Estimation of Vegetative Growth in Strawberry Plants Using Mobile LiDAR Laser Scanner

Monitoring of plant vegetative growth can provide the basis for precise crop management. In this study, a 2D light detection and ranging (LiDAR) laser scanner, mounted on a linear conveyor, was used to acquire multi-temporal three-dimensional (3D) data from strawberry plants (‘Honeoye’ and ‘Malling Centenary’) 14–77 days after planting (DAP). Canopy geometrical variables, i.e., points per plant, height, ground projected area, and canopy volume profile, were extracted from 3D point cloud. The manually measured leaf area exhibited a linear relationship with LiDAR-derived parameters (R2 = 0.98, 0.90, 0.93, and 0.96 with number of points per plant, volume, height, and projected canopy area, respectively). However, the measuring uncertainty was high in the dense canopies. Particularly, the canopy volume estimation was adapted to the plant habitus to remove gaps and empty spaces in the canopy point cloud. The parametric values for maximum point to point distance (Dmax) = 0.15 cm and slice height (S) = 0.10 cm resulted in R² = 0.80 and RMSPE = 26.93% for strawberry plant volume estimation considering actual volume measured by water displacement. The vertical volume profiling provided growth data for cultivars ‘Honeoye’ and ‘Malling Centenary’ being 51.36 cm³ at 77 DAP and 42.18 cm3 at 70 DAP, respectively. The results contribute an approach for estimating plant geometrical features and particularly strawberry canopy volume profile based on LiDAR point cloud for tracking plant growth.


Introduction
Strawberry (Fragaria × ananassa) is one of the worldwide grown berry crops with high market value thanks to its perishable but unique appearance, aroma, and being rich in secondary phytonutrients [1,2]. Strawberry is a perennial herbaceous plant that develops fast, with fruit-bearing and maturation occurring within one season after planting [3]. Monitoring of the plant growth is essential to ensure high yield and profitable strawberry production. In the concept of precise horticulture, spatio-temporally resolved data of biomass at different phenological stages can support the optimization of drip irrigation, spraying, and yield prediction [4]. For effective implementation of such precise, data-based production management, timely and non-destructive recording of plant growth information is a prerequisite.
Manual measurements of the leaf area and plant volume can be performed after defoliation. However, after defoliation, the information on the canopy profile and, therefore, light distribution in the canopy, is lost. Frequently analysed leaf area and light interception are, however, not linearly correlated owing to varying distribution of leaf area in the canopy and shading effects as shown in tree crops [5]. The non-destructive analysis of vegetative plant structure and its distribution along the canopy axis (vertical volume profile) would enable new research on the yield physiology of strawberry and other fruit bearing into vertical prisms was shown to improve estimation of canopy volume [36]. However, few LiDAR applications were presented for small fruit-bearing herbaceous plants.
This study was carried out to acquire multi-temporal 3D point cloud data of individual strawberry canopy utilizing a 2D laser scanner mounted on a portable linear conveyor. The objectives of the present study on strawberry plants were (i) to confirm the leaf area estimation with LiDAR, (ii) to adapt the canopy volume estimation with LiDAR considering the habitus of herbal plant, and (iii) to monitor the temporal juvenile growth by means of vertical profiling of canopy volume.
For monitoring juvenile strawberry plants, 'Malling Centenary' (juvenile-1 and juvenile-2, n = 20) and additionally the commercial cultivar 'Honeoye' (n = 20) were analysed from April to July in 2020. Strawberry plants were purchased from the local market in Potsdam, Germany. All juvenile samples were transplanted at 2-3 leaves stage (BBCH 13 [37]) in a greenhouse equipped with drip-fertigation. 'Honeoye' plants were transplanted on 2 April 2020 and the late season cultivar 'Malling Centenary' plants were transplanted on 30 April 2020. Juvenile plants were grown in plastic 5 L planting pot with dimensions of 18 cm × 18 cm × 18 cm.
During the experiment, all plants were measured non-destructively. The plants of four size classes were destructively measured after the experiments considering leaf area, fresh mass, and dry mass. At the end of the monitoring experiments, additionally, the canopy volume was measured destructively (n = 12).

