  As one of the most fundamental and challenging problems in computer vision,
object detection tries to locate object instances and find their categories in
natural images. The most important step in the evaluation of object detection
algorithm is calculating the intersection-over-union (IoU) between the
predicted bounding box and the ground truth one. Although this procedure is
well-defined and solved for planar images, it is not easy for spherical image
object detection. Existing methods either compute the IoUs based on biased
bounding box representations or make excessive approximations, thus would give
incorrect results. In this paper, we first identify that spherical rectangles
are unbiased bounding boxes for objects in spherical images, and then propose
an analytical method for IoU calculation without any approximations. Based on
the unbiased representation and calculation, we also present an anchor free
object detection algorithm for spherical images. The experiments on two
spherical object detection datasets show that the proposed method can achieve
better performance than existing methods.
