# Detecting Crop Circles in Google Earth Images with Mask R-CNN and YOLOv3
## 3 Experimental Results  
The experiments were carried out on an image dataset corresponding to the East Oweinat, in the South Western Desert of Egypt (22\({}^{\circ}\)39\({}^{\prime}\)00.7\({}^{\prime\prime}\) N 28\({}^{\circ}\)48\({}^{\prime}\)47.7\({}^{\prime\prime}\) E). The images were exported from Google Earth Pro at an altitude of 20 km. The overall view of the study area and sample images from the dataset are illustrated in Figure 3.  
Figure 3: Left: study area. Right: Sample images at 20 km altitude (Source: Google Earth Pro). Figure 2: Adopted YOLOv3-based crop circle detection network. The dataset totals 24 images, which were split into 4 images for training, 4 images for validation and 16 images for testing purposes. In terms of crop circles, it contains 437 training samples, 519 validation samples and 1555 test samples, making up 17%, 21% and 62% of the total count, respectively. It is worth noting that we adopt a large test set and a small training set in order to mimic a real scenario, where the number of data are limited. Image labeling was carried out by means of the Visual Geometry Group (VGG) image annotator [45]. Note that the crop circles that are not visually clear to the naked eye, or that are partially occluded (e.g., only half of the crop circle is visible, or that the crop circle lies at the border of the image), are omitted during the labeling process. The training was performed via the Google Colab platform on a Tesla T4 GPU with 16 GB memory and a 16 GB RAM; the training rates were set to 0.001 and the remaining parameters were set as mentioned in the original papers of both models. In order to quantify the results, we followed the state-of-the-art object detection metrics, namely the Precision and the Recall. The precision measures the ratio of detected objects that are relevant (i.e., how many crop circles are detected among all the detected objects), whilst the recall measures the ratio of relevant crop circles that were successfully detected, as follow:  
\[Precision\ =\ \frac{True\ Positives}{True\ Positives\ +\ False\ Positives} \tag{2}\]  
\[Recall\ =\ \frac{True\ Positives}{True\ Positives\ +\ False\ Negatives} \tag{3}\]  
where _True Positives_ indicates the crop circles samples that were indeed identified as crop circles, _False Positives_ refers to non-crop circle objects that were mistakenly identified as crop circles and _False Negatives_ refers to crop circles that were not identified. It can be seen from Table 1 that both models yield satisfactory results. However, while Mask R-CNN tends to be more precise, YOLOv3 favors detection over precision. This can be explained by the fact that Mask R-CNN inherently integrates the mask attribute into the learning process, which allows it to learn finer details of the target, yet it is less likely to infer irrelevant objects. However, this comes at the cost of more processing overheads as it runs nearly three times slower. YOLOv3, on the other hand, emphasizes object search over several scale grids, paying more attention to the existence of the target object in the context of the input image, which is translated into a high Recall and a relatively lower precision, while cutting down sharply on the inference time. Detection instances are depicted in Figures 4 and 5, for Mask R-CNN and YOLOv3, respectively. It can be observed that both of the models become less accurate when the crop circles share nearly the same color with the background which constitutes a bottleneck for most object detection endeavors. Further, the detection seems to be achieved rather easily when the crop circle manifests uniform texture/color cues. However, an advantage of Mask R-CNN is that it performs an instance segmentation, providing thereby the precise segment of the crop circle, which suggests a potential farming area measurement. This property can not be availed with the YOLO model as the bounding box does not fit perfectly the crop circle.