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Prediction and discovery of new materials with desired properties are at the forefront of quantum science and technology research. A major bottleneck in this field is the computational resources and time complexity related to finding new…

Assume that a finite set of points is randomly sampled from a subspace of a metric space. Recent advances in computational topology have provided several approaches to recovering the geometric and topological properties of the underlying…

Algebraic Topology · Mathematics 2021-01-29 Peter Bubenik , Peter T. Kim

A fundamental tool in topological data analysis is persistent homology, which allows extraction of information from complex datasets in a robust way. Persistent homology assigns a module over a principal ideal domain to a one-parameter…

Algebraic Topology · Mathematics 2019-06-19 Heather A. Harrington , Nina Otter , Hal Schenck , Ulrike Tillmann

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 often constrained…

Quantum Physics · Physics 2024-02-28 Bernardo Ameneyro , George Siopsis , Vasileios Maroulas

An automatic segmentation algorithm for delineation of the gross tumour volume and pathologic lymph nodes of head and neck cancers in PET/CT images is described. The proposed algorithm is based on a convolutional neural network using the…

Image and Video Processing · Electrical Eng. & Systems 2019-08-05 Yngve Mardal Moe , Aurora Rosvoll Groendahl , Martine Mulstad , Oliver Tomic , Ulf Indahl , Einar Dale , Eirik Malinen , Cecilia Marie Futsaether

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs). PDs exhibit, however, complex structure and are difficult to integrate in today's machine…

Machine Learning · Statistics 2019-06-11 Bartosz Zieliński , Michał Lipiński , Mateusz Juda , Matthias Zeppelzauer , Paweł Dłotko

With the advanced imaging technology, digital pathology imaging of tumor tissue slides is becoming a routine clinical procedure for cancer diagnosis. This process produces massive imaging data that capture histological details in high…

Applications · Statistics 2020-12-10 Esteban Fernández Morales , Cong Zhang , Guanghua Xiao , Chul Moon , Qiwei Li

This study evaluates the reliability of two deep learning models for skin cancer detection, focusing on their explainability and fairness. Using the HAM10000 dataset of dermatoscopic images, the research assesses two convolutional neural…

Image and Video Processing · Electrical Eng. & Systems 2024-09-09 Tanish Jain

In recent years there has been noticeable interest in the study of the "shape of data". Among the many ways a "shape" could be defined, topology is the most general one, as it describes an object in terms of its connectivity structure:…

Machine Learning · Statistics 2017-09-22 Tullia Padellini , Pierpaolo Brutti

Convolutional neural networks (CNNs) are a standard tool for computer vision tasks such as image classification. However, typical model architectures may result in the loss of topological information. In specific domains such as…

Image and Video Processing · Electrical Eng. & Systems 2026-03-05 Shrunal Pothagoni , Benjamin Schweinhart

Persistent homology (PH) is a rigorous mathematical theory that provides a robust descriptor of data in the form of persistence diagrams (PDs) which are 2D multisets of points. Their variable size makes them, however, difficult to combine…

Machine Learning · Statistics 2019-06-14 Bartosz Zielinski , Michal Lipinski , Mateusz Juda , Matthias Zeppelzauer , Pawel Dlotko

Persistent homology theory is a relatively new but powerful method in data analysis. Using simplicial complexes, classical persistent homology is able to reveal high dimensional geometric structures of datasets, and represent them as…

Algebraic Topology · Mathematics 2023-12-05 Yaru Gao , Yan Xu , Fengchun Lei

Persistent homology is an effective method for extracting topological information, represented as persistent diagrams, of spatial structure data. Hence it is well-suited for the study of protein structures. Attempts to incorporate…

Machine Learning · Computer Science 2024-08-01 An Wu , Yu Pan , Fuqi Zhou , Jinghui Yan , Chuanlu Liu

Melanoma is the deadliest form of skin cancer. Uncontrollable growth of melanocytes leads to melanoma. Melanoma has been growing wildly in the last few decades. In recent years, the detection of melanoma using image processing techniques…

Machine Learning · Computer Science 2023-01-03 Shakti Kumar , Anuj Kumar

Anomaly detection aims at identifying images that deviate significantly from the norm. We focus on algorithms that embed the normal training examples in space and when given a test image, detect anomalies based on the features distance to…

Computer Vision and Pattern Recognition · Computer Science 2023-05-30 Ori Nizan , Ayellet Tal

Topological data analysis is an emerging area in exploratory data analysis and data mining. Its main tool, persistent homology, has become a popular technique to study the structure of complex, high-dimensional data. In this paper, we…

Graphics · Computer Science 2017-10-04 Mustafa Hajij , Bei Wang , Carlos Scheidegger , Paul Rosen

We present a novel discrete optimization-based approach to generate downsampled versions of binary images that are guaranteed to have the same topology as the original, measured by the zeroth and first Betti numbers of the black regions,…

Computer Vision and Pattern Recognition · Computer Science 2024-07-26 Chia-Chia Chen , Chi-Han Peng

This study demonstrates that incorporating a consistency heuristic into the point-matching algorithm \cite{yerebakan2023hierarchical} improves robustness in matching anatomical locations across pairs of medical images. We validated our…

Computer Vision and Pattern Recognition · Computer Science 2025-08-01 Halid Ziya Yerebakan , Gerardo Hermosillo Valadez

Many datasets can be viewed as a noisy sampling of an underlying space, and tools from topological data analysis can characterize this structure for the purpose of knowledge discovery. One such tool is persistent homology, which provides a…

Persistent homology is a widely used tool in Topological Data Analysis that encodes multiscale topological information as a multi-set of points in the plane called a persistence diagram. It is difficult to apply statistical theory directly…

Statistics Theory · Mathematics 2013-12-03 Frédéric Chazal , Brittany Terese Fasy , Fabrizio Lecci , Alessandro Rinaldo , Larry Wasserman