# PARN: Pyramidal Affine Regression Networks for Dense Semantic Correspondence

arXiv: https://arxiv.org/abs/1807.02939 · HTML: https://mlsanity.com/paper/1807.02939/

## Key facts

- Cited by 26 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Jul 2018.

## Built on by (most cited first, 26 of 26)

- [A Tale of Two Features: Stable Diffusion Complements DINO for Zero-Shot Semantic Correspondence](https://mlsanity.com/paper/2305.15347/) (2023)
- [AMT: All-Pairs Multi-Field Transforms for Efficient Frame Interpolation](https://mlsanity.com/paper/2304.09790/) (2023)
- [CATs: Cost Aggregation Transformers for Visual Correspondence](https://mlsanity.com/paper/2106.02520/) (2021)
- [CATs++: Boosting Cost Aggregation with Convolutions and Transformers](https://mlsanity.com/paper/2202.06817/) (2022)
- [Convolutional Hough Matching Networks](https://mlsanity.com/paper/2103.16831/) (2021)
- [Warp Consistency for Unsupervised Learning of Dense Correspondences](https://mlsanity.com/paper/2104.03308/) (2021)
- [Neural Matching Fields: Implicit Representation of Matching Fields for Visual Correspondence](https://mlsanity.com/paper/2210.02689/) (2022)
- [Learning Semantic Correspondence with Sparse Annotations](https://mlsanity.com/paper/2208.06974/) (2022)
- [Deep Matching Prior: Test-Time Optimization for Dense Correspondence](https://mlsanity.com/paper/2106.03090/) (2021)
- [Probabilistic Warp Consistency for Weakly-Supervised Semantic Correspondences](https://mlsanity.com/paper/2203.04279/) (2022)
- [TransforMatcher: Match-to-Match Attention for Semantic Correspondence](https://mlsanity.com/paper/2205.11634/) (2022)
- [ASIC: Aligning Sparse in-the-wild Image Collections](https://mlsanity.com/paper/2303.16201/) (2023)
- [Self-Supervised Geometric Correspondence for Category-Level 6D Object Pose Estimation in the Wild](https://mlsanity.com/paper/2210.07199/) (2022)
- [CoordGAN: Self-Supervised Dense Correspondences Emerge from GANs](https://mlsanity.com/paper/2203.16521/) (2022)
- [Unifying Feature and Cost Aggregation with Transformers for Semantic and Visual Correspondence](https://mlsanity.com/paper/2403.11120/) (2024)
- [Convolutional Hough Matching Networks for Robust and Efficient Visual Correspondence](https://mlsanity.com/paper/2109.05221/) (2021)
- [Learning Contrastive Representation for Semantic Correspondence](https://mlsanity.com/paper/2109.10967/) (2021)
- [SHIC: Shape-Image Correspondences with no Keypoint Supervision](https://mlsanity.com/paper/2407.18907/) (2024)
- [Zero-Shot Image Feature Consensus with Deep Functional Maps](https://mlsanity.com/paper/2403.12038/) (2024)
- [Integrative Feature and Cost Aggregation with Transformers for Dense Correspondence](https://mlsanity.com/paper/2209.08742/) (2022)
- [Efficient Semantic Matching with Hypercolumn Correlation](https://mlsanity.com/paper/2311.04336/) (2023)
- [SpaceJAM: a Lightweight and Regularization-free Method for Fast Joint Alignment of Images](https://mlsanity.com/paper/2407.11850/) (2024)
- [Learning 3D Scene Analogies with Neural Contextual Scene Maps](https://mlsanity.com/paper/2503.15897/) (2025)
- [DocAligner: Annotating Real-world Photographic Document Images by Simply Taking Pictures](https://mlsanity.com/paper/2306.05749/) (2023)
- [Semantic Correspondence: Unified Benchmarking and a Strong Baseline](https://mlsanity.com/paper/2505.18060/) (2025)
- [Independently Keypoint Learning for Small Object Semantic Correspondence](https://mlsanity.com/paper/2404.02678/) (2024)

## Abstract (arXiv)

This paper presents a deep architecture for dense semantic correspondence, called pyramidal affine regression networks (PARN), that estimates locally-varying affine transformation fields across images. To deal with intra-class appearance and shape variations that commonly exist among different instances within the same object category, we leverage a pyramidal model where affine transformation fields are progressively estimated in a coarse-to-fine manner so that the smoothness constraint is naturally imposed within deep networks. PARN estimates residual affine transformations at each level and composes them to estimate final affine transformations. Furthermore, to overcome the limitations of insufficient training data for semantic correspondence, we propose a novel weakly-supervised training scheme that generates progressive supervisions by leveraging a correspondence consistency across image pairs. Our method is fully learnable in an end-to-end manner and does not require quantizing infinite continuous affine transformation fields. To the best of our knowledge, it is the first work that attempts to estimate dense affine transformation fields in a coarse-to-fine manner within deep networks. Experimental results demonstrate that PARN outperforms the state-of-the-art methods for dense semantic correspondence on various benchmarks.