🍩 Database of Original & Non-Theoretical Uses of Topology

1. Topology-Aware Segmentation Using Discrete Morse Theory (2021)

   Xiaoling Hu, Yusu Wang, Li Fuxin, Dimitris Samaras, Chao Chen

   Abstract

   In the segmentation of fine-scale structures from natural and biomedical images, per-pixel accuracy is not the only metric of concern. Topological correctness, such as vessel connectivity and membrane closure, is crucial for downstream analysis tasks. In this paper, we propose a new approach to train deep image segmentation networks for better topological accuracy. In particular, leveraging the power of discrete Morse theory (DMT), we identify global structures, including 1D skeletons and 2D patches, which are important for topological accuracy. Trained with a novel loss based on these global structures, the network performance is significantly improved especially near topologically challenging locations (such as weak spots of connections and membranes). On diverse datasets, our method achieves superior performance on both the DICE score and topological metrics.

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   • Pattern recognition
   • computer vision
   • computer vision:image analysis
   • computer vision:image analysis:image segmentation
   • computer vision:image analysis:image segmentation:topology‑preserving segmentation
   • images
   • images:2D
   • images:2D:natural and biomedical
   • CNN backbone
   • Discrete Morse theory
   • topology-aware loss (DMT-loss)

2. TDAExplore: Quantitative Analysis of Fluorescence Microscopy Images Through Topology-Based Machine Learning (2021)

   Parker Edwards, Kristen Skruber, Nikola Milićević, James B. Heidings, Tracy-Ann Read, Peter Bubenik, Eric A. Vitriol

   Abstract

   Recent advances in machine learning have greatly enhanced automatic methods to extract information from fluorescence microscopy data. However, current machine-learning-based models can require hundreds to thousands of images to train, and the most readily accessible models classify images without describing which parts of an image contributed to classification. Here, we introduce TDAExplore, a machine learning image analysis pipeline based on topological data analysis. It can classify different types of cellular perturbations after training with only 20–30 high-resolution images and performs robustly on images from multiple subjects and microscopy modes. Using only images and whole-image labels for training, TDAExplore provides quantitative, spatial information, characterizing which image regions contribute to classification. Computational requirements to train TDAExplore models are modest and a standard PC can perform training with minimal user input. TDAExplore is therefore an accessible, powerful option for obtaining quantitative information about imaging data in a wide variety of applications.

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   • Actin cytoskeleton
   • Biology
   • Image classification
   • Image segmentation
   • images
   • images:grayscale
   • Machine learning
   • Persistence landscape
   • Persistent homology