees. This method extracted the treetops and bottoms from the input point cloud data and then combined them to reconstruct the individual trees using the notion of relevant topological features. Xi et al. (2024) [24] classified and extracted individual trees with a transformer-based neural network. They integrated ALS and TLS data using deep neural networks to accurately extract stem information and achieve the improved segmentation of individual trees. This method effectively reduced the loss of accuracy for short and occluded trees, but it is sensitive to factors such as tree height and neighboring conditions. Cabo et al. (2018) [25] compared the performance of TLS and WLS for tree detection. The detection accuracy of TLS was slightly better than WLS after the measurement of two variables: diameter at breast height (DBH) and tree height (TH).

With the development of neural networks and deep learning, deep learning has been applied more in the fields of computer vision and remote sensing. Deep learning can detect individual trees without considering the value change in key parameters. Zhang et al. (2024) [26] extracted the spatial extent of tree canopies using Mask R-CNN. However, the accuracy of this method was not high enough for precise orchard management. Weinstein et al. (2019) [27] used a semi-supervised deep learning network to extract crowns in RGB imagery. Ferreira et al. (2020) [28] developed a method to map Amazonian palm species at the individual tree crown, based on the results of morphological operations after processing by a fully convolutional neural network model. Lassalle et al. (2022) [29] combined deep learning and watershed segmentation to identify individual trees based on satellite imagery. Ercanlı et al. (2020) [30] applied a deep learning algorithm to predict the relationships between DBH and TH. They trained different models to determine the optimum and best predictive network structure. Zhu et al. (2021) [31] detected the number of individual trees based on the RetinaNet model and PCS algorithm in a coniferous forest and a mixed coniferous forest. Although deep learning is capable of isolating individual trees from large forests and is not affected by the changes in the key parameters of trees, it is time-consuming to select the best deep learning model.

In this paper, we develop a method to extract fruit tree crowns by combining Gaussian fitting and watershed segmentation based on the canopy height model in orchards. There are often crowns overlapping between adjacent fruit trees in some kinds of orchards like citrus orchards. The traditional marker-controlled watershed algorithm is effective for segmenting relatively isolated fruit trees. However, it tends to suffer from under-segmentation when dealing with overlapping trees, often merging adjacent overlapping trees into a single entity. We could obtain the profile points of single rows or columns of fruit trees with treetop locations obtained by local maxima because fruit trees in orchards are generally arranged in rows or columns. And then, Gaussian fitting is adopted to fit the contour curve of the fruit tree crown. After that, we could find the treetop points in LiDAR data by searching in the interval around the local maxima of the fitted curve. Finally, the detected treetop locations are used as markers for the marker-controlled watershed algorithm, enabling the precise segmentation of individual trees.

2. Materials and Methods

2.1. Study Area

This study focused on a citrus orchard located in San Luis Obispo County, California. The farmland of the citrus orchard in this area is divided into several irregularly shaped blocks, with varying planting densities and canopy sizes of citrus trees in different blocks (Figure 1). Watershed Sciences, Inc. (Corvallis, OR, USA), collected Light Detection and Ranging (LiDAR) data and orthophotography across the DCPP San Simeon survey area from 29 January 2013 to 25 February 2013. This dataset is freely available to the public and can be downloaded from OpenTopography [32].

The LiDAR survey utilized a Leica ALS70 sensor in a Cessna Caravan airplane. The Leica system was used for the acquisition of the inland portion of the study area. It was set to acquire 240,000 laser pulses per second and flown at 1100 m above ground level, capturing a scan angle of ±15° from nadir. This laser system was programmed to yield an average native pulse density of ≥8 pulses per square meter over terrestrial surfaces.

2.2. Algorithm Overview

Figure 2 illustrates the workflow from point cloud data preprocessing to the Gaussian fitting–watershed fusion algorithm. In the preprocessing stage (represented by the orange box), by subtracting ground points from the DSM, we primarily isolate the non-ground points that contain tree canopies. Subsequently, all fruit trees within the non-ground points are normalized to the same height plane. After rasterization, we obtain the canopy height model of the orchard. Then, the Gaussian fitting–watershed fusion algorithm is applied to the CHM (represented by the green box). Yellow dots in the blue image represent treetops detected by variable window size. The green line in the cropped blue image is fitted from a column of treetops. The blue curve is the Gaussian curve fitted from the crown profile points. Each component of the algorithm is explained in the following subsections.