Plant Reference Data
Non-destructive reference data were recorded after each LiDAR scan, capturing the height, width, and number of leaves for each individual plant (n = 55) and repeatedly 5 times for the monitored juvenile plants.
In total, 15 plants of 4 size classes (4 juvenile-1, 4 juvenile-2, 4 mature-1, and 3 mature-2) and 7 plants per cultivar for monitoring the juvenile plant growth were measured destructively in the laboratory to determine fresh mass (FM), dry mass (DM), and leaf area (LA). Plant canopies were cut at ground surface and leaves were separated from stems. The area of all leaves was analysed with a desktop scanner (Scanjet 4850, HP, Palo Alto, CA, USA), in groups of 5-10 leaves. The RGB-images were analysed, considering the sum of pixels of each leaf, with Matlab (2017b, Mathworks, Natick, MA, USA) script [38]. An area of 6241 pixels in the image equaled the area of 1 cm 2 . Finally, entire plants were cut into smaller parts and oven-dried in a thin layer at 80 • C for 24 h until a stable weight was reached [39].
Plant reference volume was analysed by the water displacement method [40]. For this purpose, strawberry canopies (n = 12) were subdivided and submerged, avoiding air bubbles, into a water container with a valve. The displaced water was collected in a beaker and weighed. The weight of the displaced water was divided by temperature-corrected density of water to obtain the canopy volume.

LiDAR Data Acquisition
A 2D LiDAR laser scanner (LMS511 pro, Sick AG, Düsseldorf, Germany), operating based on the time of flight (TOF) measuring principle, was utilized to scan the potted plants at its growing location in field conditions. The sensor emitted photons at 905 nm, with a scanning angle of 180 • , angular resolution of 0.1667 • , and frequency of 25 Hz. The laser scanner was installed at a rigid frame and mounted on a linear tooth-belt conveyor system (Module 115/42, IEF Werner, Germany) of 800 mm length, equipped with a servo positioning controller (LV-servoTEC S2, IEF Werner, Furtwangen, Germany) (Figure 1a,b). The LiDAR sensor was connected via Ethernet to a laptop computer with software developed in Visual Studio (version 16.1, Microsoft, Redmond, WA, USA) for acquisition of data as described earlier [14]. In parallel, the positioning controller was connected to the same computer for data acquisition with a RS-232 serial port, while a S2 Commander software (version 4.1.4201.1.1, IEF Werner, Furtwangen, Germany) was used for configuration and operation. The linear conveyor was configured at 10 mm s −1 (±0.05 mm accuracy) forward speed, with the sensor mounted at 0.6 m from ground level, being at the same height as the strawberry plants.
plants at its growing location in field conditions. The sensor emitted photons at 905 nm, with a scanning angle of 180°, angular resolution of 0.1667°, and frequency of 25 Hz. The laser scanner was installed at a rigid frame and mounted on a linear tooth-belt conveyor system (Module 115/42, IEF Werner, Germany) of 800 mm length, equipped with a servo positioning controller (LV-servoTEC S2, IEF Werner, Furtwangen, Germany) ( Figure  1a,b). The LiDAR sensor was connected via Ethernet to a laptop computer with software developed in Visual Studio (version 16.1, Microsoft, Redmond, WA, USA) for acquisition of data as described earlier [14]. In parallel, the positioning controller was connected to the same computer for data acquisition with a RS-232 serial port, while a S2 Commander software (version 4.1.4201.1.1, IEF Werner, Furtwangen, Germany) was used for configuration and operation. The linear conveyor was configured at 10 mm s −1 (± 0.05 mm accuracy) forward speed, with the sensor mounted at 0.6 m from ground level, being at the same height as the strawberry plants.
Each strawberry plant was scanned from a 1 m distance, presenting each plant from two opposite sides to the laser scanner by turning the pots manually. Scanning the plants at different size classes summed up to 30 scans (15 scans from each side). Juvenile plants were measured in a 2-week interval during the growing season starting from 14 DAP to 77 DAP, summing up to 400 scans when measuring 40 plants from two sides on five dates. Additional, 24 scans were carried out on 12 plants to finally analyse the plant volume destructively.
(a) (b) Figure 1. (a) Photograph of the LiDAR laser scanning system (LMS511 pro, Sick AG, Düsseldorf, Germany) during strawberry plant measurement and (b) a schematic view of the LiDAR system mounted on a linear conveyor measuring strawberry 3D point cloud. θ is the angular step and d is the measured distance by the LiDAR laser scanner.

Reconstruction of 3D Plant Model
Raw LiDAR data were recorded in polar coordinates describing the angle (θ) from 0° to 180° and the distance (d) of each laser hit, which converted to Cartesian coordinates (x, y, z) with Python code (version 3.7, Python Software Foundation, Beaverton, OR, USA). Specifically, x-y planes were defined considering d from sensor centre as origin of coordinate system (Equations (1) and (2)). The displacement of LiDAR scanner in z direction was calculated from the constant forward speed (v) and time difference (Δt) between each vertical line of scan (Equations (3) and (4)).

=
(1) Each strawberry plant was scanned from a 1 m distance, presenting each plant from two opposite sides to the laser scanner by turning the pots manually. Scanning the plants at different size classes summed up to 30 scans (15 scans from each side). Juvenile plants were measured in a 2-week interval during the growing season starting from 14 DAP to 77 DAP, summing up to 400 scans when measuring 40 plants from two sides on five dates. Additional, 24 scans were carried out on 12 plants to finally analyse the plant volume destructively.

