# Scale-Free Image Keypoints Using Differentiable Persistent Homology

arXiv: https://arxiv.org/abs/2406.01315 · HTML: https://mlsanity.com/paper/2406.01315/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 60 references that are in the map.
- First posted on arXiv 3 Jun 2024.

## Builds on (most cited first, 28 of 28)

- [SuperPoint: Self-Supervised Interest Point Detection and Description](https://mlsanity.com/paper/1712.07629/) (2017)
- [ORB-SLAM: a Versatile and Accurate Monocular SLAM System](https://mlsanity.com/paper/1502.00956/) (2015)
- [MegaDepth: Learning Single-View Depth Prediction from Internet Photos](https://mlsanity.com/paper/1804.00607/) (2018)
- [From Coarse to Fine: Robust Hierarchical Localization at Large Scale](https://mlsanity.com/paper/1812.03506/) (2018)
- [DISK: Learning local features with policy gradient](https://mlsanity.com/paper/2006.13566/) (2020)
- [LIFT: Learned Invariant Feature Transform](https://mlsanity.com/paper/1603.09114/) (2016)
- [HPatches: A benchmark and evaluation of handcrafted and learned local descriptors](https://mlsanity.com/paper/1704.05939/) (2017)
- [Large-Scale Image Retrieval with Attentive Deep Local Features](https://mlsanity.com/paper/1612.06321/) (2016)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Topological Autoencoders](https://mlsanity.com/paper/1906.00722/) (2019)
- [ALIKED: A Lighter Keypoint and Descriptor Extraction Network via Deformable Transformation](https://mlsanity.com/paper/2304.03608/) (2023)
- [Key.Net: Keypoint Detection by Handcrafted and Learned CNN Filters](https://mlsanity.com/paper/1904.00889/) (2019)
- [Deep Learning with Topological Signatures](https://mlsanity.com/paper/1707.04041/) (2017)
- [ALIKE: Accurate and Lightweight Keypoint Detection and Descriptor Extraction](https://mlsanity.com/paper/2112.02906/) (2021)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Repeatability Is Not Enough: Learning Affine Regions via Discriminability](https://mlsanity.com/paper/1711.06704/) (2017)
- [Quad-networks: unsupervised learning to rank for interest point detection](https://mlsanity.com/paper/1611.07571/) (2016)
- [Topology-Aware Uncertainty for Image Segmentation](https://mlsanity.com/paper/2306.05671/) (2023)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [Are Local Features All You Need for Cross-Domain Visual Place Recognition?](https://mlsanity.com/paper/2304.05887/) (2023)
- [Learning Probabilistic Topological Representations Using Discrete Morse Theory](https://mlsanity.com/paper/2206.01742/) (2022)
- [Persistent homology machine learning for fingerprint classification](https://mlsanity.com/paper/1711.09158/) (2017)
- [Recent Advances in Features Extraction and Description Algorithms: A Comprehensive Survey](https://mlsanity.com/paper/1703.06376/) (2017)
- [FFD: Fast Feature Detector](https://mlsanity.com/paper/2012.00859/) (2020)
- [Large scale evaluation of local image feature detectors on homography datasets](https://mlsanity.com/paper/1807.07939/) (2018)
- [Comparing Feature Detectors: A bias in the repeatability criteria, and how to correct it](https://mlsanity.com/paper/1409.2465/) (2014)
- [From handcrafted to deep local features](https://mlsanity.com/paper/1807.10254/) (2018)

## Built on by (most cited first, 2 of 2)

- [Deep Learning Reforms Image Matching: A Survey and Outlook](https://mlsanity.com/paper/2506.04619/) (2025)
- [From Pairs to Sequences: Track-Aware Policy Gradients for Keypoint Detection](https://mlsanity.com/paper/2602.20630/) (2026)

## Abstract (arXiv)

In computer vision, keypoint detection is a fundamental task, with applications spanning from robotics to image retrieval; however, existing learning-based methods suffer from scale dependency and lack flexibility. This paper introduces a novel approach that leverages Morse theory and persistent homology, powerful tools rooted in algebraic topology. We propose a novel loss function based on the recent introduction of a notion of subgradient in persistent homology, paving the way toward topological learning. Our detector, MorseDet, is the first topology-based learning model for feature detection, which achieves competitive performance in keypoint repeatability and introduces a principled and theoretically robust approach to the problem.