Extracting and exploiting edge information is important for various computer vision tasks. According to the physical characteristics, edges are further categorized into reflectance, illumination, normal, and depth discontinuities. Previous studies for edge discontinuity classification have achieved impressive performance in extracting discontinuities, but the capacity of classification remains limited. This paper proposes TriDecTr, a novel network comprising a transformer-based encoder to improve semantic understanding and a tri-directional decoder to explore relationships among categories. Extensive experiments demonstrate that TriDecTr achieves state-of-the-art performance on the BSDS-RIND dataset with 0.531 in ODS, 0.571 in OIS, and 0.461 in AP. Moreover, TriDecTr significantly narrows the performance gap between illumination edges and the other categories from 0.191 to 0.118 in ODS.