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Found 13 papers, 8 papers with code
Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation
Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy.
Efficient Betti Matching Enables Topology-Aware 3D Segmentation via Persistent Homology
In this work, we propose an efficient algorithm for the calculation of the Betti matching, which can be used as a loss function to train topology aware segmentation networks.
Topologically Faithful Multi-class Segmentation in Medical Images
Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting.
Topologically faithful image segmentation via induced matching of persistence barcodes
In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching.
clDice - A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research.
Topological data analysis identifies emerging adaptive mutations in SARS-CoV-2
By leveraging the stratification by time in sequence data, our method enables the high-resolution longitudinal analysis of topological signals of adaptation.
Lifespan Functors and Natural Dualities in Persistent Homology
We introduce lifespan functors, which are endofunctors on the category of persistence modules that filter out intervals from barcodes according to their boundedness properties.
Algebraic Topology Computational Geometry 55N31, 55U10, 16G20, 18G05
clDice -- A Novel Topology-Preserving Loss Function for Tubular Structure Segmentation
Accurate segmentation of tubular, network-like structures, such as vessels, neurons, or roads, is relevant to many fields of research.
Ripser: efficient computation of Vietoris-Rips persistence barcodes
We present an algorithm for the computation of Vietoris-Rips persistence barcodes and describe its implementation in the software Ripser.
Algebraic Topology Computational Geometry Mathematical Software 55N31, 55-04
On the Metric Distortion of Embedding Persistence Diagrams into separable Hilbert spaces
Persistence diagrams are important descriptors in Topological Data Analysis.
Statistical Topological Data Analysis - A Kernel Perspective
We consider the problem of statistical computations with persistence diagrams, a summary representation of topological features in data.
A Stable Multi-Scale Kernel for Topological Machine Learning
Topological data analysis offers a rich source of valuable information to study vision problems.
Clear and Compress: Computing Persistent Homology in Chunks
We present a parallelizable algorithm for computing the persistent homology of a filtered chain complex.
Algebraic Topology