2.3. Point Cloud Data Preprocessing

The preprocessing of point clouds typically involves the stitching and adjustment of flight strips, as well as steps such as outlier removal, noise reduction, filtering, and normalization. The point cloud data we used have already undergone flight strip stitching and adjustment, so the preprocessing steps involved in this paper mainly include noise reduction, filtering, and normalization.

The difference between the DSM and ground points is computed to obtain non-ground points, which serves to eliminate the influence of ground information on the segmentation algorithm. Subsequently, normalization is applied so that the Z-axis position of each point in the point cloud represents its absolute height in three-dimensional space. Consequently, the location of the highest point of each fruit tree in the normalized point cloud on the Z-axis can be interpreted as the tree height. The CHM utilized in this study is derived from the rasterization of the processed point cloud, during which the inverse distance weighting interpolation is employed to fill the unfilled grid corners.

2.4. Gaussian Fitting–Watershed Fusion Algorithm

2.4.1. Morphological Reconstruction

We use the pc2dem function in MATLAB to generate the canopy height model of fruit orchards. There are invalid values and noise in the original model that need to be smoothed before treetop detection. This study applies Gaussian filtering [33,34] to get rid of noise, and the mean square error σ in the Gaussian filtering is set to 1. A larger smoothing window size will weaken the effect of crown height transformation, which will make the demarcation in the canopy height model not obvious. We select the 5 × 5 window size to perform smoothing.

There are still some points that could not be removed by smoothing and cause inaccurate detection for treetops. The influence of noise points in the crown and the edge of the crown can be further eliminated through morphological opening and closing, which could reduce the occurrence of false treetops and over-segmentation in the watershed segmentation process. Morphological reconstruction can not only reduce the wrong detection of treetops caused by noise points but also retain the edge information of crowns. Morphological opening reconstruction and closing reconstruction, respectively, use Equations (1) and (2):

(1)$f\circ b={\mathsf{\Phi }}^{\mathit{rec}}(f\circ b,f)$

(2)$f•b={\mathsf{\Psi }}^{\mathit{rec}}(f•b,f)$

In Equations (1) and (2), ∘ and • respectively represent morphological opening operation and morphological closing operation, f represents raster image, b represents structural element, Φ^rec represents morphological dilation reconstruction image, and Ψ^rec represents morphological erosion reconstruction image.

It is possible to simultaneously filter out bright and dark details in gradient images by combining morphological opening and closing reconstructions, reducing position shifts in segmentation caused by noise interference while eliminating over-segmentation resulting from excessive local minima.

2.4.2. Treetop Detection

The variable window size was employed to detect the treetops of fruit trees. This method assigns a variable-size window centered at each point and then iterates through all points to find local maxima as treetop markers. Variable window sizes are obtained by assuming the relationship between tree height and crown width. Crown width is calculated from tree height. The parameters a and b in Equation (3) for this model were estimated using the Least Median of Squares regression.

(3)$cw=a+bh$

where cw presents maximum width of a tree crown and h presents tree height.

2.4.3. Target Point Cloud Extraction

We employ a linear function to fit the distribution of treetops in the plane perpendicular to the Z-axis at Z = 0 because trees in orchards are typically planted in rows or columns in most cases. The polynomial curve fitting model employed in this study is as follows:

(4)$p\left(x\right)=p_1{x}^n+p_2{x}^{n-1}+\dots +p_{n}x+p_n+1$

where n is set to 1.

The distribution of treetop points for single rows or single columns of fruit trees in the orchard always follows the fitted curves. A cuboid space is designed with a fixed width and unlimited height, using the fitted curve as the center. And then, this cuboid space is used to extract target point clouds in canopy height model from LiDAR data. Extracting those points located within this cuboid space yields a series of points that are strip-like, containing location information about the treetops of single rows or columns of fruit trees.

2.4.4. Gaussian Fitting

Polynomial fitting is a common method used to fit curves. But it is limited with regard to effectively expressing complex data such as samples with different features. Polynomial curve fitting is sensitive to noise points, making it inadequate for fitting the profile curve of overlapping fruit trees. Gaussian fitting involves fitting all data points as a whole. It can better reflect the overall distribution of the data [35] and is less sensitive to noise points. The Gaussian curve is a symmetric curve suitable for describing data with symmetrical features. So, it is highly effective for fitting data with symmetric distribution. Additionally, the Gaussian curve has only three main parameters: peak value, peak coordinates, and full-width at half of the maximum [36].