Reconstruction of 3D Plant Model
Raw LiDAR data were recorded in polar coordinates describing the angle (θ) from 0 • to 180 • and the distance (d) of each laser hit, which converted to Cartesian coordinates (x, y, z) with Python code (version 3.7, Python Software Foundation, Beaverton, OR, USA). Specifically, x-y planes were defined considering d from sensor centre as origin of coordinate system (Equations (1) and (2)). The displacement of LiDAR scanner in z direction was calculated from the constant forward speed (v) and time difference (∆t) between each vertical line of scan (Equations (3) and (4)).
x LiDAR = d cosθ (1) where d is the distance between a laser point and the sensor, x LiDAR and y LiDAR signify the position of laser point in x and y axes, z LiDAR is the LiDAR position along the linear conveyor axis, z' is the previous position of LiDAR sensor, v is the forward speed of LiDAR sensor (0.01 ms −1 ), and ∆z is the displacement of the LiDAR sensor during time ∆t (s). A distance filter was applied to segment laser points above 2 m distance and discard points generated from background objects. In the pre-processing step, a statistical outlier removal (SOR) filter was applied based on the maximum distance calculated by the sum of mean distance and standard deviation of each point measured to its six neighboring points to determine whether it is an outlier [41]. Subsequently, the point clouds from both sides of strawberry plant were roughly aligned using open-source CloudCompare ® (version 2.10) software [42]. Fine registration was done by minimizing corresponding points' distances according to the iterative closest point algorithm [43], resulting in a complete point cloud of each potted strawberry plant.

Estimation of Plant Parameters
The difference between maximum and minimum point of entire point cloud in the z axis including the growing container was exploited to estimate the plant height. Subsequently, the height of the container was subtracted manually.
The number of canopy points was plotted in the x and y axis. A line connected the points on the boundaries, creating a polygon. Subsequently, the concave hull algorithm was applied for estimating the projected canopy area of each plant [44].
Canopy volume was calculated by segmenting the canopy point cloud in horizontal slices of equal height (S). Each slice of varying height (0.05-10 cm) was projected in the x and y plane, while the Delaunay approach was performed for triangulation to create a network of triangles having no points inside circumscribing circles. The line connecting points was considered as an edge. The network of edges of the triangles was analyzed to detect holes and concavities. To extract holes or voids, a maximum point to point distance (D max ) was set based on minimizing the root mean square percentage error (RMSPE) for volume estimation. Edges greater than D max were removed from the network. In the next step, the bounding polygon using the remaining edges was created. The edges present in the triangulated network were analysed individually. Only those edges that belong to a single triangle were selected [45], because only outer triangles can have edges not belonging to more than one triangle. After connecting the selected edges, one or more polygons were created. The area of the bounding polygon was recorded for each slice and multiplied by its height [46]. The sum provided the volume of canopy (Equation (5)) as one value ( Figure 2).
where V plant is total volume of strawberry canopy, k is number of slices, A k is area of the k-th slice, and S is the height of the slice. The performance of this slicing and summing slice volume estimation approach was compared with two widely-used volume estimation approaches: 3D convex hull [28,29] and voxel-grid [29,30], with a grid size of 1 cm. The accuracy of these three approaches was evaluated in terms of mean bias error (MBE), root mean square error (RMSE), RMSPE, and coefficient of determination (R 2 ) between reference and estimated strawberry canopy volumes. Computational time was recorded and compared.
Applying the most accurate method, the volume of each slice was plotted against the canopy height to obtain the canopy volume profiles during plant growth. Strawberry plant growth rate was calculated from the changes in plant volume during the monitoring period (14 to 77 DAP) [47]. gaps and empty spaces were observed underneath the leaves, while the stem and petiole were still visible in the point clouds (Figure 2a,b). In the matured stage, stem and petiole disappeared from the 3D point cloud owing to a dense canopy with an enhanced numbe of leaves, but gaps and concavities were still present between the leaves (Figure 2c,d). Th results obtained with established 3D point cloud analysis are consistent with earlier stud ies (Table 1).

