# Fast and Accurate Tumor Segmentation of Histology Images using Persistent Homology and Deep Convolutional Features

arXiv: https://arxiv.org/abs/1805.03699 · HTML: https://mlsanity.com/paper/1805.03699/

## Key facts

- Cited by 28 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2018.

## Built on by (most cited first, 28 of 28)

- [Multi-Layer Pseudo-Supervision for Histopathology Tissue Semantic Segmentation using Patch-level Classification Labels](https://mlsanity.com/paper/2110.08048/) (2021)
- [Masked Pre-Training of Transformers for Histology Image Analysis](https://mlsanity.com/paper/2304.07434/) (2023)
- [Topology-Aware Focal Loss for 3D Image Segmentation](https://mlsanity.com/paper/2304.12223/) (2023)
- [Topological Signatures vs. Gradient Histograms: A Comparative Study for Medical Image Classification](https://mlsanity.com/paper/2507.03006/) (2025)
- [HOG-CNN: Integrating Histogram of Oriented Gradients with Convolutional Neural Networks for Retinal Image Classification](https://mlsanity.com/paper/2507.22274/) (2025)
- [Self-Rule to Multi-Adapt: Generalized Multi-source Feature Learning Using Unsupervised Domain Adaptation for Colorectal Cancer Tissue Detection](https://mlsanity.com/paper/2108.09178/) (2021)
- [PHG-Net: Persistent Homology Guided Medical Image Classification](https://mlsanity.com/paper/2311.17243/) (2023)
- [Cycle Registration in Persistent Homology with Applications in Topological Bootstrap](https://mlsanity.com/paper/2101.00698/) (2021)
- [WSI-SAM: Multi-resolution Segment Anything Model (SAM) for histopathology whole-slide images](https://mlsanity.com/paper/2403.09257/) (2024)
- [SRPN: similarity-based region proposal networks for nuclei and cells detection in histology images](https://mlsanity.com/paper/2106.13556/) (2021)
- [Glo-In-One: Holistic Glomerular Detection, Segmentation, and Lesion Characterization with Large-scale Web Image Mining](https://mlsanity.com/paper/2206.00123/) (2022)
- [Consistency Regularisation in Varying Contexts and Feature Perturbations for Semi-Supervised Semantic Segmentation of Histology Images](https://mlsanity.com/paper/2301.13141/) (2023)
- [Rethinking Persistent Homology for Visual Recognition](https://mlsanity.com/paper/2207.04220/) (2022)
- [TopoCL: Topological Contrastive Learning for Medical Imaging](https://mlsanity.com/paper/2603.14647/) (2026)
- [A digital score of tumour-associated stroma infiltrating lymphocytes predicts survival in head and neck squamous cell carcinoma](https://mlsanity.com/paper/2104.12862/) (2021)
- [A review of machine learning approaches, challenges and prospects for computational tumor pathology](https://mlsanity.com/paper/2206.01728/) (2022)
- [PathoPainter: Augmenting Histopathology Segmentation via Tumor-aware Inpainting](https://mlsanity.com/paper/2503.04634/) (2025)
- [Classification of COVID-19 via Homology of CT-SCAN](https://mlsanity.com/paper/2102.10593/) (2021)
- [Topology-Aware Loss for Aorta and Great Vessel Segmentation in Computed Tomography Images](https://mlsanity.com/paper/2307.03137/) (2023)
- [Hybrid guiding: A multi-resolution refinement approach for semantic segmentation of gigapixel histopathological images](https://mlsanity.com/paper/2112.03455/) (2021)
- [A fast topological approach for predicting anomalies in time-varying graphs](https://mlsanity.com/paper/2305.06523/) (2023)
- [Train-Free Segmentation in MRI with Cubical Persistent Homology](https://mlsanity.com/paper/2401.01160/) (2024)
- [AI-based Carcinoma Detection and Classification Using Histopathological Images: A Systematic Review](https://mlsanity.com/paper/2201.07231/) (2022)
- [Segmentation of Non-Small Cell Lung Carcinomas: Introducing DRU-Net and Multi-Lens Distortion](https://mlsanity.com/paper/2406.14287/) (2024)
- [PI-Att: Topology Attention for Segmentation Networks through Adaptive Persistence Image Representation](https://mlsanity.com/paper/2408.08038/) (2024)
- [Classification of Histopathology Slides with Persistent Homology Convolutions](https://mlsanity.com/paper/2507.14378/) (2025)
- [Topological Invariant-Based Iris Identification via Digital Homology and Machine Learning](https://mlsanity.com/paper/2508.09555/) (2025)
- [Sparse cubical complexes for efficient topology-preservation in image data](https://mlsanity.com/paper/2609.37177/) (2026)

## Abstract (arXiv)

Tumor segmentation in whole-slide images of histology slides is an important step towards computer-assisted diagnosis. In this work, we propose a tumor segmentation framework based on the novel concept of persistent homology profiles (PHPs). For a given image patch, the homology profiles are derived by efficient computation of persistent homology, which is an algebraic tool from homology theory. We propose an efficient way of computing topological persistence of an image, alternative to simplicial homology. The PHPs are devised to distinguish tumor regions from their normal counterparts by modeling the atypical characteristics of tumor nuclei. We propose two variants of our method for tumor segmentation: one that targets speed without compromising accuracy and the other that targets higher accuracy. The fast version is based on the selection of exemplar image patches from a convolution neural network (CNN) and patch classification by quantifying the divergence between the PHPs of exemplars and the input image patch. Detailed comparative evaluation shows that the proposed algorithm is significantly faster than competing algorithms while achieving comparable results. The accurate version combines the PHPs and high-level CNN features and employs a multi-stage ensemble strategy for image patch labeling. Experimental results demonstrate that the combination of PHPs and CNN features outperforms competing algorithms. This study is performed on two independently collected colorectal datasets containing adenoma, adenocarcinoma, signet and healthy cases. Collectively, the accurate tumor segmentation produces the highest average patch-level F1-score, as compared with competing algorithms, on malignant and healthy cases from both the datasets. Overall the proposed framework highlights the utility of persistent homology for histopathology image analysis.