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03/27/2023
Recognizing Rigid Patterns of Unlabeled Point Clouds by Complete and Continuous Isometry Invariants with no False Negatives and no False Positives
Rigid structures such as cars or any other solid objects are often repre...
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03/24/2023
Simplexwise Distance Distributions for finite spaces with metrics and measures
A finite set of unlabelled points in Euclidean space is the simplest rep...
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03/23/2023
The strength of a simplex is the key to a continuous isometry classification of Euclidean clouds of unlabelled points
This paper solves the continuous classification problem for finite cloud...
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01/12/2023
Density functions of periodic sequences of continuous events
Periodic Geometry studies isometry invariants of periodic point sets tha...
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12/19/2022
Compact Graph Representation of molecular crystals using Point-wise Distance Distributions
Use of graphs to represent molecular crystals has become popular in rece...
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08/19/2022
Counterexamples expose gaps in the proof of time complexity for cover trees introduced in 2006
This paper is motivated by the k-nearest neighbors search: given an arbi...
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07/18/2022
Computable complete invariants for finite clouds of unlabeled points under Euclidean isometry
A finite cloud of unlabeled points is the simplest representation of man...
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05/09/2022
Exactly computable and continuous metrics on isometry classes of finite and 1-periodic sequences
The inevitable noise in real measurements motivates the problem to conti...
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05/04/2022
Density functions of periodic sequences
Periodic point sets model all solid crystalline materials whose structur...
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02/24/2022
Entropic trust region for densest crystallographic symmetry group packings
Molecular crystal structure prediction (CSP) seeks the most stable perio...
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01/31/2022
Families of point sets with identical 1D persistence
Persistent homology is a popular and useful tool for analysing point set...
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01/17/2022
Paired compressed cover trees guarantee a near linear parametrized complexity for all k-nearest neighbors search in an arbitrary metric space
This paper studies the important problem of finding all k-nearest neighb...
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11/30/2021
A new compressed cover tree guarantees a near linear parameterized complexity for all k-nearest neighbors search in metric spaces
This paper studies the classical problem of finding all k nearest neighb...
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11/08/2021
Isometry invariant shape recognition of projectively perturbed point clouds by the mergegram extending 0D persistence
Rigid shapes should be naturally compared up to rigid motion or isometry...
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09/23/2021
A complete and continuous map of the Lattice Isometry Space for all 3-dimensional lattices
This paper extends the recently obtained complete and continuous map of ...
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09/22/2021
Easily computable continuous metrics on the space of isometry classes of all 2-dimensional lattices
A periodic lattice in Euclidean space is the infinite set of all integer...
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08/11/2021
Fast predictions of lattice energies by continuous isometry invariants of crystal structures
Crystal Structure Prediction (CSP) aims to discover solid crystalline ma...
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08/10/2021
Pointwise distance distributions of periodic sets
The fundamental model of a periodic structure is a periodic set of point...
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04/22/2021
The Density Fingerprint of a Periodic Point Set
Modeling a crystal as a periodic point set, we present a fingerprint con...
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03/03/2021
Introduction to Periodic Geometry and Topology
This monograph introduces key concepts and problems in the new research ...
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07/22/2020
The mergegram of a dendrogram and its stability
This paper extends the key concept of persistence within Topological Dat...
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07/17/2020
A fast approximate skeleton with guarantees for any cloud of points in a Euclidean space
The tree reconstruction problem is to find an embedded straight-line tre...
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10/29/2019
Resolution-independent meshes of super pixels
The over-segmentation into superpixels is an important preprocessing ste...
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01/10/2019
Skeletonisation Algorithms with Theoretical Guarantees for Unorganised Point Clouds with High Levels of Noise
Data Science aims to extract meaningful knowledge from unorganised data....
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01/10/2019
Skeletonisation Algorithms for Unorganised Point Clouds with Theoretical Guarantees
Real datasets often come in the form of an unorganised cloud of points. ...
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12/05/2013
Book embeddings of Reeb graphs
Let X be a simplicial complex with a piecewise linear function f:X→R. Th...
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12/05/2013
Approximating persistent homology for a cloud of n points in a subquadratic time
The Vietoris-Rips filtration for an n-point metric space is a sequence o...
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12/05/2013