# Measuring Tree Diameter with Photogrammetry Using Mobile Phone Cameras

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## Abstract

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^{2}= 0.95; RMSE = 2.71 cm compared to manual measurements) while saving time during both the data-collection stage and data-entry stage of field sampling. Importantly, we compare measurements of the same tree across users of the phone application in order to determine the per-user, per-tree, and per-species uncertainty associated with each form of measurement. Strong agreement between manual and digital measurements suggests that digital sensing technologies have the potential to facilitate the efficient collection of high-quality and auditable data collected by non-experts but with some important limitations compared to traditional tree measurement approaches. Most people in the world own a smartphone. Enabling accurate tree inventory data collection through mobile phones at scale can improve our understanding of tree growth and biomass accumulation and the key factors (e.g., climate change or management practices) that affect these processes, ultimately advancing forest science and management.

## 1. Introduction and Background

#### 1.1. Background and Previous Work

^{2}= 0.96) between LiDAR-based and manual measurements. However, the LiDAR hardware required for this application is only available on iPhones from 2020 onwards, which prohibits the use of the approach on older mobile phone models, which make up the majority of mobile devices in most areas of the world. Fan et al. (2019) [10] developed an algorithm based on Simultaneous Localization and Mapping (SLAM; [19]) applied to a Time of Flight (TOF) camera that uses infrared light in order to estimate tree diameters. Their results suggest a relative RMSE of 1.26 cm, or 6.4%. Although promising, this approach requires an infrared light source, which is not typically included with mobile phone camera units. Holcomb et al. (2023) [14] developed an algorithm that uses LiDAR and camera data in order to estimate tree diameter via segmentation, filtering, depth estimation, and trunk boundary identification. The approach produced an RMSE of 3.7 cm and an R

^{2}of 0.97 when evaluated against manually measured diameters and has the advantage of adequate performance, even in occluded conditions.

#### 1.2. Study Goals

## 2. Methods

#### 2.1. Description of Mobile Phone Application

#### 2.2. Description of Field Trials

#### Preprocessing of Field Data

_{manual}× N

_{phone}= 2 × 2 = 4). Similarly, there were six combinations for trees measured thrice through the mobile application (N

_{manual}× N

_{phone}= 2 × 3 = 6). Because 47 trees were measured thrice using the phone application, while 61 were only measured twice, iterating through all combinations provided a total of 567 samples ([47 × 6] + [61 × 4]). However, because some diameter measurements collected for a given tree matched exactly (i.e., there was no difference between the first and second manual diameter measurements for that tree, which produces duplicates when making pairs), we eliminated duplicate points from the dataset. This final step in the procedure resulted in 367 paired samples describing the 108 total trees at the Kentland site. When combined with the data collected at Catawba (measured only once using each method), the total size of paired data describing both manual and phone-based measurements was 414 samples.

#### 2.3. Statistical Analyses

_{i}are the true values, x

_{i}are the predicted values, and n is the number of samples.

_{i}are the true values, x

_{i}are the predicted values, and n is the number of samples.

^{2}correlation coefficient measures the strength of correlation between two variables. It is defined as follows:

_{i}are the true values, x

_{i}are the predicted values, and $\stackrel{-}{y}$ is the mean of the true values.

_{i}are the true values, x

_{i}are the predicted values, and n is the number of samples.

_{c}) measures the degree of agreement between two variables that rate, code, or assess the same phenomenon. It is defined as follows:

^{2}); σ

_{x}and σ

_{y}are the variances of x and y, respectively; and µ

_{x}and µ

_{y}are the means of x and y, respectively. In general, a higher ρ

_{c}denotes a stronger relationship between the data.

