# PI-Att: Topology Attention for Segmentation Networks through Adaptive Persistence Image Representation

arXiv: https://arxiv.org/abs/2408.08038 · HTML: https://mlsanity.com/paper/2408.08038/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 15 Aug 2024.

## Builds on (most cited first, 29 of 29)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [TransUNet: Transformers Make Strong Encoders for Medical Image Segmentation](https://mlsanity.com/paper/2102.04306/) (2021)
- [clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation](https://mlsanity.com/paper/2003.07311/) (2020)
- [Persistence Images: A Stable Vector Representation of Persistent Homology](https://mlsanity.com/paper/1507.06217/) (2015)
- [Topology-Preserving Deep Image Segmentation](https://mlsanity.com/paper/1906.05404/) (2019)
- [The KiTS19 Challenge Data: 300 Kidney Tumor Cases with Clinical Context, CT Semantic Segmentations, and Surgical Outcomes](https://mlsanity.com/paper/1904.00445/) (2019)
- [A Topological Loss Function for Deep-Learning based Image Segmentation using Persistent Homology](https://mlsanity.com/paper/1910.01877/) (2019)
- [Reducing the Hausdorff Distance in Medical Image Segmentation with Convolutional Neural Networks](https://mlsanity.com/paper/1904.10030/) (2019)
- [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)
- [Neural Persistence: A Complexity Measure for Deep Neural Networks Using Algebraic Topology](https://mlsanity.com/paper/1812.09764/) (2018)
- [Z-GCNETs: Time Zigzags at Graph Convolutional Networks for Time Series Forecasting](https://mlsanity.com/paper/2105.04100/) (2021)
- [A Topological Regularizer for Classifiers via Persistent Homology](https://mlsanity.com/paper/1806.10714/) (2018)
- [Learning metrics for persistence-based summaries and applications for graph classification](https://mlsanity.com/paper/1904.12189/) (2019)
- [Deep Distance Transform for Tubular Structure Segmentation in CT Scans](https://mlsanity.com/paper/1912.03383/) (2019)
- [Topologically faithful image segmentation via induced matching of persistence barcodes](https://mlsanity.com/paper/2211.15272/) (2022)
- [Connectivity-Optimized Representation Learning via Persistent Homology](https://mlsanity.com/paper/1906.09003/) (2019)
- [Psi-Net: Shape and boundary aware joint multi-task deep network for medical image segmentation](https://mlsanity.com/paper/1902.04099/) (2019)
- [Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features](https://mlsanity.com/paper/1805.03699/) (2018)
- [A persistent homology-based topological loss for CNN-based multi-class segmentation of CMR](https://mlsanity.com/paper/2107.12689/) (2021)
- [Kernel method for persistence diagrams via kernel embedding and weight factor](https://mlsanity.com/paper/1706.03472/) (2017)
- [Exposition and Interpretation of the Topology of Neural Networks](https://mlsanity.com/paper/1810.03234/) (2018)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Persistent Homology with Improved Locality Information for more Effective Delineation](https://mlsanity.com/paper/2110.06295/) (2021)
- [Applying Topological Persistence in Convolutional Neural Network for Music Audio Signals](https://mlsanity.com/paper/1608.07373/) (2016)
- [Visual Object Recognition in Indoor Environments Using Topologically Persistent Features](https://mlsanity.com/paper/2010.03196/) (2020)
- [Rethinking Persistent Homology for Visual Recognition](https://mlsanity.com/paper/2207.04220/) (2022)
- [PHom-GeM: Persistent Homology for Generative Models](https://mlsanity.com/paper/1905.09894/) (2019)
- [Topology-Aware Loss for Aorta and Great Vessel Segmentation in Computed Tomography Images](https://mlsanity.com/paper/2307.03137/) (2023)

## Abstract (arXiv)

Segmenting multiple objects (e.g., organs) in medical images often requires an understanding of their topology, which simultaneously quantifies the shape of the objects and their positions relative to each other. This understanding is important for segmentation networks to generalize better with limited training data, which is common in medical image analysis. However, many popular networks were trained to optimize only pixel-wise performance, ignoring the topological correctness of the segmentation. In this paper, we introduce a new topology-aware loss function, which we call PI-Att, that explicitly forces the network to minimize the topological dissimilarity between the ground truth and prediction maps. We quantify the topology of each map by the persistence image representation, for the first time in the context of a segmentation network loss. Besides, we propose a new mechanism to adaptively calculate the persistence image at the end of each epoch based on the network's performance. This adaptive calculation enables the network to learn topology outline in the first epochs, and then topology details towards the end of training. The effectiveness of the proposed PI-Att loss is demonstrated on two different datasets for aorta and great vessel segmentation in computed tomography images.