# Persistent Homology with Improved Locality Information for more Effective Delineation

arXiv: https://arxiv.org/abs/2110.06295 · HTML: https://mlsanity.com/paper/2110.06295/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 37 references that are in the map.
- First posted on arXiv 12 Oct 2021.

## Builds on (most cited first, 17 of 17)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [SpaceNet: A Remote Sensing Dataset and Challenge Series](https://mlsanity.com/paper/1807.01232/) (2018)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [RoadTracer: Automatic Extraction of Road Networks from Aerial Images](https://mlsanity.com/paper/1802.03680/) (2018)
- [Beyond the Pixel-Wise Loss for Topology-Aware Delineation](https://mlsanity.com/paper/1712.02190/) (2017)
- [A Topology Layer for Machine Learning](https://mlsanity.com/paper/1905.12200/) (2019)
- [Topology-Aware Segmentation Using Discrete Morse Theory](https://mlsanity.com/paper/2103.09992/) (2021)
- [Localization in the Crowd with Topological Constraints](https://mlsanity.com/paper/2012.12482/) (2020)
- [Topological Map Extraction from Overhead Images](https://mlsanity.com/paper/1812.01497/) (2018)
- [Explicit topological priors for deep-learning based image segmentation using persistent homology](https://mlsanity.com/paper/1901.10244/) (2019)
- [A Framework for Differential Calculus on Persistence Barcodes](https://mlsanity.com/paper/1910.00960/) (2019)
- [A Topological "Reading" Lesson: Classification of MNIST using TDA](https://mlsanity.com/paper/1910.08345/) (2019)
- [Promoting Connectivity of Network-Like Structures by Enforcing Region Separation](https://mlsanity.com/paper/2009.07011/) (2020)
- [Joint Segmentation and Path Classification of Curvilinear Structures](https://mlsanity.com/paper/1905.03892/) (2019)
- [Duality in Persistent Homology of Images](https://mlsanity.com/paper/2005.04597/) (2020)

## Built on by (most cited first, 10 of 10)

- [Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods](https://mlsanity.com/paper/2404.18539/) (2024)
- [Euler Characteristic Transform Based Topological Loss for Reconstructing 3D Images from Single 2D Slices](https://mlsanity.com/paper/2303.05286/) (2023)
- [CAPE: Connectivity-Aware Path Enforcement Loss for Curvilinear Structure Delineation](https://mlsanity.com/paper/2504.00753/) (2025)
- [Towards High-Quality Image Segmentation: Improving Topology Accuracy by Penalizing Neighbor Pixels](https://mlsanity.com/paper/2603.18671/) (2026)
- [Complex Wavelet Mutual Information Loss: A Multi-Scale Loss Function for Semantic Segmentation](https://mlsanity.com/paper/2502.00563/) (2025)
- [TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy](https://mlsanity.com/paper/2503.03365/) (2025)
- [Disconnect to Connect: A Data Augmentation Method for Improving Topology Accuracy in Image Segmentation](https://mlsanity.com/paper/2503.05541/) (2025)
- [PI-Att: Topology Attention for Segmentation Networks through Adaptive Persistence Image Representation](https://mlsanity.com/paper/2408.08038/) (2024)
- [Unsupervised Assessment of Landscape Shifts Based on Persistent Entropy and Topological Preservation](https://mlsanity.com/paper/2410.04183/) (2024)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Persistent Homology (PH) has been successfully used to train networks to detect curvilinear structures and to improve the topological quality of their results. However, existing methods are very global and ignore the location of topological features. In this paper, we remedy this by introducing a new filtration function that fuses two earlier approaches: thresholding-based filtration, previously used to train deep networks to segment medical images, and filtration with height functions, typically used to compare 2D and 3D shapes. We experimentally demonstrate that deep networks trained using our PH-based loss function yield reconstructions of road networks and neuronal processes that reflect ground-truth connectivity better than networks trained with existing loss functions based on PH. Code is available at https://github.com/doruk-oner/PH-TopoLoss.