# Beyond Cartesian Representations for Local Descriptors

arXiv: https://arxiv.org/abs/1908.05547 · HTML: https://mlsanity.com/paper/1908.05547/

## Key facts

- Cited by 35 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Aug 2019.

## Built on by (most cited first, 30 of 35)

- [COTR: Correspondence Transformer for Matching Across Images](https://mlsanity.com/paper/2103.14167/) (2021)
- [Efficient LoFTR: Semi-Dense Local Feature Matching with Sparse-Like Speed](https://mlsanity.com/paper/2403.04765/) (2024)
- [P2-Net: Joint Description and Detection of Local Features for Pixel and Point Matching](https://mlsanity.com/paper/2103.01055/) (2021)
- [MatchAnything: Universal Cross-Modality Image Matching with Large-Scale Pre-Training](https://mlsanity.com/paper/2501.07556/) (2025)
- [SNAP: Self-Supervised Neural Maps for Visual Positioning and Semantic Understanding](https://mlsanity.com/paper/2306.05407/) (2023)
- [Decoupling Makes Weakly Supervised Local Feature Better](https://mlsanity.com/paper/2201.02861/) (2022)
- [SFD2: Semantic-guided Feature Detection and Description](https://mlsanity.com/paper/2304.14845/) (2023)
- [Self-Supervised Equivariant Learning for Oriented Keypoint Detection](https://mlsanity.com/paper/2204.08613/) (2022)
- [Local Feature Matching Using Deep Learning: A Survey](https://mlsanity.com/paper/2401.17592/) (2024)
- [RoI Tanh-polar Transformer Network for Face Parsing in the Wild](https://mlsanity.com/paper/2102.02717/) (2021)
- [Learning Rotation-Equivariant Features for Visual Correspondence](https://mlsanity.com/paper/2303.15472/) (2023)
- [ECO-TR: Efficient Correspondences Finding Via Coarse-to-Fine Refinement](https://mlsanity.com/paper/2209.12213/) (2022)
- [Dense-SfM: Structure from Motion with Dense Consistent Matching](https://mlsanity.com/paper/2501.14277/) (2025)
- [Deep Learning for Visual Localization and Mapping: A Survey](https://mlsanity.com/paper/2308.14039/) (2023)
- [S-TREK: Sequential Translation and Rotation Equivariant Keypoints for local feature extraction](https://mlsanity.com/paper/2308.14598/) (2023)
- [ScaleNet: A Shallow Architecture for Scale Estimation](https://mlsanity.com/paper/2112.04846/) (2021)
- [Enhancing Deformable Local Features by Jointly Learning to Detect and Describe Keypoints](https://mlsanity.com/paper/2304.00583/) (2023)
- [Self-Supervised Learning of Image Scale and Orientation](https://mlsanity.com/paper/2206.07259/) (2022)
- [Extracting Deformation-Aware Local Features by Learning to Deform](https://mlsanity.com/paper/2111.10617/) (2021)
- [Learning-Based Dimensionality Reduction for Computing Compact and Effective Local Feature Descriptors](https://mlsanity.com/paper/2209.13586/) (2022)
- [Deep Learning Reforms Image Matching: A Survey and Outlook](https://mlsanity.com/paper/2506.04619/) (2025)
- [SDGMNet: Statistic-based Dynamic Gradient Modulation for Local Descriptor Learning](https://mlsanity.com/paper/2106.04434/) (2021)
- [Learning Geodesic-Aware Local Features from RGB-D Images](https://mlsanity.com/paper/2203.12016/) (2022)
- [DeDA: Deep Directed Accumulator](https://mlsanity.com/paper/2303.08434/) (2023)
- [A Detector-oblivious Multi-arm Network for Keypoint Matching](https://mlsanity.com/paper/2104.00947/) (2021)
- [pySLAM: An Open-Source, Modular, and Extensible Framework for SLAM](https://mlsanity.com/paper/2502.11955/) (2025)
- [CNSv2: Probabilistic Correspondence Encoded Neural Image Servo](https://mlsanity.com/paper/2503.00132/) (2025)
- [Efficient Feature Description for Small Body Relative Navigation using Binary Convolutional Neural Networks](https://mlsanity.com/paper/2304.04985/) (2023)
- [DAGrid: Directed Accumulator Grid](https://mlsanity.com/paper/2306.02589/) (2023)
- [Cross Spatial Temporal Fusion Attention for Remote Sensing Object Detection via Image Feature Matching](https://mlsanity.com/paper/2507.19118/) (2025)

## Abstract (arXiv)

The dominant approach for learning local patch descriptors relies on small image regions whose scale must be properly estimated a priori by a keypoint detector. In other words, if two patches are not in correspondence, their descriptors will not match. A strategy often used to alleviate this problem is to "pool" the pixel-wise features over log-polar regions, rather than regularly spaced ones. By contrast, we propose to extract the "support region" directly with a log-polar sampling scheme. We show that this provides us with a better representation by simultaneously oversampling the immediate neighbourhood of the point and undersampling regions far away from it. We demonstrate that this representation is particularly amenable to learning descriptors with deep networks. Our models can match descriptors across a much wider range of scales than was possible before, and also leverage much larger support regions without suffering from occlusions. We report state-of-the-art results on three different datasets.