Here, we use the following form to describe Gaussian distribution in Equation (5):

(5)$y_i=y_{\mathit{max}}\ast \exp \left[-{\displaystyle \frac{{\left(x_i-x_{\max }\right)}^2}{S}}\right]$

where (x_i,y_i) presents the coordinates of each input point. y_max presents peak value, x_max presents the position of the peak point on the X-axis, and S presents full-width at half of the maximum.

We need to calculate these three parameters in order to obtain the desired fitted curves based on the point cloud data. Below is the progress of how to calculate the three parameters.

Take the natural logarithm on both sides of Equation (5) to obtain Equation (6):

(6)$\ln y_i=\ln y_{\mathit{max}}-{\displaystyle \frac{x_i^2}{S}}+{\displaystyle \frac{{2x}_i^2{x}_{\mathit{max}}}{S}}-{\displaystyle \frac{x_{\mathit{max}}^2}{S}}$

After substitution, using b₀, b₁, b₂ to simplify Equation (6), we obtain Equation (7):

(7)$Z_i=b_0+b_1{x}_i+b_2{x}_i^2=\left(1x_i{x}_i^2\right)\left[\begin{array}{c}{b}_0\\ b_1\\ b_2\end{array}\right]$

where

(8)$\ln y_i=Z_i,\ln y_{\mathit{max}}-{\displaystyle \frac{x_{\mathit{max}}^2}{S}}=b_0,{\displaystyle \frac{2x_{\mathit{max}}}{S}}=b_1,-{\displaystyle \frac{1}{S}}=b_2$

After rewriting Equation (7) in matrix form and taking measurement error into consideration, we obtain Equation (9):

(9)$\left[\begin{array}{c}{Z}_1\\ \begin{array}{c}{Z}_2\\ ⋮\end{array}\\ Z_n\end{array}\right]=\left[\begin{array}{ccc}1& x_1& x_1^2\\ \begin{array}{c}1\\ ⋮\end{array}& \begin{array}{c}{x}_2\\ ⋮\end{array}& \begin{array}{c}{x}_2^2\\ ⋮\end{array}\\ 1& x_3& x_n^2\end{array}\right]\left[\begin{array}{c}{b}_0\\ b_1\\ b_2\end{array}\right]+\left[\begin{array}{c}{\xi }_1\\ \begin{array}{c}{\xi }_2\\ ⋮\end{array}\\ {\xi }_3\end{array}\right]$

where ξ represents measurement error. However, the effect of the measurement error on the results can be ignored in the actual fitting process, so Equation (9) can be simplified as follows:

(10)$Z=XB$

The least square method is used to estimate the optimal solution of Matrix B so that the variance between the values of the Gaussian curve and the input points is minimized. To solve Matrix B, it is necessary to prove that Matrix X^TX is a non-singular matrix, and the proof procedure is not given in this paper. According to the principle of least squares, the generalized least squares solution for Matrix B can be constructed as follows:

(11)$B={(X^{T}X)}^{-1}{X}^{T}Z$

And then, we can solve parameters y_max, x_max, and S:

(12)$y_{\mathit{max}}=e^{\left(b_0+{\displaystyle \frac{b_1^{2}S}{4}}\right)},x_{\mathit{max}}={\displaystyle \frac{b_{1}S}{2}},S=-{\displaystyle \frac{1}{b_2}}$

A smooth Gaussian curve can be calculated by inputting the X-axis coordinates of the scatters with the above parameters. The spherical points in Figure 3 are the extracted profile point clouds, and the color changes from blue to red, representing the height of the points from low to high. The blue scatter points on the YZ plane result from projecting the profile points onto a plane centered on the line fitted by treetop points and parallel to the Z-axis, effectively representing the profile of adjacent crowns.

The fitted Gaussian curve can be regarded as a one-dimensional vector: V = [v₁, v₂, ⋯, v_n], where v_i, i ∈ [1, 2, 3, ⋯, N] represents splitting the curve into several points and sorting them. To search for the peaks or valleys of the curve, it is necessary to perform first-order differencing on the vector V using Equation (13).

