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Fractal Calibration for Long-tailed Object Detection
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Proposes FRACAL, a training-free post-hoc logit calibration for long-tailed object detection that combines class-frequency priors with a fractal-dimension-based spatial-uniformity term computed from box-counting over training-set object centers.
Problem
Long-tailed object detection degrades rare-class performance; existing post-calibration methods use only class frequency and ignore how classes are distributed across image locations.
Approach
Estimate each class's spatial uniformity with the box-counting fractal dimension (grid-size-independent, robust for rare classes) and use it at inference to downweight uniformly spread class predictions, jointly with frequency-based logit adjustment.
Key results
- On LVISv1 with ResNet50 Mask R-CNN, FRACAL reaches 28.6 AP_m and 23.0 AP_r, surpassing GOL (27.7 / 21.4) and LogN (27.5 / 21.8).
- With Swin-S, FRACAL improves rare mask AP by 2.2pp over Seesaw (27.8 vs 25.6), described as 8.6% relative improvement for rare classes.
- Applied to Cascade R-CNN, FRACAL raises box AP from 28.6 to 31.5 on LVISv1 without any training.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add fractal space calibration (S) to class calibration (C) (ablation) | Mask R-CNN ResNet50 with random sampler · LVISv1 val | APm: 26.3 -> 27.3 | Helped |
| Add fractal space calibration (S) to class calibration (C) (ablation) | Mask R-CNN ResNet50 with random sampler · LVISv1 val | APm_r: 16.5 -> 19.0 | Helped |
| Add class calibration (C) without fractal space calibration (ablation) | Mask R-CNN ResNet50 with random sampler · LVISv1 val | APm_r: 8.2 -> 16.5 | Helped |
| Add fractal space calibration (S) without class calibration (ablation) | Mask R-CNN ResNet50 with random sampler · LVISv1 val | APm_r: 8.2 -> 13.7 | Helped |
| Use fractal dimension coefficient λ=2 (ablation) | FRACAL on Mask R-CNN ResNet50 with RFS · LVISv1 val | APm: 28.0 -> 28.6 | Helped |
| Use class-calibration log base β=10 (ablation) | Class calibration on Mask R-CNN ResNet50 with random sampler · LVISv1 val | APm: 19.9 -> 26.3 | Helped |
| Replace fractal calibration with grid-based calibration at G=4 (ablation) | Mask R-CNN ResNet50 · LVISv1 val | APm_r: 23.0 -> 10.5 | Hurt |
| Invert space weighting to upweight uniformly located classes (ablation) | FRACAL on Mask R-CNN ResNet50 · LVISv1 val | APm: 27.4 -> 28.6 | Hurt |
| Apply FRACAL to ATSS | ATSS ResNet50 · LVISv1 val | APb_f: 31.6 -> 30.9 | Hurt |
| Apply FRACAL to GFLv2 | GFLv2 ResNet50 · LVISv1 val | APb: 26.6 -> 28.2 | Helped |
| Apply FRACAL to Mask R-CNN | Mask R-CNN ResNet50 · COCO | APm: 35.4 -> 35.8 | Helped |
| Apply FRACAL to APA | APA Faster R-CNN ResNet50 · V3Det | APb: 29.9 -> 30.3 | Helped |
Surprising findings
- Naively adding a grid-based location prior hurts rare-class performance as grid size grows (G=4 gives 10.5 AP_r vs 22.4 at G=1), due to sparsity.
- Inverting the spatial weighting (FRACAL-Opposite, upweighting uniform classes) performs worse than standard FRACAL, suggesting removing spatial bias is preferable to rectifying it.
Limitations
- Gains on sigmoid detectors (ATSS, GFLv2) require a binary variant and reduce frequent-class AP slightly.
- Fractal dimension correlates only weakly with class frequency, and hyperparameters (log base beta, lambda) are tuned via search on LVIS.
- Assumes object distribution p(o,u) is the same in train and test sets; gains on less imbalanced datasets are modest (~0.5pp).
Experimental setup
Datasets: LVISv1 MS-COCO V3Det OpenImages
Benchmarks: LVISv1 MS-COCO V3Det OpenImages
Metrics: mask AP box AP rare AP common AP frequent AP AP50
Baselines: NorCal GOL ECM CRAT w/ LOCE LogN Seesaw ROG APA
Builds on: logit adjustment PCSA NorCal LogN repeat factor sampling
Closest papers by meaning
- On Model Calibration for Long-Tailed Object Detection and Instance Segmentation (NeurIPS 2021 · similarity 0.89)
- Adaptive Hierarchical Representation Learning for Long-Tailed Object Detection (CVPR 2022 · similarity 0.87)
- SimLTD: Simple Supervised and Semi-Supervised Long-Tailed Object Detection (CVPR 2025 · similarity 0.86)
- Long-tailed Object Detection Pretraining: Dynamic Rebalancing Contrastive Learning with Dual Reconstruction (NeurIPS 2024 · similarity 0.85)
- Out-of-Distribution Detection in Long-Tailed Recognition with Calibrated Outlier Class Learning (AAAI 2024 · similarity 0.84)
- TailedCore: Few-Shot Sampling for Unsupervised Long-Tail Noisy Anomaly Detection (CVPR 2025 · similarity 0.83)
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