Complete Rotated Localization Loss Based on Super-Gaussian Distribution for Remote Sensing Images

Localization regression in oriented object detection tasks has long faced boundary discontinuity and angular discontinuity problems induced by periodic angles. These problems were successfully resolved by using a 2d Gaussian distribution to modelling the oriented bounding box (OBB). However, the angular information of square-like objects will be lost when they are converted to 2d Gaussian distribution, forming a systematic problem. Its fundamental reason is that when the aspect ratio of the object tends to 1, the equiprobability curve of 2d Gaussian distribution degenerates from an ellipse to a circle, thus losing the orientation information of the rotated object. This results in the bounding boxes of such square-like objects not being learned effectively. To resolve this problem, we used the Lamé curve (or superellipse) to modify the existing 2d Gaussian function and designed a super-Gaussian distribution. This distribution can maintain anisotropy at arbitrary aspect ratios, thus preserving the angular information of the oriented object. We used the Kullback-Leibler (KL) divergence to measure the distance between two super-Gaussian distributions and convert it into a localization loss (SGKLD) by a function. SGKLD is an improved version of KLD loss. By modifying the form of the probability distribution, we elegantly fix the angle missing problem of the traditional Gaussian distribution. We validated the effectiveness of the proposed algorithm on several datasets and obtained the performance of SOTA. Our algorithm achieves a mean average precision (mAP) of 80.07, 76.59, 62.27, and 90.55/98.13 on the DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and HRSC2016 datasets, respectively.