(13)$\mathit{Diffv}\left(i\right)=V\left(i+1)-V\right(i)$

where i ∈ [1, 2, 3, ⋯, N − 1]. Then, we use Equation (14) to determine the sign of each element in Diffv. If Diffv(i) is greater than 0, take 1. If it is less than 0, take −1. If it is equal to 0, take 0.

(14)$\mathrm{sign}\left(x\right)=\left\{\begin{array}{c}1\hspace{1em}\mathrm{if}(x>0)\\ 0\hspace{1em}\mathrm{if}(x=0)\\ -1\mathrm{if}(x<0)\end{array}\right.$

The red marks in Figure 4 mean there is more than one peak point within the same wave peak. We use a new vector Trend to represent the results after the sign operation: Trend = sign(Diffv). And we perform the following operations on the Trend vector: If Trend(i) = 0 and Trend(i + 1) ≥ 0, then set Trend(i) = 1. If Trend(i) = 0 and Trend(i + 1) < 0, then set Trend(i) = −1. Next, perform a first-order difference on the Trend vector to obtain the following vector: R = Diff(Trend). If R(i) = −2, then V(i + 1) represents a peak; if R(i) = 2, then V(i + 1) represents a valley.

In Figure 5, the blue scatter points are the projection points of the crown profile, and the orange curve is the Gaussian curve based on the fitting of these projection points. The red triangles represent the peak points found by our algorithm.

Our algorithm incorporates Gaussian fitting to delineate the contour curves of overlapping tree crowns, using the fitted curves to identify peak points with the findpeaks algorithm (Equations (13) and (14)). This approach enables the detection of all treetop points, providing precise location information for each fruit tree and ensuring accurate treetop markers. Utilizing these precise markers, the watershed algorithm is able to achieve optimal crown segmentation. As shown in Figure 6, two trees with distinct crown sizes and heights are identified as one tree by the traditional watershed algorithm due to the lack of precise markers. The Gaussian fitting approach effectively identifies the treetop of the shorter fruit tree, the crown of which merged with the bigger crown of the taller tree so that these two crowns could be perfectly segmented.

2.4.5. Watershed Segmentation

In the grayscale domain of an image, each pixel is assigned a specific grayscale value, representing a point on the image’s intensity map. These values vary across the image, with regions of higher grayscale intensity resembling mountain peaks and those with lower intensity corresponding to ridges or plains, analogous to topographic features in the real world. The watershed segmentation algorithm operates by inverting the grayscale map and iteratively traversing the pixel values. This process can be visualized as flipping a mountain landscape into a basin and gradually filling it with water. As the water level rises, it begins to overflow from one valley to another. To prevent merging between adjacent regions, virtual dams are constructed along the watershed lines, effectively segmenting the image into distinct pixel groups. In the context of the CHM, individual tree crowns resemble isolated mountains, making the watershed method particularly suitable for segmenting single-tree crowns. However, the performance of the watershed method is highly sensitive to noise, which can lead to over-segmentation or under-segmentation. To mitigate this, Gaussian fitting is employed to identify precise treetop locations, providing robust starting points for pixel traversal and significantly improving segmentation accuracy.

2.4.6. Evaluation Metrics for Detection Accuracy

The tree/non-tree classification accuracies were evaluated using three indicators, i.e., the recall, the precision, and the F1 score:

(15)$\mathit{Recall}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FN}}}\times 100\%$

(16)$\mathit{Precision}={\displaystyle \frac{\mathit{TP}}{\mathit{TP}+\mathit{FP}}}\times 100\%$

(17)$F1={\displaystyle \frac{2·\mathit{Recall}·\mathit{Precision}}{\mathit{Recall}+\mathit{Precision}}}\times 100\%$

where TP is true positive, indicating the number of fruit trees accurately classified as tree crowns. FP, false positive, is the amount of non-tree points mistakenly classified as tree crowns. And FN is false negative, indicating the amount of fruit trees failed to be correctly classified as tree crowns.

The accuracy of tree crown segmentation can be categorized into six classes, each representing different spatial relationships between the reference crown and the segmented crown. The six classes are as follows:

Perfect Match (PM): When a single segmented crown is compared with its reference crown, if the overlapping area between the two exceeds 50% of each crown’s area, it is categorized as a perfect match.

Good Match (GM): When a single segmented crown is compared with its reference crown, if the overlapping area between the two exceeds 50% of either the reference crown’s area or the segmented crown’s area, it is categorized as a good match.

