# Deep-Learning-Based Automated Palm Tree Counting and Geolocation in Large Farms from Aerial Geotagged Images

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## Abstract

**:**

## 1. Introduction

## 2. Theoretical Overview

#### 2.1. YOLOv3

- Localization loss: we try to maximize the overlap between the ground-truth bounding box of the object and the predicted one.
- Classification loss: the difference between the predicted vector probabilities over the classes and the true one.
- Confidence loss: the disparity metric between the real box confidence score and the predicted one.

- ${\lambda}_{coord}$: This is the weight of the localization loss.
- ${\lambda}_{noobj}$: This is the specific weight of the confidence loss for boxes that do not contain objects.
- ${1\phantom{\rule{-0.166667em}{0ex}}\mathrm{l}}_{ij}^{obj}$: This is an indicator function. It is equal to 1 if the object exists in the cell $ij$, and 0 otherwise.
- ${1\phantom{\rule{-0.166667em}{0ex}}\mathrm{l}}_{i}^{obj}$: This is also a binary weight. It is equal to 1 if the $j$th bounding box is responsible for the prediction, and 0 otherwise.
- ${x}_{i}$ is the ground truth of x while ${\widehat{x}}_{i}$ is its predicted value. Similarly for other variables: y, $\omega $ (width), and h.
- C: This is the confidence score estimated for the bounding box.
- ${p}_{i}\left(c\right)$: The ground truth probability that the $i$th grid cell belongs to the class c, while $\widehat{p}$ denotes the predicted probability by YOLOv3.

#### 2.2. YOLOv4

#### 2.2.1. Bag of Freebies (BoF)

#### 2.2.2. Bag of Specials (BoS)

#### 2.3. Faster R-CNN

- ${p}_{i}$ is the probability that the ith anchor inside a mini-batch corresponds to an object; this probability is generated by the network.
- ${p}_{i}^{\ast}$ is a binary value that equals 1 if the anchor is positive, and 0 otherwise. The anchor is positive if it has one highest IoU overlap with one ground-truth box or the IoU overlap with the ground-truth box is superior to 0.7. The anchor is negative if, for all the ground-truth boxes, the IoU overlap is inferior to 0.3.
- ${t}_{i}$ corresponds to the coordinates of the bounding box predicted by the network.
- ${t}_{i}^{\ast}$ corresponds to the ground-truth bounding box’s coordinates for which the anchor is positive.
- ${L}_{cls}$ corresponds to the classification loss.
- ${L}_{reg}$ corresponds to the regression loss.
- ${N}_{cls}$ and ${N}_{reg}$ are the normalization factors.
- $\lambda $ corresponds to the weight used to balance the two losses.

#### 2.4. Efficient-Det

#### 2.5. Geolocation

#### 2.5.1. Calculation of the Distance to Image Center

#### 2.5.2. Distance Correction

#### 2.5.3. Conversion to GPS Coordinates

Algorithm 1 Palm detection and geolocation. |

## 3. Experiments

#### 3.1. Datasets

#### 3.2. Object Detection

#### 3.2.1. Experimental Setup

#### 3.2.2. Metrics

- IoU: intersection over union. It measures the overlap between the predicted (${B}_{det}$) and the ground-truth (${B}_{gt}$) bounding boxes by dividing the area of their intersection by the area of their union:$$\begin{array}{c}IoU=\frac{Area({B}_{det}\cap {B}_{gt})}{Area({B}_{det}\cup {B}_{gt})}\end{array}$$
- Precision: ratio of true positives (TP) over all detections (true positives and false positives (FP)).$$Precision=\frac{TP}{TP+FP}$$
- Recall: ratio of true positives over the number of relevant objects (true positives and false negatives (FN)).$$Recall=\frac{TP}{TP+FN}$$
- F1 score: harmonic mean of precision and recall.$$F1=2\xb7\frac{Precision\xb7Recall}{Precision+Recall}$$
- AP: average precision for one class. It is an approximation of the area under the precision vs. recall curve (AUC). AP was measured for different values of IoU thresholds (0.5, 0.6, 0.7, 0.8, and 0.9).
- mAP: mean average precision over the two classes. The mAP is the main metric used for evaluating object detectors [48].
- Inference time (in millisecond per image): it measures the average inference processing time per image.

