## 3 Proposed Method
### Pseudocode of the Proposed Networks
Additionally, we employ the idea of learning anchor boxes based on k-means and genetic algorithm with the distribution of the bounding boxes in real fisheye image dataset, following the method in YOLOv5 ([[https://github.com/ultralytics/yolov5](https://github.com/ultralytics/yolov5)]([https://github.com/ultralytics/yolov5](https://github.com/ultralytics/yolov5)) (accessed on 5 November 2020)). Finally, we use total of 3217 images and evaluate the accuracy with 806 images. #### 4.4.2 Comparison of the Projection

Figure 13 shows the detection result from fisheye and spherical images. Contrary to our expectations, the result shows that the model achieves the highest performance with the fisheye image dataset and the projected image from the spherical-based method gives no positive effect in the accuracy. Accuracy of different projections of YOLOv3-SPP model on WoodScape is shown in Table 9

The assumption of our algorithm is that a principal axis of the camera is parallel to the ground such that the distorted objects appear more vertically straight and conformal when comparing the same category object in other photos. However, the images from the WoodScape, as we understand, are captured with the camera looking down so that more road scene and less sky view is visible, as illustrated in Figure 14.

#### 4.4.3 Comparison of the Concatenated Models

Tables 10-12 shows the \(AP\) of differently concatenated models on fisheye and spherical image from the WoodScape. When evaluating the models with original fisheye images, the YOLOv3-SPP obtains the best results. On the other hand, the SLCat achieves the best \(AP\) on spherical and expanded spherical projection, improving up to 0.4%. Figure 14: (**a**) Camera with a principal axis parallel to the ground from Fisheye-Dongseongro. (**b**) Camera looking downward from WoodScape. (i) and (iii) are the fisheye images and (ii) and (iv) are the spherically projected images. Figure 13: Detection results: (**a**) Synthetic fisheye image; (**b**) Spherical-projected image; (**c**) Expanded-Spherical-Projected image. ### Experiments on Fisheye-Dongseongro

#### 4.5.1 Implementation Details

We set 20 as the mini-batch size, 640 as the size of the image, 350 epochs, 0.00019 initial learning rates, and apply the cosine decay scheduling strategy. The momentum and weight decay are, respectively, set as 0.843 and 0.00036. Additionally, the method of learning the anchor boxes is employed in this dataset as well. Finally, our dataset consists of total of 4012 images, and we evaluate the proposed methods on a test dataset with 1004 images. #### 4.5.2 Comparison of the Projection

Since the proposed method expands in the overall region of the image, especially the center areas where most of small objects are located, the accuracy result shows 11.4% improvement in \(AP_{S}\) compared to the fisheye images, shown in Table 13. Additionally, the expandable projection shows higher detection results in \(AP\) and \(AP_{S}\) from most of the models. At YOLOv3-SPP model, our method achieves 2.6% improvement in \(AP\). The detection results are shown in Figure 15. Since most of the objects are much smaller than the image size, we present cropped example images of the detection result on YOLOv3-SPP from differently projected images. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Image** & \(AP\) & \(AP_{50}\) & \(AP_{75}\) & \(AP_{S}\) & \(AP_{M}\) & \(AP_{L}\) \\ \hline Fisheye & **23.1** & **46.0** & 20.2 & 7.7 & **24.8** & **40.4** \\ Spherical & 22.3 & 44.6 & 19.6 & **8.7** & 23.7 & 38.1 \\ Expanded Spher. & **23.1** & 45.6 & **20.4** & 8.5 & 23.8 & 37.7 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: Accuracy of different projections of SCat model on the WoodScape.