Canopy Volume Extraction Capturing Four Size Classes
Reconstructed 3D point clouds were obtained from outdoor measurement of four size classes of strawberry plants ( Figure 2). Strawberry plants showed no consistent growth direction, while the shape varied over the plant developmental stages. In the juvenile stage, strawberry canopy was less dense (average 60,660 points per plant) compared with the matured stage (average 451,817 points per plant). In the juvenile stage, gaps and empty spaces were observed underneath the leaves, while the stem and petioles were still visible in the point clouds (Figure 2a,b). In the matured stage, stem and petioles disappeared from the 3D point cloud owing to a dense canopy with an enhanced number of leaves, but gaps and concavities were still present between the leaves (Figure 2c,d). The results obtained with established 3D point cloud analysis are consistent with earlier studies (Table 1). Table 1. Descriptive statistics of estimated strawberry canopy volume using three approaches (slicing and summing slice volume, voxel-grid, and 3D convex hull); errors are provided in terms of mean bias error (MBE), root mean square error (RMSE), root mean square percent error (RMSPE), coefficient of determination (R 2 ) between estimated and reference volume (n = 12), and average computational time per plant. The approach of slicing and summing slice for volume estimation was tested on the strawberry point cloud slice considering the combination of two parameters-maximum point to point distance (D max ) and slice height (S). D max has a key role in the proposed  Figure 3. After removal of the boundary lines larger than D max , the outer lines were applied to calculate the area of the polygon. Considering all size class cases, using D max of 0.15 cm resulted in the lowest boundary and, therefore, area. The use of 10.0 cm D max enhanced the estimated areas, whereas 0.15 cm was visually appropriate for removing gaps and voids, but not working on randomly appearing points. was visually appropriate for removing gaps and voids, but not working on randomly appearing points. The slicing and summing slice volume estimation approaches with Dmax values ranging from 0.05 cm to 10.0 cm were applied on the point clouds of all size classes of strawberry plants, while S was still kept constant (0.1 cm) to demonstrate the effect of Dmax (Figure 4). An overestimation became apparent in the estimated canopy volume of all size classes owing to the gradual increase of Dmax. For Dmax = 10.0 cm, the boundary line connected all the outer points, including the inner spaces and gaps of the slice, resulting in average canopy volumes of 2074 cm 3 , 3369 cm 3 , 50,768 cm 3 , and 105,360 cm 3 for juvenile-1, juvenile-2, mature-1, and mature-2 size classes, respectively. With the smallest Dmax (0.05 cm), the lowest areas for each horizontal slices were obtained as 0.023 cm 3 , 0.025 cm 3 , 0.046 cm 3 , and 0.133 cm 3 considering average canopy volumes for juvenile-1, juvenile-2, mature- The slicing and summing slice volume estimation approaches with D max values ranging from 0.05 cm to 10.0 cm were applied on the point clouds of all size classes of strawberry plants, while S was still kept constant (0.1 cm) to demonstrate the effect of D max (Figure 4). An overestimation became apparent in the estimated canopy volume of all size classes owing to the gradual increase of D max . For D max = 10.0 cm, the boundary line connected all the outer points, including the inner spaces and gaps of the slice, resulting in average canopy volumes of 2074 cm 3 , 3369 cm 3 , 50,768 cm 3 , and 105,360 cm 3 for juvenile-1, juvenile-2, mature-1, and mature-2 size classes, respectively. With the smallest D max (0.05 cm), the lowest areas for each horizontal slices were obtained as 0.023 cm 3 , 0.025 cm 3 , 0.046 cm 3 , and 0.133 cm 3 considering average canopy volumes for juvenile-1, juvenile-2, mature-1, and mature-2 size classes, respectively. These volume results were certainly an underestimation of the actual volume, pointing to the necessary optimisation of D max and S before application of the proposed volume approach.  To determine the optimum value of Dmax and S, reference plant (n = 12) volume data obtained by water displacement technique were used. The proposed volume estimation technique was applied for all reference strawberry plant point clouds using a combination of Dmax ranging from 0.05 cm to 1.0 cm and S ranging from 0.05 to 1.0 cm applied iteratively. Root mean squared percent error (RMSPE) between reference volume and volume obtained using the proposed approach showed RMSPE starting from 99.93 % at 0.05 cm of Dmax and gradually decreasing to 26.93 % at 0.15 cm. However, RMSPE again increased with a higher Dmax. Dmax of 1 cm produced the highest RMSPE of 1318 %. Similarly, the RMSPE for varying S from 0.05 to 1.0 cm, with Dmax = 0.15 cm, is shown in Figure 5b. Minimal RMSPE values were found for S ≤ 0.1 cm, whereas enhanced S resulted in higher measuring uncertainty (Figure 5b). The computational time increased with enhanced Dmax and reduced S (Figure 5c,d). To determine the optimum value of D max and S, reference plant (n = 12) volume data obtained by water displacement technique were used. The proposed volume estimation technique was applied for all reference strawberry plant point clouds using a combination of D max ranging from 0.05 cm to 1.0 cm and S ranging from 0.05 to 1.0 cm applied iteratively. Root mean squared percent error (RMSPE) between reference volume and volume obtained using the proposed approach showed RMSPE starting from 99.93% at 0.05 cm of D max and gradually decreasing to 26.93% at 0.15 cm. However, RMSPE again increased with a higher D max . D max of 1 cm produced the highest RMSPE of 1318%. Similarly, the RMSPE for varying S from 0.05 to 1.0 cm, with D max = 0.15 cm, is shown in Figure 5b. Minimal RMSPE values were found for S ≤ 0.1 cm, whereas enhanced S resulted in higher measuring uncertainty (Figure 5b). The computational time increased with enhanced D max and reduced S (Figure 5c,d).