#### 3.2.3. Results

#### 3.2.4. Discussion

#### 3.3. Geolocation Accuracy

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Geolocation of palm trees on PSU campus from different altitudes without any distance correction. Ground truth locations (measured in situ) of 17 selected palms (15 of them placed on a circle, and 2 slightly outside) are indicated as red stars with circles of radius 5 × 10${}^{-5}$ degrees (approximately 5 m) around them, while calculated locations of all detected palms (more than 17), in a series of 4 to 6 images with different yaw angles for each altitude, are indicated as dots of different colors corresponding to different altitudes.

**Figure 2.**Distance correction (d) for the geolocation of palm trees from drone images. H is the drone altitude, h is the (average) palm tree height, and D is the distance between the image center (drone’s vertical projection on earth) and the position of the palm tree summit in the image (supposedly corresponding to the detected bounding box center).

**Figure 4.**Average precision (AP) for each of the two classes (

**left**: Palm,

**middle**: Other trees), and mean average precision (mAP,

**right**) for both classes at different IoU threshold values of the four algorithms on the testing dataset.

**Figure 5.**Box plot of the precision (

**left**) and recall (

**right**) for each algorithm and each class on the testing dataset for different values of IoU (from 0.5 to 0.9).

**Figure 6.**Comparison of the four algorithms in terms of mAP (averaged for IoU values between 0.5 and 0.9 by step of 0.1) and inference time.

**Figure 7.**Comparison of the four algorithms in terms of mAP (averaged for IoU values between 0.5 and 0.9 by step of 0.1) and number of floating operations (in GFLOPS) needed for executing inference on one image. The radius of the circles is proportional to the number of parameters of each network.

**Figure 8.**Average intersection over union (IoU) for each object detector and each class on the testing dataset.

**Figure 9.**Summary of the results of the four object detectors on the ‘Palm’ class for different IoU thresholds (from 0.5 to 0.9). The relative FPS corresponds to the frames per second divided by the maximum obtained value (7.35). The color of inner sectors (representing algorithms and IoU thresholds) corresponds to the average colors of outer sectors belonging to them. The lighter the color, the better the results.

**Figure 10.**Summary of the results of the four object detectors on the ‘Other trees’ class for different IoU thresholds (from 0.5 to 0.9). The relative FPS corresponds to the frames per second divided by the maximum obtained value (7.35). The color of inner sectors (representing algorithms and IoU thresholds) corresponds to the average colors of outer sectors belonging to them. The lighter the color, the better the results.

**Figure 11.**Sample image of the palm counting and geolocation application (from Kharj farm), showing.

**Figure 12.**Sample image of the palm counting and geolocation application (from PSU campus), showing at the top of each detected bounding box (in green for palm and yellow for other trees): the class name, the confidence level, the latitude, and the longitude. The numbers inside the bounding boxes are meant to automatically identify each palm tree by comparing its calculated location to predefined locations (for only 17 palms in this case, enumerated in counter-clockwise order). A few detection mistakes are visible in this image: palm 3 was not detected; palms 12 and 13 were mistaken for palms 11 and 12, respectively; and two false positives appear at the top left.

**Figure 13.**Original UAV image of palms on PSU campus (

**right**) and 4 selected palms (

**left**) used for assessing the accuracy of our geolocation method. The remaining parts of the left image were hidden to obtain only 4 detections and compare their calculated location to the location measured in situ.