_{i}are the true values, y

_{i}are the predicted values, N is the total number of samples, and

#### 2.4. Graphical Statistical Analysis

#### 2.5. Analysis of Uncertainty among Users and Species

#### Statistical Tests

## 3. Results and Discussion

#### 3.1. Results of Statistical Analysis and Species-Level Analysis

^{2}= 0.95) between phone-based and manual tree diameter measurements (Figure 3) was comparable to R

^{2}values reported in past studies that utilized LiDAR or offline postprocessing (e.g., [13,14]). The line of best fit (shown in red in Figure 3; equation shown in legend) and slope of 0.91 also suggest that the phone-based approach underpredicts the true mean diameter for most trees (a slope of 1 would suggest a strong prediction, while a slope of >1 would suggest an overprediction). The analysis included trees with diameters between 0 and 50 cm.

#### 3.2. Graphical Statistical Analysis

#### 3.3. Results of User and Species-Uncertainty Analysis

^{2}= 0.95; RMSE = 2.48 cm).

_{crit}< 1.65), and the p values are < 0.05, the paired T test suggests that we fail to reject the null hypothesis that there is no difference between the means of the two samples at a 95% confidence level.

_{crit}< 1.55), and the p values are all <0.05, which suggests that we can reject the null hypothesis that samples in both groups are drawn from populations with the same mean values. These results intuitively make sense because we observe in the data that the mean diameter values determined using the mobile application are generally lower than those produced by manual measurements. This supports the finding that the sample means and the means of the two underlying distributions are also not the same.

#### 3.4. Limitations and Assumptions

#### 3.5. Discussion of Results and Future Work

^{2}> 0.95; p < 0.01; RMSE = 2.71 cm; concordance correlation > 0.9; Intraclass Correlation > 0.9) indicate this technology can provide reasonable, rapid, and conservative estimates of woody biomass in orchard systems (Figure 3, Figure 4, Figure 5 and Figure 6). Additionally, the phone application has the advantage of automatically logging measurements (as well as images and metadata) to an online database, saving time that technicians would use for data entry and preventing transcription errors. These data can also be used for post hoc quality control and removal of any erroneous measurements.

## 4. Conclusions

^{2}= 0.95) between mobile and manual estimates of diameter suggest that, with modifications, this system can be robust, accurate, and more time-effective than traditional measurement techniques. Widespread adoption of digital technologies for tree inventories has been limited due to (1) the requirements of LiDAR and (2) offline postprocessing. The software developed for this study does not require LiDAR or postprocessing; therefore, such an approach has the potential to be widely deployed on existing phones, which would permit fast, cheap, and accurate data collection by non-experts. This study also analyzed the uncertainty between repeat samples acquired by multiple individuals using the mobile application and multiple acquisitions of manual diameter measurements. Such an exercise is essential to validate the application for broad-scale use, but this type of work has not been widely carried out in previous studies. Although more studies are needed to better understand the context-dependent limitations and uncertainties of mobile phone sensing technology (including the time savings), mobile-enabled estimates of diameter may ultimately help facilitate widespread data collection by non-experts. This stands to improve data collection practices, increase available data, and afford a richer understanding of the environmental and management factors that influence tree growth.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Screen captures of the mobile phone application workflow, demonstrating, in order, measurement of tree (

**A**) height and (

**B**) diameter; (

**C**) selection of species; (

**D**) recording of location; and (

**E**) summary screen of collected data. To measure diameter, the user is prompted to place ‘anchor points’ at the left and right sides of the tree trunk, respectively. The application uses Apple’s ARKit library to detect surfaces and place anchor points.

**Figure 2.**Map data from Google, NASA. (

**A**) Map of the study location in Blacksburg (red star), Virginia (black shading), USA, is shown. (

**B**) Aerial image of the Kentland Study site composed of 58 Honey Locusts and 50 Black Walnuts aged 27 years; (

**C**) Aerial image of the Catawba Study Site, composed of 20 Black Walnuts, 14 Black Locusts, and 13 Loblolly Pines, all aged 7 years.

**Figure 3.**Scatterplot showing the tree diameter measured manually (x-axis) and by the mobile application (y-axis). Results are color-coded by species, and results for the Catawba study area are shown as crosses, while the results for the Kentland study area are shown as circles. The mean error between phone-based and manual measurements was 1.9 cm, and the RMSE was 2.71 cm.

