The Euler characteristic transform (ECT) is a simple to define yet powerful representation of
shape. The idea is to encode an embedded shape by tracking how the Euler characteristic …

Methods of topological data analysis have been successfully applied in a wide range of
fields to provide useful summaries of the structure of complex data sets in terms of …

Applications in data science, shape analysis, and object classification frequently require
comparison of probability distributions defined on different ambient spaces. To accomplish …

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods
measure some features but fail to measure the information embedded in shape …

Background: In recent geometric design, many effective toolkits for geometric modeling and
optimization have been proposed and applied in practical cases, while effective and efficient …

We study the inverse problem for persistent homology: For a fixed simplicial complex K, we
analyze the fiber of the continuous map PH on the space of filters that assigns to a filter f: K→ …

Persistent homology is a tool that can be employed to summarize the shape of data by
quantifying homological features. When the data is an object in $\mathbb {R}^ d $, the …

This article describes a method to analyze time series with a neural network using a matrix
of area-normalized persistence landscapes obtained with topological data analysis. The …

We employ the recent discovery of functoriality for persistent homology to recast the
Persistent Homology Transform of a geometric complex as a cosheaf of combinatorial …

Recent developments in shape reconstruction and comparison call for the use of many
different types of topological descriptors (persistence diagrams, Euler characteristic …