The Impact of Changes in Resolution on the Persistent Homology of Images
Digital images enable quantitative analysis of material properties at micro and macro length scales, but choosing an appropriate resolution when acquiring the image is challenging. A high resolution means longer image acquisition and larger data requirements for a given sample, but if the resolution is too low, significant information may be lost. This paper studies the impact of changes in resolution on persistent homology, a tool from topological data analysis that provides a signature of structure in an image across all length scales. Given prior information about a function, the geometry of an object, or its density distribution at a given resolution, we provide methods to select the coarsest resolution yielding results within an acceptable tolerance. We present numerical case studies for an illustrative synthetic example and samples from porous materials where the theoretical bounds are unknown.
Code (1)
Tasks
Topological Data AnalysisSimilar Papers 제목 키워드 기반
Persistent topological Laplacian analysis of SARS-CoV-2 variants
Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persisten…
Topological Data AnalysisDory: Overcoming Barriers to Computing Persistent Homology
Persistent homology (PH) is an approach to topological data analysis (TDA) that computes multi-scale topologically invariant properties of high-dimensional data that are robust to noise. While PH has revealed useful patt…
Topological Data AnalysisMultiresolution topological simplification
Persistent homology has been devised as a promising tool for the topological simplification of complex data. However, it is computationally intractable for large data sets. In this work, we introduce multiresolution pers…
domain classificationAnalyzing Brain Tumor Connectomics using Graphs and Persistent Homology
Recent advances in molecular and genetic research have identified a diverse range of brain tumor sub-types, shedding light on differences in their molecular mechanisms, heterogeneity, and origins. The present study perfo…
Topological Data AnalysisQuantum Persistent Homology for Time Series
Persistent homology, a powerful mathematical tool for data analysis, summarizes the shape of data through tracking topological features across changes in different scales. Classical algorithms for persistent homology are…
Time SeriesTime Series Analysis