**Figure 4.**Violin plots showing the mean error for each species as a white dot, while error distributions around the mean are shown for each species.

**Figure 5.**Histograms depicting bins and fitted distributions (lines) of manual diameter measurements (blue for Honey Locust, orange for Black Walnut, Green for Black Locust, red for Loblolly Pine) and phone-based diameter measurements (black) for each species. The histograms and fitted distributions show that diameter and height measured using the application are conservative relative to manual measurements, and both approaches have similar distributions.

**Figure 6.**Bland–Altman Plot for tree diameter showing that phone-based measurements of heights and diameters are conservative, and >95% of all measurements are within a two-standard deviation range.

**Figure 7.**Scatterplot showing the tree diameter measured manually (x-axis) and by the mobile application (y-axis). Points correspond to the mean value for each tree, while error bars correspond to the standard deviation of each tree. Results are color-coded by species. The mean error between phone-based and manual measurements was 2.03 cm, and the RMSE was 2.48 cm.

**Figure 8.**Violin plots depicting the mean (white dots) and distribution of diameter (cm, y-axis), estimated by each user (colors), for the two species at the Kentland study site (x-axis).

Mean Error (cm) | Mean Percent Error (%) | RMSE (cm) | R^{2} (Dimensionless) | Concordance Correlation (Dimensionless) | Intraclass Correlation (Dimensionless) | |
---|---|---|---|---|---|---|

Honey Locust (N = 207) | 1.33 | −5.50 | 2.18 | 0.84 | 0.87 | 0.87 |

Black Walnut (N = 180) | 2.45 | −9.62 | 3.19 | 0.95 | 0.94 | 0.93 |

Black Locust (N = 14) | 1.29 | −15.42 | 1.54 | 0.95 | 0.89 | 0.89 |

Pitch-Loblolly Pine (N = 13) | 1.58 | −17.49 | 1.65 | 0.99 | 0.94 | 0.94 |

All (N = 414) | 1.90 | −8.27 | 2.71 | 0.90 | 0.91 | 0.91 |

**Table 2.**Results of statistical tests applied to the field data collected at Kentland. The columns depict the two sets of measurements collected manually, while columns depict the three sets of measurements collected using the mobile application.

(A) Paired T Test | (B) One Way ANOVA | (C) Levene’s Test | ||||
---|---|---|---|---|---|---|

T Statistic (p Value) | F Statistic (p Value) | W Statistic (p Value) | ||||

Manual 1 | Manual 2 | Manual 1 | Manual 2 | Manual 1 | Manual 2 | |

User 1 | −3.27 (0.0014) | −3.45 (0.0008) | 6.81 (0.0097) | 7.46 (0.0068) | 1.21 (0.2735) | 1.03 (0.312) |

User 1 repeat | −2.82 (0.0057) | −2.98 (0.0036) | 5.7 (0.0178) | 6.29 (0.0129) | 1.6 (0.2078) | 1.39 (0.2391) |

User 2 | −3.04 (0.0039) | −3.06 (0.0037) | 6.31 (0.0131) | 6.8 (0.01) | 0.07 (0.7928) | 0.04 (0.8398) |

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**MDPI and ACS Style**

Ahamed, A.; Foye, J.; Poudel, S.; Trieschman, E.; Fike, J.
Measuring Tree Diameter with Photogrammetry Using Mobile Phone Cameras. *Forests* **2023**, *14*, 2027.
https://doi.org/10.3390/f14102027

**AMA Style**

Ahamed A, Foye J, Poudel S, Trieschman E, Fike J.
Measuring Tree Diameter with Photogrammetry Using Mobile Phone Cameras. *Forests*. 2023; 14(10):2027.
https://doi.org/10.3390/f14102027

**Chicago/Turabian Style**

Ahamed, Aakash, John Foye, Sanjok Poudel, Erich Trieschman, and John Fike.
2023. "Measuring Tree Diameter with Photogrammetry Using Mobile Phone Cameras" *Forests* 14, no. 10: 2027.
https://doi.org/10.3390/f14102027