Missed (Mi): When a single segmented crown is compared with its reference crown, if the overlapping area between the two is less than 50% of each crown’s area, it is categorized as a missed detection.

Merging (Me): When a single segmented crown contains multiple reference crowns, and at least two reference crowns overlap with the segmented extracted crown, with each overlapping area greater than 50% of the corresponding reference crown’s area, it is con-sidered a merging crown.

Splitting (Sp): When a single reference crown contains multiple segmented extracted crowns, and at least two segmented crowns overlap with the reference crown, with each overlapping area being greater than 50% of the corresponding segmented crown’s area, it is considered a splitting crown.

Wrong Detection (Wr): Non-tree parts are mistakenly identified as trees.

Based on the above classifications, perfect match and good match are considered accurately segmented crowns, while merged crowns and undetected crowns are considered under-segmentation. Split crowns and wrong detections are considered to be over-segmentation. We use omission error and commission error to evaluate the degree of under-segmentation and over-segmentation of individual tree crowns, respectively. Accuracy (AR, %), Omission Error (OE, %), and Commission Error (CE, %) were calculated according to Equations (18)–(21):

(18)$\mathit{AR}={\displaystyle \frac{N_{\mathit{PM}}+N_{\mathit{GM}}}{N_{\mathit{ALL}}}}\times 100\%$

(19)$\mathit{OE}={\displaystyle \frac{N_{\mathit{Mi}}+N_{\mathit{Me}}}{N_{\mathit{ALL}}}}\times 100\%$

(20)$\mathit{CE}={\displaystyle \frac{N_{\mathit{Sp}}+N_{\mathit{Wr}}}{N_{\mathit{ALL}}}}\times 100\%$

(21)$N_{\mathit{ALL}}=N_{\mathit{PM}}+N_{\mathit{GM}}+N_{\mathit{Mi}}+N_{\mathit{Me}}{+N}_{\mathit{Sp}}+N_{\mathit{Wr}}$

where N_ALL represents the total number of tree crowns corresponding to the six classifications.

3. Results

3.1. Fruit Tree Number Measurement Results

We selected a local area with mixed-overlapping crown trees, and the grid size was set to 0.15 m. Figure 7 shows the canopy height model of citrus orchards. The color variations reflect changes in height, with brighter areas corresponding to higher point cloud elevations. The minimum tree height detection threshold is set to 0.5 m, considering points below this threshold to be non-tree crown points, which are then removed. Following the generation of CHM, morphological reconstruction operations are performed by using approximately circular-shaped structuring elements chosen in this study for their isotropic properties. Subsequently, we use variable window size to detect treetops based on the reconstructed CHM (Figure 7a). Figure 7b demonstrates the result after Gaussian fitting processing. We can find from the figure that the missing treetops are significantly reduced.

The accuracy of fruit treetop detection is shown in Table 1. The recall of only using variable window size is 81.77%, while after Gaussian fitting processing, the recall reached 97.04%. There is also a significant improvement in the F1 score after Gaussian processing, increasing from 89.49% to 98.01%. Since Gaussian fitting processing has a relatively minor impact on FP, the recall is not affected significantly.

3.2. Accuracy of Fruit Tree Crown Segmentation

The peak points obtained from Gaussian fitting are returned to CHM as markers, supplementing the treetops that were undetected using variable window size. After that, the watershed algorithm is used for segmentation. Figure 8 shows the performance of the traditional CHM algorithm and Gaussian fitting–watershed fusion algorithm. Each tree crown is assigned a random color label. The purple crown in Figure 8a is the result of two large adjacent crowns merging, and there are two small crowns on both sides of the purple crown that have been missed. In Figure 8b, it can be found that the purple merging crowns are correctly segmented into a carmine crown and a pink crown, and the small crowns on both sides are also correctly segmented.

The cases of tree crowns merging decreased after supplementing the treetop markers. However, not all extracted individual fruit tree crowns are within their corresponding reference crowns. Some extracted crowns may contain a small number of neighboring crown points. The matching results and accuracy of the traditional algorithm and Gaussian fitting–watershed algorithm are shown in Table 2. The accuracy increased from 70.73% to 90.16%, while the omission error decreased from 28.05% to 8.81%. After Gaussian fitting processing, the number of merged crowns decreased from 46 to 17, while the number of perfect-match crowns increased from 105 to 154, and the number of good-match crowns increased from 11 to 20, which indicates that Gaussian fitting processing followed by watershed segmentation can effectively reduce the merging of adjacent tree crowns during the segmentation process.

