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EFDTR: Learnable Elliptical Fourier Descriptor Transformer for Instance Segmentation
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Proposes EFDTR, a polygon-based instance segmentation transformer that predicts elliptical Fourier descriptors in a first stage and refines contours with phase-aligned vertex regression in a second stage, reaching 43.6 AP on COCO val2017 with ResNet-50.
Problem
Polygon-based instance segmentation suffers from ambiguous vertex-to-target assignment and restrictive geometric assumptions (polar and Cartesian matching), limiting accuracy relative to pixel-based methods.
Approach
Uses elliptical Fourier descriptor phase values as a bijective correspondence between contour points and targets, enabling phase-domain target assignment and a vertex regression loss without rasterization; combines a global EFD-regressing decoder with a polygon refinement decoder, and merges multi-polygon instances via minimum spanning tree auxiliary edges.
Key results
- EFDTR with ResNet-50 reaches 43.6 AP on COCO val2017 (36 epochs), outperforming polygon-based methods such as PolarMask (32.1) and DANCE (34.5).
- With ResNet-101, EFDTR achieves 45.1 AP, surpassing Mask2Former (44.2) and DynaMask (39.0) per the paper's comparison.
- Ablation: first-order EFD gives 40.6 AP versus 29.4 (2nd order) and 31.2 (4th order) under the 12-epoch setting; axis-aligned IoU in varifocal loss gives 41.1 AP vs 40.6 for rotated IoU.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use 6 EFD decoder layers and 3 polygon decoder layers rather than fewer decoder layers (ablation) | EFDTR · COCO val2017 | AP: 39.4 -> 40.6 | Helped |
| Use 1st-order rather than higher-order EFD harmonics (ablation) | EFDTR · COCO val2017 | AP: 40.6 vs 29.4; 40.6 vs 31.2 | Helped |
| Use groups of 2 rather than 4 vertices (ablation) | EFDTR · COCO val2017 | AP: 40.6 -> 40.8 | Helped |
| Use groups of 8 or 16 rather than 4 vertices (ablation) | EFDTR · COCO val2017 | AP: 40.6 -> 40.1; 40.6 -> 39.1 | Hurt |
| Use weighted rather than mean or only-P2 multi-scale feature fusion (ablation) | EFDTR · COCO val2017 | AP: 40.3 -> 40.6; 40.1 -> 40.6 | Helped |
| Use axis-aligned rather than rotated box IoU in varifocal loss (ablation) | EFDTR · COCO val2017 | AP: 40.6 -> 41.1 | Helped |
Surprising findings
- Higher-order EFD prediction (2nd and 4th order) substantially degrades AP relative to first-order EFDs, which the authors attribute to optimization complexity.
- Axis-aligned IoU in the varifocal loss outperforms rotated IoU by 0.5 AP.
Limitations
- Auxiliary edges connecting multiple polygons are not always brought close together, causing artifacts for multi-polygon instances.
- Higher-order EFD terms introduce noise and hinder coarse localization, limiting the expressiveness used in practice.
Experimental setup
Datasets: COCO
Benchmarks: COCO val2017
Metrics: AP AP50 AP75 APS APM APL
Baselines: Mask R-CNN Mask DINO DeepSnake PolarMask DANCE SharpContour BoundaryFormer Mask2Former DynaMask BEIS MixingMask
Builds on: RT-DETR DINO Deformable DETR BoundaryFormer E2EC
Closest papers by meaning
- Instance Segmentation With Mask-Supervised Polygonal Boundary Transformers (CVPR 2022 · similarity 0.88)
- Eigencontours: Novel Contour Descriptors Based on Low-Rank Approximation (CVPR 2022 · similarity 0.87)
- Generalizable Fourier Augmentation for Unsupervised Video Object Segmentation (AAAI 2024 · similarity 0.84)
- PolarNeXt: Rethink Instance Segmentation with Polar Representation (CVPR 2025 · similarity 0.83)
- ShapeEmbed: a self-supervised learning framework for 2D contour quantification (NeurIPS 2025 · similarity 0.83)
- Rethinking Decoders for Transformer-based Semantic Segmentation: A Compression Perspective (NeurIPS 2024 · similarity 0.82)
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