TL;DR
This paper introduces a method for calculating bar codes of point cloud data with real coefficients, advancing persistence theory through level set analysis, and is based on a Ph.D. thesis.
Contribution
It develops a new method for computing persistence bar codes for point cloud data using level set techniques, expanding the theoretical framework.
Findings
New computational method for bar codes with real coefficients
Integration of level set analysis into persistence theory
Application to point cloud data analysis
Abstract
This paper provides a method to calculate the bar codes of a PCD (point cloud data) with real coefficients in Section 3. With Dan Burghelea and Tamal Dey we developed a persistence theory which involves level sets discussed in Section 4. This paper is the Ph.D thesis written under the direction of Dan Burghelea at OSU.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Cell Image Analysis Techniques · Digital Image Processing Techniques