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Laboratory of Discrete and Computational Geometry

Invited researcher Herbert Edelsbrunner
Contract number
11.G34.31.0053
Time span of the project
2011-2013
Head of the laboratory

As of 30.01.2020

8
Number of staff members
245
scientific publications
15
Objects of intellectual property
General information

Name of the project: Discrete and computational geometry

Strategy for Scientific and Technological Development Priority Level: а, в


Goals and objectives

Research directions: 3D modeling, real-time digital processing of images, prototyping, discrete and computational geometry

Project objective: Solving current applied mathematical problems


The practical value of the study

  • We have solved a number of recognized hard problems in the field of geometry and topology. An ideology has been developed for applications of algebraic and topological methods to problems of image processing. On the basis of this ideology we succeeded to apply methods of topology to problems of segmentation and classification of medical images and generalization of cartographic images.
  • The Laboratory has created a new algorithm for generalization of cartographic data that preserves their topological properties, new algorithms and methods for classification and segmentation of gastroendoscopy images.
  • We have developed a software complex that is intended for usage in modern schools that allows not only to conduct all the necessary operations for development of stereometric models but also to automatically form models for production using 3D printers.

Implemented results of research:

  • New algorithms of classification and segmentation of gastroendoscopy images have been developed for automation of diagnostics of oncological diseases of gastrointestinal tract.
  • The editor of stereometric models with 3D printing capabilities is aimed at development of spatial intuition of school students.
  • New algorithms of cartographic generalization are being developed for enhancing quality of representation of information in modern electronic maps.

Education and career development:

  • We have organized two mathematical schools for additional training of students, postgraduates and young scientists.
  • The Laboratory conducted the International Interactive Exhibition «IMAGINARY with mathematicians' eyes» (2013).
  • Our Laboratory is conducting active work with school students. Members of the staff of the Laboratory participate in organization of exhibitions, runs workshops and competitions in mathematics, read popular science lectures.

Organizational and structural changes: We have created a computation cluster that is currently used by many divisions of the Yaroslavl State University.

   Collaborations:

  • Institute of Science and Technology Austria, University of Texas at Brownsville (USA), V.A. Steklov Mathematical Institute of the Russian Academy of Sciences (Russia), Moscow State University (Russia): joint scientific conferences and publications
  • Free University of Brussels (Belgium): joint research and publications

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Akopyan A.V., Karasev R.N.
Kadets-Type Theorems for Partitions of a Convex Body. Discrete and Computational Geometry 48(3): 766–776 (2012).
Dolbilin N.P., Edelsbrunner H., Glazyrin A., Musin O.R.
Functionals on Triangulations of Delaunay Sets. Moscow Mathematical Journal 14(3): 491–504 (2014).
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