Digital Geometry and its Applications: Geometrical and Topological Data Processing

Speaker:  Li Chen – Washington, DC, United States
Topic(s):  Artificial Intelligence, Machine Learning, Computer Vision, Natural language processing

Abstract

Digital geometry focuses on digital objects, which are usually represented by a finite number of integer points or vectors. However, in a much larger sense, digital objects could be digital data saved in computers or data sets in electronic form. Digital geometry comes from two primary sources: image processing and computer graphics. Digital geometry can be viewed as a branch of discrete geometry that mainly consists of the study of geometric relationships among discrete objects. 

Topics in digital geometry include: (1) Search and determination of curves and surfaces in 2D and 3D images, (2) Data recovery and reconstruction, (3) Connectivity of components among digital objects, (4) Object generation and reconstruction, (5) Digital manifolds and discrete manifolds, (6) Topological properties of digital objects, and (7) Efficient algorithm design for geometric data processing in digital space. These topics are usually applied to image segmentation, object recognition, mesh generation, and data reconstruction. Digital geometry is also closely related to computational geometry, especially computational topology. Digital geometry has been widely used in medical image processing.

In this talk, we will discuss the definition of digital curves and surfaces, the connectivity of digital space, algorithms for digitally connected components, and digital manifolds.  In terms of applications, we focus on the digital method of geometric data reconstruction and topological computation in data science. For example, we will discuss gradually varied surface fitting, hole counting for digital data, and persistent homology analysis.

This talk is mainly an introduction aimed at a general audience in computer science, information technology, mathematics, electrical engineering, etc. At the end of the talk, we will present some recent developments in digital geometry including some advanced materials such as the digital version of the Gauss-Bonnet theorem and computational topology.
 

About this Lecture

Number of Slides:  52
Duration:  60 minutes
Languages Available:  Chinese (Simplified), English
Last Updated: 

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