3.3. The Influence of the Crown Overlap Degree

In practical orchard cultivation, the degree of overlap between fruit tree crowns can vary significantly within a given area. Therefore, this study further investigated the accuracy of treetop identification and individual tree segmentation under varying degrees of crown overlap, using both traditional CHM and the Gaussian fitting–watershed fusion algorithm.

Three plots of identical size were selected within the same orchard, as shown in Figure 9. These plots were categorized into three groups based on the degree of crown overlap: (1) non-overlapping, (2) mixed overlapping, and (3) highly overlapping. The mixed-overlapping plot includes trees with both highly overlapping and slightly overlapping crowns.

The traditional algorithm and Gaussian fitting algorithm were applied to detect the treetops of fruit trees in the three plots. The performance using the traditional algorithm is shown in Figure 10. In Plot 1, no treetops were missed, but there were instances where two treetops were detected within the same crown. In Plot 2, a higher number of shorter trees were undetected compared to the trees of average height. Although the tree crowns in Plot 3 exhibited significant overlap, the number of undetected trees was lower compared to Plot 2 when using a variable window size.

The detection accuracy for fruit tree treetops with varying degrees of crown overlap is summarized in Table 3. No trees were missed in Plot 1, resulting in the precision, recall, and F1 scores all exceeding 99%. Although the degree of crown overlap in Plot 3 is significantly higher than that in Plot 2, the recall in Plot 3 (89.14%) is considerably higher than that in Plot 2 (70.47%). Therefore, the degree of crown overlap does not appear to be the primary factor affecting the performance of the traditional CHM-based algorithm.

Figure 11 demonstrates that every single individual tree in Plot 1 was correctly segmented. A significant portion of the crowns in Plot 2 were under-segmented. Most of the crowns in Plot 3 were correctly segmented, but a few under-segmented ones were merged. The accuracy of the marker-controlled watershed segmentation without Gaussian fitting for the three plots with varying crown overlap is shown in Table 4. The traditional algorithm achieved an accuracy of 99.51% in Plot 1, with an omission error of 0.5% and no commission error. In Plot 2, the accuracy was 65.44%, with an omission error of 33.09% and a commission error of 1.47%. In Plot 3, the accuracy was 86.36%, which represents a decrease compared to Plot 2, with an omission error of 13.64% and no commission error.

By comparing the segmentation results for Plot 2 and 3, we observed that when the tree height and crown width of the adjacent trees were similar, crown overlap did not significantly affect the accuracy of the traditional algorithm. However, when there was both overlap and a noticeable height difference between adjacent trees, the number of undetected trees increased.

The traditional algorithm achieved no missed detections in Plot 1, eliminating the need for the Gaussian fitting algorithm to supplement undetected treetop markers. Since the traditional algorithm already performed perfectly in Plot 1, the use of the Gaussian fitting algorithm was unnecessary. Figure 12 illustrates the performance of the Gaussian fitting algorithm in Plot 2 and Plot 3, respectively. When applying the traditional algorithm to detect treetops in Plot 2, shorter trees adjacent to taller trees were more likely to be missed compared to when the Gaussian fitting algorithm was used. Most treetops that were missed by the traditional algorithm in Plot 2 were correctly detected by the Gaussian fitting algorithm. Furthermore, no treetops were left undetected after Gaussian fitting processing in Plot 3. Table 3 shows that the recall of the Gaussian fitting algorithm in Plot 2 and Plot 3 exceeded 98%, with precision and F1 scores both surpassing 99%.

Figure 13a,b present the segmentation results after Gaussian fitting processing in Plot 2 and Plot 3, respectively. The number of merged crowns of adjacent trees decreased following Gaussian fitting. In Plot 3, crowns that were previously under-segmented by the traditional algorithm were correctly segmented after supplementing treetop markers using the Gaussian fitting algorithm.

The matching results and segmentation accuracy of the traditional algorithm and the Gaussian fitting–watershed fusion algorithm are summarized in Table 4. Compared to the traditional method, our approach improved the accuracy from 65.44% to 93.78% in Plot 2, reduced the omission error from 33.09% to 4.66%, and caused a slight increase in commission error from 1.47% to 1.55%. In Plot 3, the accuracy increased from 86.36% to 97.16%, the omission error decreased from 13.64% to 2.84%, and the commission errors were still zero.

