Title: Edge Wasserstein Distance Loss for Oriented Object Detection. Abstract: Regression loss design is an essential topic for oriented object detection. Due to the periodicity of the angle and the ambiguity of width and height definition, traditional L1-distance losses and its variants have been suffered from the metric discontinuity and the square-like problem. As a solution, the distribution based methods show significant advantage by representing oriented boxes as distributions. Differing from exploited the Gaussian distribution to get analytical form of distance measure, we propose a novel oriented regression loss, Wasserstein Distance(EWD) loss, to alleviate the square-like problem.Specifically, for the oriented box representation,  we choose a specially-designed distribution whose probability density function is only nonzero over the edges. On this basis, we develop Wasserstein distance as the measure. Besides, based on the edge representation of oriented box, the EWD loss can be generalized to quadrilateral and polynomial regression scenery. Experiments on multiple popular datasets and different detectors show the effectiveness of the proposed method.