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The Euler characteristic transform (ECT) is a simple to define yet powerful representation of shape.
Tomography of constructible functions
P. Schapira · 1995
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Tame Topology and O-minimal Structures
L. P. D. van den Dries · 1998
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Algebraic Topology
Allen Hatcher · 2002
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Procrustes Problems
John C Gower and Garmt B Dijksterhuis · 2004
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Algorithms to automatically quantify the geometric similarity of anatomical surfaces
Doug M. Boyer, Yaron Lipman, Elizabeth St. Clair, Jesus Puente, Biren A. Patel, Thomas Funkhouser, Jukka Jernvall, and Ingrid Daubechies · 2011
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Persistent homology transform for modeling shapes and surfaces
K. Turner, S. Mukherjee, and D. M. Boyer · 2014
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ShapeWorks
Joshua Cates, Shireen Elhabian, and Ross Whitaker · 2017
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Streaming algorithm for Euler characteristic curves of multidimensional images
Teresa Heiss and Hubert Wagner · 2017
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A user’s guide to topological data analysis
Elizabeth Munch · 2017
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A History of Folding in Mathematics
Michael Friedman · 2018
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Persistent homology and Euler integral transforms
Robert Ghrist, Rachel Levanger, and Huy Mai · 2018
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Predicting clinical outcomes in glioblastoma: An application of topological and functional data analysis
Lorin Crawford, Anthea Monod, Andrew X. Chen, Sayan Mukherjee, and Raúl Rabadán · 2019
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A faithful discretization of the augmented persistent homology transform
Brittany Terese Fasy, Samuel Micka, David L. Millman, Anna Schenfisch, and Lucia Williams · 2019
Cited alongside, same era.
The shape of things to come: Topological data analysis and biology, from molecules to organisms
Erik J. Amézquita, Michelle Y. Quigley, Tim Ophelders, Elizabeth Munch, and Daniel H. Chitwood · 2020
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Reconstructing embedded graphs from persistence diagrams
Robin Lynne Belton, Brittany Terese Fasy, Rostik Mertz, Samuel Micka, David L. Millman, Daniel Salinas, Anna Schenfisch, Jordan Schupbach, and Lucia Williams · 2020
Cited alongside, same era.
Searching and Reconstruction: Algorithms with Topological Descriptors
Samuel A. Micka · 2020
Cited alongside, same era.
Understanding flow features in drying droplets via Euler characteristic surfaces—a topological tool
A. Roy, R. A. I. Haque, A. J. Mitra, M. Dutta Choudhury, S. Tarafdar, and T. Dutta · 2020
Cited alongside, same era.
Euler characteristic curves and profiles: a stable shape invariant for big data problems
Paweł Dłotko and Davide Gurnari · 2022
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Efficient graph reconstruction and representation using augmented persistence diagrams
Brittany Terese Fasy, Samuel Micka, David L. Millman, Anna Schenfisch, and Lucia Williams · 2022
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Detecting temporal shape changes with the Euler characteristic transform
Lewis Marsh, Felix Y. Zhou, Xiao Qin, Xin Lu, Helen M. Byrne, and Heather A. Harrington · 2022
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Randomness and statistical inference of shapes via the smooth Euler characteristic transform
Kun Meng, Jinyu Wang, Lorin Crawford, and Ani Eloyan · 2022
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A topological data analytic approach for discovering biophysical signatures in protein dynamics
Wai Shing Tang, Gabriel Monteiro da Silva, Henry Kirveslahti, Erin Skeens, Bibo Feng, Timothy Sudijono, Kevin K. Yang, Sayan Mukherjee, Brenda Rubenstein, and Lorin Crawford · 2022
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Generating segmentation masks of herbarium specimens and a data set for training segmentation models using deep learning
Alexander E. White, Rebecca B. Dikow, Makinnon Baugh, Abigail Jenkins, and Paul B. Frandsen · 2020
Cited alongside, same era.
Measuring hidden phenotype: quantifying the shape of barley seeds using the Euler characteristic transform
Erik J Amézquita, Michelle Y Quigley, Tim Ophelders, Jacob B Landis, Daniel Koenig, Elizabeth Munch, and Daniel H Chitwood · 2021
Cited alongside, same era.
Computational Topology for Data Analysis
Tamal K Dey and Yusu Wang · 2021
Cited alongside, same era.
Representing fields without correspondences: the lifted Euler characteristic transform
Henry Kirveslahti and Sayan Mukherjee · 2021
Cited alongside, same era.
A statistical pipeline for identifying physical features that differentiate classes of 3d shapes
Bruce Wang, Timothy Sudijono, Henry Kirveslahti, Tingran Gao, Douglas M. Boyer, Sayan Mukherjee, and Lorin Crawford · 2021
Cited alongside, same era.
Euler characteristic surfaces
Gabriele Beltramo, , Primoz Skraba, Rayna Andreeva, Rik Sarkar, Ylenia Giarratano, and Miguel O. Bernabeu · 2022
Cited alongside, same era.
How many directions determine a shape and other sufficiency results for two topological transforms
Justin Curry, Sayan Mukherjee, and Katharine Turner · 2022
Cited alongside, same era.
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The extended persistent homology transform of manifolds with boundary
Katharine Turner, Vanessa Robins, and James Morgan · 2022
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Gpu computation of the Euler characteristic curve for imaging data
Fan Wang, Hubert Wagner, and Chao Chen · 2022
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Topological Reconstruction of Grayscale Images
Leo M. Betthauser · 2023
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Stability and inference of the Euler characteristic transform
Lewis Marsh and David Beers · 2023
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Euler characteristic transform based topological loss for reconstructing 3d images from single 2d slices
Kalyan Varma Nadimpalli, Amit Chattopadhyay, and Bastian Rieck · 2023
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Invariant representations of embedded simplicial complexes
Taejin Paik · 2023
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A distance for geometric graphs via the labeled merge tree interleaving distance
Elena Wang, Elizabeth Munch, and Erin Chambers · 2023
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