Related papers: Topology-preserving digitization of n-dimensional …
We analyse the axioms of Euclidean geometry according to standard object-oriented software development methodology. We find a perfect match: the main undefined concepts of the axioms translate to object classes. The result is a suite of C++…
We survey structure-preserving discretizations of minimal surfaces in Euclidean space. Our focus is on a discretization defined via parallel face offsets of polyhedral surfaces, which naturally leads to a notion of vanishing mean curvature…
Understanding the topological characteristics of data is important to many areas of research. Recent work has demonstrated that synthetic 4D image-type data can be useful to train 4D convolutional neural network models to see topological…
3D shape creation and modeling remains a challenging task especially for novice users. Many methods in the field of computer graphics have been proposed to automate the often repetitive and precise operations needed during the modeling of…
Topological data analysis leverages topological features to analyze datasets, with applications in diverse fields like medical sciences and biology. A key tool of this theory is the persistence diagram, which encodes topological information…
The skeleton is an essential shape characteristic providing a compact representation of the studied shape. Its computation on the image grid raises many issues. Due to the effects of discretization, the required properties of the skeleton -…
The singular cubical homology theory for the category of quivers or digraphs can be constructed similarly to the classical singular homology theory for topological spaces. The case of digraphs and quivers differs from the topological case…
This work is concerned with a representation of shapes that disentangles fine, local and possibly repeating geometry, from global, coarse structures. Achieving such disentanglement leads to two unrelated advantages: i) a significant…
Existing research highlights the crucial role of topological priors in image segmentation, particularly in preserving essential structures such as connectivity and genus. Accurately capturing these topological features often requires…
The article presents a new perspective on the isomorphism problem for non-ergodic measure-preserving dynamical systems with discrete spectrum which is based on the connection between ergodic theory and topological dynamics constituted by…
A new methodological approach for the study of topology for shapes made of arrangements of lines, planes or solids is presented. Topologies for shapes are traditionally built on the classical theory of point-sets. In this paper, topologies…
The described works have been carried out in the framework of a mid-term study initiated by the Centre Electronique de l'Armement, then by an advanced study launched by the Direction de la Recherche et des Etudes Technologiques in France in…
We present a novel topology-preserving 3D medial axis computation framework based on volumetric restricted power diagram (RPD), while preserving the medial features and geometric convergence simultaneously, for both 3D CAD and organic…
This paper presents the classification of digital n-manifolds based on the notion of complexity and homotopy equivalence. We introduce compressed n-manifolds and study their properties. We show that any n-manifold with p points is homotopy…
Various kinds of data are routinely represented as discrete probability distributions. Examples include text documents summarized by histograms of word occurrences and images represented as histograms of oriented gradients. Viewing a…
Several recent papers in digital topology have sought to obtain fixed point results by mimicking the use of tools from classical topology, such as complete metric spaces and homotopy invariant fixed point theory. We show that in many cases,…
An n-dimensional analogue of the Klein bottle arose in our study of topological complexity of planar polygon spaces. We determine its integral cohomology algebra and stable homotopy type, and give an explicit immersion and embedding in…
Mathematical objects are generally abstract and not very approachable. Illustrations and interactive visualizations help both students and professionals to comprehend mathematical material and to work with it. This approach lends itself…
We study connectivity preserving multivalued functions between digital images. This notion generalizes that of continuous multivalued functions studied mostly in the setting of the digital plane $Z^2$. We show that connectivity preserving…
We give a topological characterization of the n-dimensional pseudo-boundary of the (2n+1)-dimensional Euclidean space.