Figure 14 visually demonstrates the performance improvement in treetop detection and crown segmentation achieved by the Gaussian fitting algorithm over the traditional algorithm in Plot 2 and Plot 3.

4. Discussion

This study proposes a crown segmentation method based on airborne LiDAR point cloud data, which can effectively and accurately extract canopy metrics, providing a reliable basis for automated orchard harvesting and path planning for orchard operation vehicles. Compared to traditional watershed segmentation algorithms, the proposed method improves detection accuracy by using Gaussian fitting to supplement treetops missed by local maximum-based detection. This approach effectively reduces the under-segmentation of overlapping crowns, thereby enhancing the accuracy of individual tree segmentation. In contrast to deep learning-based methods, our approach leverages the geometric distribution characteristics of the canopy point cloud for segmentation, eliminating the need for training models on different datasets. This allows for the rapid and accurate segmentation of orchard canopies.

The proposed method relies on the geometric features of canopy point clouds derived from airborne LiDAR. When airborne LiDAR scans tree species with sparse foliage and small crowns, the resulting canopy point clouds may lack sufficient density to accurately extract meaningful crown features. Utilizing LiDAR systems with higher scan frequencies, which generate denser point clouds, could help improve the results. Additionally, lowering the scanning height could increase point cloud density, although this approach would also extend the data collection time. However, in the absence of foliage, it becomes challenging to extract valid crown features from the tree point cloud, which limits the algorithm’s effectiveness under such conditions. Our future research could be focused on optimizing the individual tree segmentation algorithm by utilizing the geometric characteristics of leafless canopies, enabling efficient and accurate segmentation even for trees without foliage.

5. Conclusions

This study proposed the Gaussian fitting–watershed fusion algorithm for accurately detecting and segmenting fruit trees with crown overlap. Based on the variable window size search method, the fusion of the Gaussian fitting algorithm improves the detection accuracy of fruit trees with overlapping crowns, which solves the problem of low accuracy of the traditional algorithm in isolating individual fruit trees in orchards with overlapping tree crowns. The Gaussian fitting–watershed fusion algorithm achieves higher precision, recall, and F1 scores compared to the traditional algorithm.

After separately applying the traditional algorithm and the Gaussian fitting–watershed fusion algorithm in three orchards with different degrees of crown overlap, it is concluded that the degree of crown overlap is not the primary factor affecting the segmentation accuracy of the traditional algorithm. When adjacent tree crowns simultaneously meet the conditions of overlap and with an obvious height difference, the segmentation accuracy of the traditional algorithm will decrease sharply.

By comparing the results of applying our method and the traditional method in orchards with different degrees of crown overlap, it is evident that the Gaussian fitting–watershed fusion algorithm is less affected by variations in the tree height and overlap degree of adjacent crowns.

These outcomes suggest that the proposed approach can accurately obtain information about fruit trees in orchards, therefore leading to better decisions in agricultural operations without an increment in the costs of manual labor.

Author Contributions

Conceptualization, S.W. and J.J.; methodology, S.W.; software, S.W.; validation, L.Z., J.J., S.W., and S.L.; formal analysis, S.W., J.L., and S.L.; investigation, L.Z.; resources, J.J. and L.Z.; data curation, J.L. and M.Z.; writing—original draft preparation, S.W.; writing—review and editing, S.W. and J.J.; visualization, M.Z.; supervision, J.J.; project administration, J.J.; funding acquisition, L.Z. All authors have read and agreed to the published version of the manuscript.

Data Availability Statement

The data presented in this study are openly available in OpenTopography at https://doi.org/10.5069/G9CN71V5 (accessed on 24 January 2025), reference number OT.032013.26910.2.

Conflicts of Interest

The authors declare no conflicts of interest.

Footnotes

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

Figures and Tables

Figure 1. An overview of the study area. (a) The location of the study area and plots. (b1) plot with non-overlapping trees, (b2) plot with mixed overlapping trees, (b3) plot with highly overlapping trees.

Figure 2. Workflow of point cloud data preprocessing and Gaussian fitting–watershed fusion algorithm.

Figure 3. Canopy profile points and their projection points on the corresponding plane.

Figure 4. The graph displays a curve with red markers indicating more than two peaks within a single crest and a green marker representing a valley.