**Figure 14.**Calculated locations of 4 selected palms on PSU campus from a series of 15 UAV images, before (

**left**) and after (

**right**) the distance correction explained in Section 2.5.2. The object detector used is Faster R-CNN, and the average palm height used for distance correction is 10 m. The outer red circles around ground truth locations have a radius of 5 × 10${}^{-5}$ degrees (approximately 5 m), while the inner purple circles have a radius of 3 × 10${}^{-5}$ degrees (approximately 3 m).

**Figure 15.**Box plot of the accuracy of our geolocation method for two object detectors and different values of mean palm height used for correction. The value 0 is equivalent to no correction. The locations were calculated from 15 images of 4 selected palms and compared to GPS locations measured in situ.

**Figure 16.**Box plot of the accuracy of our geolocation method after using two different detectors for different values of relative drone altitude. The mean palm height used for distance correction is 10 m.

**Figure 17.**Box plot of the accuracy of our geolocation method on Phantom 4 Pro images, for different values of relative drone altitude. The object detector used is Faster R-CNN, and the mean palm height used for distance correction is 10 m.

Training Dataset | Testing Dataset | |
---|---|---|

Number of images | 279 | 70 |

Percentage | 80% | 20% |

Instances of class “Palm tree” | 8805 | 2345 |

Instances of class “Other tree” | 1596 | 325 |

Object Detector | Feature Extractor | Input Size | Number of Parameters | FLOPS | Learning Rate | Batch Size | Number of Steps | Code Repository |
---|---|---|---|---|---|---|---|---|

Faster R-CNN | Resnet-50 | - Conserves the aspect ratio of the original image. - Either the smallest dimension is 600, or the largest dimension is 1024. | 3.4 × 10${}^{7}$ | 64 G | 3 × 10${}^{-5}$ | 1 | 30,000 | github.com/tensorflow/models/tree/master/research/object_detection Accessed on 21/07/2021 |

YOLO v3 | Darknet-53 | 608 × 608 | 6.2 × 10${}^{7}$ | 139 G | 1 × 10${}^{-4}$ | 64 | 30,000 | github.com/AlexeyAB/darknet Accessed on 21/07/2021 |

YOLO v4 | CSPDarknet-53 | 608 × 608 | 6.4 × 10${}^{7}$ | 127 G | 1 × 10${}^{-3}$ | 64 | 1400 | github.com/AlexeyAB/darknet Accessed on 21/07/2021 |

EfficientDet-D5 | EfficientNet-B5 | 1280 × 1280 | 3.4 × 10${}^{7}$ | 135 G | 1 × 10${}^{-4}$ | 4 | 30,000 | github.com/xuannianz/EfficientDet Accessed on 21/07/2021 |

**Table 3.**Real height (measured in situ) of 17 selected palm trees organized in a circle on PSU campus (see Figure 12).

Palm ID | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Height (in meters) | 15 | 14 | 14 | 13 | 13 | 11 | 8.3 | 8.3 | 9.1 | 8.9 | 10 | 10.1 | 11 | 10.5 | 9.8 | 8.4 | 8.1 |

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**MDPI and ACS Style**

Ammar, A.; Koubaa, A.; Benjdira, B.
Deep-Learning-Based Automated Palm Tree Counting and Geolocation in Large Farms from Aerial Geotagged Images. *Agronomy* **2021**, *11*, 1458.
https://doi.org/10.3390/agronomy11081458

**AMA Style**

Ammar A, Koubaa A, Benjdira B.
Deep-Learning-Based Automated Palm Tree Counting and Geolocation in Large Farms from Aerial Geotagged Images. *Agronomy*. 2021; 11(8):1458.
https://doi.org/10.3390/agronomy11081458

**Chicago/Turabian Style**

Ammar, Adel, Anis Koubaa, and Bilel Benjdira.
2021. "Deep-Learning-Based Automated Palm Tree Counting and Geolocation in Large Farms from Aerial Geotagged Images" *Agronomy* 11, no. 8: 1458.
https://doi.org/10.3390/agronomy11081458