Comparative Analysis of Different Canopy Volume Estimation Approaches
The estimation of canopy volume of 12 reference strawberry plants was carried out using three approaches of 3D convex hull and voxel-grid methods along with the slicing and summing slice volume estimation approach. The comparison with manual measurement, which was done by the water displacement technique, confirms the feasibility of the proposed volume estimation approach with optimum parameters (D max = 0.15 cm and S = 0.1 cm), as shown in Table 1. Voxel-grid returned slightly enhanced R 2 (0.62) compared with the 3D convex hull approach (R 2 = 0.41), because the voxel-grid approach was able to remove the gaps and holes within the canopy. However, estimation using the voxel-grid approach depends on the voxel-grid size and the approach requires a high computational time. The 3D convex hull approach does not require any optimization of parameters and was the fastest (0.85 s/plant) among these three approaches. However, it could not eliminate any gaps or holes within the point cloud, resulting in very high overestimation.
of Dmax ranging from 0.05 cm to 1.0 cm and S ranging from 0.05 to 1.0 cm applied iteratively. Root mean squared percent error (RMSPE) between reference volume and volume obtained using the proposed approach showed RMSPE starting from 99.93 % at 0.05 cm of Dmax and gradually decreasing to 26.93 % at 0.15 cm. However, RMSPE again increased with a higher Dmax. Dmax of 1 cm produced the highest RMSPE of 1318 %. Similarly, the RMSPE for varying S from 0.05 to 1.0 cm, with Dmax = 0.15 cm, is shown in Figure 5b. Minimal RMSPE values were found for S ≤ 0.1 cm, whereas enhanced S resulted in higher measuring uncertainty (Figure 5b). The computational time increased with enhanced Dmax and reduced S (Figure 5c,d).

Comparative Analysis of Different Canopy Volume Estimation Approaches
The estimation of canopy volume of 12 reference strawberry plants was carried out using three approaches of 3D convex hull and voxel-grid methods along with the slicing and summing slice volume estimation approach. The comparison with manual measurement, which was done by the water displacement technique, confirms the feasibility of the proposed volume estimation approach with optimum parameters (Dmax = 0.15 cm and S = 0.1 cm), as shown in Table 1. Voxel-grid returned slightly enhanced R 2 (0.62) compared with the 3D convex hull approach (R 2 = 0.41), because the voxel-grid approach was able to remove the gaps and holes within the canopy. However, estimation using the voxelgrid approach depends on the voxel-grid size and the approach requires a high computational time. The 3D convex hull approach does not require any optimization of parameters and was the fastest (0.85 s/plant) among these three approaches. However, it could not eliminate any gaps or holes within the point cloud, resulting in very high overestimation. Table 1. Descriptive statistics of estimated strawberry canopy volume using three approaches (slicing and summing slice volume, voxel-grid, and 3D convex hull); errors are provided in terms of mean bias error (MBE), root mean square error (RMSE), root mean square percent error (RMSPE), coefficient of determination (R 2 ) between estimated and reference volume (n = 12), and average computational time per plant.

Summary Statistics and Correlations of Reference Plant Variables for Four Size Classes
The number of points per plant, canopy height, ground projected canopy area, and manually measured data ( Table 2) appeared normally distributed. All parameters increased with enhanced plant size.
Fresh mass, dry mass, and leaf area of plants measured in the laboratory appeared to be correlated with LiDAR-estimated variables ( Table 3). The number of points per plant 3D point cloud showed the highest coefficient of determination (R 2 ) of 0.99, 0.99, and 0.98 with FM, DM, and leaf area, respectively, followed by other LiDAR-derived variables. However, the leaf area estimation appears to have high measuring uncertainty owing to occlusions in the dense canopies of mature plants. Table 2. Descriptive statistics of LiDAR-estimated parameters (points per plant (PPP), height (h), and ground projected canopy area (canopy area)) and manually measured variables (fresh mass (FM), dry mass (DM), and leaf area (LA)) of strawberry canopies capturing four size classes (n = 15). Older leaves that accumulated high biomass and leaf area were expanded, resulting in enhanced leaf density in mature leaves compared with young leaves. To obtain the relationships between manually measured leaf area of strawberry plants and LiDAR-derived variables, linear regression analysis was performed. The leaf area was highly correlated to the number of points in 3D point clouds (R 2 = 0.78). Furthermore, LiDAR-estimated canopy volume revealed a high correlation with the leaf area. However, a reduced correlation was observed between the LiDAR-estimated plant height and ground projected canopy area with leaf area in juvenile plants (R 2 = 0.20 and 0.25). However, these relationships were more pronounced when all size classes were considered (R 2 = 0.93 and 0.96), outweighing the effect of straight upright growth of young leaves in juvenile plants and measuring uncertainty due to dense canopies.

