Geometric and Topological Methods for Imaging, Graphics and Networks

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Mathematics and Computer Science".

Deadline for manuscript submissions: closed (30 September 2020) | Viewed by 9481

Special Issue Editors


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Guest Editor
Department of Applied Mathematics, Braude College, Karmiel 2161002, Israel
Interests: discrete differential geometry and its applications; mathematical imaging and vision; complex networks; quasi-conformal mappings and applications; topology and its applications
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Computer Science and Applied Mathematics & Statistics Department, Stony Brook University, Room 2425 Computer Science Building, State University of New York at Stony Brook, Stony Brook, NY 11794-4400, USA
Interests: computer graphics; computer vision; visualization; geometric modelling; networking
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

While computer science is generally not associated with geometry (and even less with topology), and practitioners in the field are, as a norm, far from being geometrically inclined, the fields of imaging and graphics stand apart. Indeed, not only are geometrical and topological methods widely used, and even prevalent, in these intensively active areas of study, they represent the main core of paradigms and tools employed. In fact, one might say—only slightly exaggerating—that large tracts of imaging and practically all of the research in graphics represents nothing else but the direct application and concrete “crystallization” of many important ideas and techniques in geometry and topology.

Mindful of this essential fact, we invite our colleagues labouring in the disciplines of imaging and graphics to submit papers illustrating the multifaceted roles of geometry and topology in the present state-of-the-art research. In particular, papers are welcomed appertaining to all areas of geometry, being it differential, projective or algebraic, smooth, discrete, or digital, as well as their manifold applications to segmentation, feature extraction, texture modelling, classification, face recognition, manifold learning, and many others. In particular, articles emphasizing the role and usefulness of the notion of curvature in all its manifold incarnations are invited. Contributions involving topological tools and applications for graphics and imaging applications, involving the study of surfaces and of higher-dimensional manifolds and more generalized structures are also appreciated.

Prof. Dr. Emil Saucan
Prof. Dr. David Gu
Guest Editors

Manuscript Submission Information

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Keywords

  • geometry
  • topology
  • imaging
  • graphics
  • geometric flows
  • registration
  • feature extraction
  • image classification
  • texture modelling
  • segmentation
  • manifold learning

Published Papers (2 papers)

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8 pages, 762 KiB  
Article
An Efficient Method for Forming Parabolic Curves and Surfaces
by Yuliy Lyachek
Mathematics 2020, 8(4), 592; https://doi.org/10.3390/math8040592 - 15 Apr 2020
Viewed by 4920
Abstract
A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages [...] Read more.
A new method for the formation of parabolic curves and surfaces is proposed. It does not impose restrictions on the relative positions in space of the sequence of reference points relative to each other, meaning it compares favorably with other prototypes. The disadvantages of the Overhauser and Brever–Anderson methods are noted. The method allows one to effectively form and edit curves and surfaces when changing the coordinates of any given point. This positive effect is achieved due to the appropriate choice of local coordinate systems for the mathematical description of each parabola, which together define a composite interpolation curve or surface. The paper provides a detailed mathematical description of the method of parabolic interpolation of curves and surfaces based on the use of matrix calculations. Analytical descriptions of a composite parabolic curve and its first and second derivatives are given, and continuity analysis of these factors is carried out. For the matrix of points of the defining polyhedron, expressions are presented that describe the corresponding surfaces, as well as the unit normal at any point. The comparative table of the required number of pseudo-codes for calculating the coordinates of one point for constructing a parabolic curve for the three methods is given. Full article
(This article belongs to the Special Issue Geometric and Topological Methods for Imaging, Graphics and Networks)
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8 pages, 972 KiB  
Article
Family of Enneper Minimal Surfaces
by Erhan Güler
Mathematics 2018, 6(12), 281; https://doi.org/10.3390/math6120281 - 26 Nov 2018
Cited by 5 | Viewed by 4073
Abstract
We consider a family of higher degree Enneper minimal surface E m for positive integers m in the three-dimensional Euclidean space E 3 . We compute algebraic equation, degree and integral free representation of Enneper minimal surface for [...] Read more.
We consider a family of higher degree Enneper minimal surface E m for positive integers m in the three-dimensional Euclidean space E 3 . We compute algebraic equation, degree and integral free representation of Enneper minimal surface for m = 1 , 2 , 3 . Finally, we give some results and relations for the family E m . Full article
(This article belongs to the Special Issue Geometric and Topological Methods for Imaging, Graphics and Networks)
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