Figure 5. The projection points of the crown profile in the target plane and the peak finding results based on the curve fitted by Gaussian function.

Figure 6. The difference between our algorithm and the traditional watershed algorithm in dealing with overlapping tree crowns.

Figure 7. CHM with treetop markers, red markers represent treetops. (a) Performance of treetop detection by traditional algorithm. (b) Performance of treetop detection by Gaussian fitting algorithm.

Figure 8. Vertical view of individual tree segmentation, the circle areas are the segmentation results comparison of the local region between the two methods. (a) Performance of individual tree segmentation by traditional algorithm. (b) Performance of individual tree segmentation by our algorithm.

Figure 9. CHM of three plots with different degrees of overlap. (a) Plot 1: completely non-overlapping tree crowns. (b) Plot 2: mixed overlapping tree crowns. (c) Plot 3: highly overlapping tree crowns.

Figure 10. Performance of treetop detection by traditional CHM algorithm. (a) Plot 1 with detected treetops. (b) Plot 2 with detected treetops. (c) Plot 2 with detected treetops.

Figure 11. Performance of individual tree segmentation processed by traditional CHM algorithm. (a) Vertical view of individual tree segmentation of Plot 1 processed by traditional CHM algorithm. (b) Vertical view of individual tree segmentation of Plot 2 processed by traditional CHM algorithm. (c) Vertical view of individual tree segmentation of Plot 3 processed by traditional CHM algorithm.

Figure 12. Performance of treetop detection by Gaussian fitting algorithm. (a) Plot 2 with detected treetops. (b) Plot 3 with detected treetops.

Figure 13. Performance of individual tree segmentation processed by Gaussian fitting algorithm. (a) Vertical view of individual tree segmentation of Plot 2 processed by Gaussian fitting algorithm. (b) Vertical view of individual tree segmentation of Plot 3 processed by Gaussian fitting algorithm.

Figure 14. Comparison of treetop detection and crown segmentation results using traditional CHM and Gaussian fitting. (a) Treetop detection accuracy in Plot 2. (b) Treetop detection accuracy in Plot 3. (c) Segmentation accuracy in Plot 2. (d) Segmentation accuracy in Plot 3.

Figure 14. Comparison of treetop detection and crown segmentation results using traditional CHM and Gaussian fitting. (a) Treetop detection accuracy in Plot 2. (b) Treetop detection accuracy in Plot 3. (c) Segmentation accuracy in Plot 2. (d) Segmentation accuracy in Plot 3.

Table 1

Accuracy of treetop detection of traditional algorithm and Gaussian fitting–watershed algorithm.

	Traditional CHM	Gaussian Fitting
Recall (%)	81.77	97.04
Precision (%)	98.81	98.99
F1 score (%)	89.49	98.01

Table 2

Matching results and accuracy of traditional algorithm and Gaussian fitting–watershed algorithm.

Number of Trees	Traditional CHM	Gaussian Fitting
Perfect Match (PM)	105	154
Good Match (GM)	11	20
Missed Mi	0	0
Merged Me	46	17
Split Sp	0	0
Wrong Wr	2	2
Accuracy AR (%)	70.73	90.16
Omission Error OE (%)	28.05	8.81
Commission Error CE (%)	1.22	1.04

Table 3

Accuracy of fruit treetop detection with three different degrees of crown overlap.

	Traditional CHM			Gaussian Fitting
	Plot 1	Plot 2	Plot 3	Plot 2	Plot 3
Recall (%)	99.51	70.47	89.14	98.97	98.64
Precision (%)	100	99.27	1	99.48	1
F1 score (%)	99.75	82.42	94.26	99.22	99.32

Table 4

Matching results and accuracy of tree crowns with three different degrees of overlap.

Number of Trees	Traditional CHM			Gaussian Fitting
	Plot 1	Plot 2	Plot 3	Plot 2	Plot 3
Perfect Match (PM)	201	71	154	152	183
Good Match (GM)	0	18	17	29	22
Missed Mi	1	0	3	1	3
Merged Me	0	45	24	8	3
Split Sp	0	1	0	2	0
Wrong Wr	0	1	0	1	0
Accuracy AR (%)	99.51	65.44	86.36	93.78	97.16
Omission Error OE (%)	0.50	33.09	13.64	4.66	2.84
Commission Error CE (%)	0	1.47	0	1.55	0

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