Canopy Volume
The juvenile development of two strawberry cultivars was measured in situ with LiDAR scanner in outdoor conditions throughout the growing season. The canopy volume was estimated from 3D LiDAR point cloud data using the proposed volume estimation method with D max 0.15 cm and S = 0.10 cm according to the findings on reference plant volume obtained by the water displacement method. Both cultivars showed a gradual change in volume during the measurement period (Figure 6a). However, cultivar 'Malling Centenary' showed a rapid increase from 14 to 28 DAP compared with cultivar 'Honeoye'. In the following observations, a similar progressive increase in canopy volume was found for both cultivars. The first LiDAR scan was performed at 14 DAP, when leaves (n = 5-7) were immature and standing straight upwards. Subsequently, more leaves grew and young leaves were expanded, and the old leaves were laid down, losing their upright habitus owing to increase in mass and loss of turgor. Consistently, the shape of plants changed during the observation period. The average volume was increased from 35.5 cm 3 to 51.36 cm 3 for 'Honeoye' cultivar, whereas for the 'Malling Centenary', the average volume was increased from 8.92 cm 3 to 42.18 cm 3 .
due to dense canopies.

Canopy Volume
The juvenile development of two strawberry cultivars was measured in situ with Li-DAR scanner in outdoor conditions throughout the growing season. The canopy volume was estimated from 3D LiDAR point cloud data using the proposed volume estimation method with Dmax 0.15 cm and S = 0.10 cm according to the findings on reference plant volume obtained by the water displacement method. Both cultivars showed a gradual change in volume during the measurement period (Figure 6a). However, cultivar 'Malling Centenary' showed a rapid increase from 14 to 28 DAP compared with cultivar 'Honeoye'. In the following observations, a similar progressive increase in canopy volume was found for both cultivars. The first LiDAR scan was performed at 14 DAP, when leaves (n = 5-7) were immature and standing straight upwards. Subsequently, more leaves grew and young leaves were expanded, and the old leaves were laid down, losing their upright habitus owing to increase in mass and loss of turgor. Consistently, the shape of plants changed during the observation period. The average volume was increased from 35.5 cm 3 to 51.36 cm 3 for 'Honeoye' cultivar, whereas for the 'Malling Centenary', the average volume was increased from 8.92 cm 3 to 42.18 cm 3 .
Absolute growth rates of the strawberry plants of both cultivars were determined from the change in plant volume (Figure 6b). It was found that, at 28 DAP, the absolute growth rate was higher for the 'Malling Centenary' cultivar (1.55 cm 3 day −1 ) compared with 'Honeoye' (0.15 cm 3 day −1 ). However, the growth rate of 'Malling Centenary' declined sharply in next 14 days. Conversely, 'Honeoye' cultivar showed a gradual increase in the absolute growth rate and displayed 0.47 cm 3 day −1 at DAP.  Absolute growth rates of the strawberry plants of both cultivars were determined from the change in plant volume (Figure 6b). It was found that, at 28 DAP, the absolute growth rate was higher for the 'Malling Centenary' cultivar (1.55 cm 3 day −1 ) compared with 'Honeoye' (0.15 cm 3 day −1 ). However, the growth rate of 'Malling Centenary' declined sharply in next 14 days. Conversely, 'Honeoye' cultivar showed a gradual increase in the absolute growth rate and displayed 0.47 cm 3 day −1 at DAP.
Time series of change in vertical volume profile were obtained when plotting the histogram of points per plant. Data are shown for a typical sample plant from 14 to 77 DAP (Figure 7). Optimum D max (0.15 cm) and S (0.10 cm) found in this study ( Figure 5) provided the most realistic LiDAR-estimated volume. From the time series of vertical volume profiles, it can be observed that the plants showed changes in volume and shape. At 14 DAP (Figure 7a), when the plants showed 3-5 leaves, the existing leaves had long petiole standing upwards, which was accountable for almost similar canopy height. At 28 DAP, new leaves were developing and the shape of profile changed with the upper part producing higher volumes. Subsequently, leaf area and total canopy volume increased until 77 DAP (Figure 7e). 14 DAP (Figure 7a), when the plants showed 3-5 leaves, the existing leaves had long petiole standing upwards, which was accountable for almost similar canopy height. At 28 DAP, new leaves were developing and the shape of profile changed with the upper part producing higher volumes. Subsequently, leaf area and total canopy volume increased until 77 DAP (Figure 7e).

