EFDTR: Learnable Elliptical Fourier Descriptor Transformer for Instance Segmentation

Polygon-based object representations efficiently model object boundaries but are limited by high optimization complexity, which hinders their adoption compared to more flexible pixel-based methods. In this paper, we introduce a novel vertex regression loss grounded in Fourier elliptic descriptors, which removes the need for rasterization or heuristic approximations and resolves ambiguities in boundary point assignment through frequency-domain matching. To advance polygon-based instance segmentation, we further propose EFDTR (Elliptical Fourier Descriptor Transformer), an end-to-end learnable framework that leverages the expressiveness of Fourier-based representations. The model achieves precise contour predictions through a two-stage approach: the first stage predicts elliptical Fourier descriptors for global contour modeling, while the second stage refines contours for fine-grained accuracy. Experimental results on the COCO dataset show that EFDTR outperforms existing polygon-based methods, offering a promising alternative to pixelbased approaches. Code is available at https: //github.com/chrisclear3/EFDTR .