###### Abstract  
Fisheye lens cameras are widely used in such applications where a large field of view (FOV) is necessary. A large FOV can provide an enhanced understanding of the surrounding environment and can be an effective solution for detecting the objects in automotive applications. However, this comes with the cost of strong radial distortions and irregular size of objects depending on the location in an image. Therefore, we propose a new fisheye image warping method called Expandable Spherical Projection to expand the center and boundary regions in which smaller objects are mostly located. The proposed method produces undistorted objects especially in the image boundary and a less unwanted background in the bounding boxes. Additionally, we propose three multi-scale feature concatenation methods and provide the analysis of the influence from the three concatenation methods in a real-time object detector. Multiple fisheye image datasets are employed to demonstrate the effectiveness of the proposed projection and feature concatenation methods. From the experimental results, we find that the proposed Expandable Spherical projection and the LCat feature concatenation yield the best AP performance, which is up to 4.7% improvement compared to the original fisheye image datasets and the baseline model. fisheye lens; spherical projection; object detection +
Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/)]([https://creativecommons.org/licenses/py/4.0/](https://creativecommons.org/licenses/py/4.0/))). Footnote †: This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([[https://creativecommons.org/licenses/py/4](https://creativecommons.org/licenses/py/4)]([https://creativecommons.org/licenses/py/4](https://creativecommons.org/licenses/py/4)). However, this advantage comes at the cost of strong radial distortion. The resulting issues, such as curving and diagonal tilting of objects are increasingly severe towards the edges of the fisheye image. Therefore, the shapes of the objects in the same category are less conformal to each other in different images and the target bounding box contains more unnecessary background. Another notable feature of the fisheye camera is that both relative size and distance are exaggerated. The ultra-wide angle lens shows nearby objects appear much larger, while objects located far away or in the boundary appear much smaller than the lens of perspective cameras. Consequently, the already poor performance of object detectors for small or tiny objects is further degraded. Due to the unique feature of the strong radial distortion, object detection in the fisheye image must solve the two problems:  
* Relatively different object size depending on the location and distance. * Inherent Curving and diagonal tilting of objects in the boundary area. To solve these problems, many investigations have been introduced and they are categorized in the following two main approaches:  
* Object detection using the original fisheye image. * Object detection after fisheye image rectification or undistortion. The first approach is using the original image. Instead of fisheye image rectification or undistortion, they investigate distortion-invariant or rotation-invariant neural networks. SphereNet [9] suggests a distortion-invariant neural network for the omnidirectional images, adapting the sampling grid locations of a convolutional kernel. The SphereNet kernel uses the projection of the spherical camera model to the tangent plane on the sphere, yielding filter outputs which are invariant to latitudinal rotations. Alternatively, a rotation-invariant model which predicts object orientations is proposed by [10; 11].