Discussion
In this study, a canopy growth estimation by means of 3D LiDAR point cloud analysis was proposed and evaluated on four different size classes of strawberry canopy ranging from young to mature. Vegetative growth of juvenile strawberry plants was assessed over the season in terms of adapted canopy volume estimated by LiDAR laser scanner introducing vertical canopy volume profiling in strawberry plants.
Yamamoto and co-workers [20] used a depth camera system placed in a stationary position while strawberry plants were placed on a movable planting bench underneath. In the present experiment, a 2D LiDAR laser scanner was mounted on a linear, electric conveyor to scan each individual strawberry plant with growing container from two sides in the fruit production environment. Because of the electric engine, LiDAR movement during scanning strawberry plants was reduced considering perturbation due to 3D rotation (roll, pitch, and yaw). However, measurements were carried out in outdoor conditions. While the light is supposed to be a marginal influencing factor in LiDAR measurements, the wind has an impact on the data, because strawberry plants have no stiff woody structure. Therefore, wind can cause considerable height reduction and shape deformation visible in the point cloud. To overcome this challenge, extreme weather conditions were avoided, but an influence can still be assumed.
Slicing the point cloud and estimation of individual slice volume method proposed in this study was applied for strawberry canopy volume estimation in different plant sizes. Xu et al. [33] proposed a tree crown volume estimation approach by slicing the point cloud, but applying a different slice volume estimation method. As the strawberry plants show an irregular shape and structure, the present volume estimation approach targeted the removal of gaps. An effective approach was shown by Yan et al. [35] for estimation of point cloud slice to calculate the canopy volume of individual trees and found the smallest volume compared with other existing canopy volume estimation methods. In this study, two parameters were introduced to improve the volume estimation accuracy: slicing and adapted Dmax and S, which were calibrated by measuring the canopy volume by means of the water displacement technique. Different S (0.05-10 cm) were tested along with varying Dmax values ranging from 0.05 to 10 cm. The lowest RMSPE was found for 0.1 cm and 0.15 cm of S and Dmax, respectively. The resulting RMSPE was still rather high with > 20 %, but comparatively smaller than the RMSPE found for different combinations of S and Dmax. The computational complexity was observed in terms of average time required per plant.

Discussion
In this study, a canopy growth estimation by means of 3D LiDAR point cloud analysis was proposed and evaluated on four different size classes of strawberry canopy ranging from young to mature. Vegetative growth of juvenile strawberry plants was assessed over the season in terms of adapted canopy volume estimated by LiDAR laser scanner introducing vertical canopy volume profiling in strawberry plants.
Yamamoto and co-workers [20] used a depth camera system placed in a stationary position while strawberry plants were placed on a movable planting bench underneath. In the present experiment, a 2D LiDAR laser scanner was mounted on a linear, electric conveyor to scan each individual strawberry plant with growing container from two sides in the fruit production environment. Because of the electric engine, LiDAR movement during scanning strawberry plants was reduced considering perturbation due to 3D rotation (roll, pitch, and yaw). However, measurements were carried out in outdoor conditions. While the light is supposed to be a marginal influencing factor in LiDAR measurements, the wind has an impact on the data, because strawberry plants have no stiff woody structure. Therefore, wind can cause considerable height reduction and shape deformation visible in the point cloud. To overcome this challenge, extreme weather conditions were avoided, but an influence can still be assumed.
Slicing the point cloud and estimation of individual slice volume method proposed in this study was applied for strawberry canopy volume estimation in different plant sizes. Xu et al. [33] proposed a tree crown volume estimation approach by slicing the point cloud, but applying a different slice volume estimation method. As the strawberry plants show an irregular shape and structure, the present volume estimation approach targeted the removal of gaps. An effective approach was shown by Yan et al. [35] for estimation of point cloud slice to calculate the canopy volume of individual trees and found the smallest volume compared with other existing canopy volume estimation methods. In this study, two parameters were introduced to improve the volume estimation accuracy: slicing and adapted D max and S, which were calibrated by measuring the canopy volume by means of the water displacement technique. Different S (0.05-10 cm) were tested along with varying D max values ranging from 0.05 to 10 cm. The lowest RMSPE was found for 0.1 cm and 0.15 cm of S and D max , respectively. The resulting RMSPE was still rather high with >20%, but comparatively smaller than the RMSPE found for different combinations of S and D max . The computational complexity was observed in terms of average time required per plant. Subsequently, after finding the optimum parameters of the proposed volume estimation approach, two other existing tree canopy volume estimation approaches (3D convex hull and voxel-grid) were compared. Effective removing of gaps and holes within the canopy was important, and reducing the computational time was in consideration. A 3D convex hull was widely used volume estimation from 3D point cloud data owing to its faster computational time. However, it could not meet the acceptable accuracy for the irregular-shaped 3D point cloud such as tree canopy when compared with accurate reference volume as shown in this study. Because its bounding geometrical approach included all the holes and cavities presented in the point cloud [34], the voxel-grid approach resulted in higher accuracy than the 3D convex hull approach for the strawberry point cloud. However, voxelization of 3D point cloud data required a high computational time and power, which mostly depended on the size of the voxel grid. The smaller voxel size is able to estimate volumes with enhanced accuracy, but it also has a high computational time cost. Therefore, optimization of voxel size can be considered as a limitation of this approach [48]. Both of these approaches were applied previously for estimation of tree crown volume in orchard or forestry where reference volume was determined by different geometrical shape approaches. In this study, methods were compared to precise reference volume determined by water displacement technique. In comparison, slicing and summing slice volume estimation approach was found more accurate and required less computational time than voxel-grid in this study.
Hosoi et al. [30] demonstrated the method for analyzing the vertical distribution of volume for individual trees estimated by voxel-based volume estimation. In the present study, time series of LiDAR 3D point cloud analysis revealed the growth patterns of juvenile strawberry plants based on total canopy volume of the two strawberry cultivars. Furthermore, the time series of canopy volume profiles additionally revealed the pattern of change in volume distribution along the vertical canopy axis (Figure 7). At first measurement at 14 DAP of plantation, an average of 5-7 leaves was found, and most of them were standing upward. Both cultivars have shown similar growth patterns considering the straight upright leaves and petioles after planting and subsequently more mature leaves with smaller and shorter petioles. More physiological explanation was provided by Takahashi et al. [19]. The authors applied an RGB-depth camera, which is affected by varying lighting conditions and, therefore, is difficult to use in a production environment. However, the effect of temperature and amount of light received by the leaves on the strawberry plant height was shown. With the present benchmark of volume estimation, a methodology is available for further physiological analysis and support of variable rate plant protection considering the volume profile of the canopies (Figure 7).
LiDAR point cloud derived plant geometrical parameters were correlated to other destructively measured variables. Strong linear relationships were observed for the number of points per plant with dry mass (R 2 = 0.99) and fresh mass (R 2 = 0.99) of plants. LiDAR derived plant volume also demonstrated good linear relationships for dry mass (R 2 = 0.92) and fresh mass (R 2 = 0.90). Walter el al. [49] found high correlations between above ground biomass and LiDAR estimated volume up to r = 0.86 for wheat. Greaves et al. [50] also revealed a strong correlation (R 2 = 0.92) between harvested biomass and LiDAR-estimated volume for arctic shrubs using terrestrial laser scanning in a close range (2 m). However, plant height and ground projected canopy area exhibited weaker linear relationships with dry mass and fresh mass of plants. Guan et al. [21] tested the linear relationship of similar parameters, although he used an RGB image to reconstruct point cloud using a structure from motion algorithm. With this approach, R 2 = 0.77 was found for canopy volume and dry mass. For LA observation, Guan et al. [21] found R 2 = 0.76 between canopy volume and LA, whereas the current results showed R 2 = 0.97 when all size classes of strawberry plants were considered. As a result, LiDAR point cloud derived strawberry plant parameters could be utilized to model the strawberry plant growth. The introduction of the method in physiological studies or applications in variable rate management should be investigated in future studies.

Conclusions
In this study, the 2D LiDAR laser scanner was mounted on a mobile linear conveyor to scan commercial strawberry plants. This type of linear conveyor mounted 2D LiDAR laser scanner can be further applied in greenhouse or greenhouse crop monitoring, providing 3D dataset of the plants.
A volume estimation technique was proposed based on slicing and summing slice volume from 3D strawberry point cloud. The approach enabled the removal of holes and gaps, resulting in R 2 = 0.80 with a low computational time. Moreover, this approach was capable of extracting volumes of different horizontal layers of canopy, which can generate the vertical canopy volume profile of strawberry plant. Analysis of time series of 3D point cloud data revealed the typical growing pattern of strawberry plants in the vertical canopy profiles.
The relationship between various LiDAR point cloud derived parameters with destructively measured biomass and geometry was confirmed in this study. In conclusion, LiDAR laser scanners mounted on near-ground linear conveyor are a feasible tool for monitoring strawberry plant growth. Data Availability Statement: The data of this study are available from the authors upon reasonable request.