"Discrete Tools for Topology-based Visual Analytics" presented by Federico Iuricich, The City University of New York
Morse theory studies the relationships between the topology of a shape and the critical points of a real-valued smooth function defined on it. It has been recognized as an important tool for shape analysis and understanding in several applications, including physics, chemistry, medicine, and geography. Morse theory is defined for smooth functions, but recently a discrete counterpart, called discrete Morse theory, has been proposed in an entirely combinatorial setting. The Forman gradient is a powerful tool provided by discrete Morse theory. Its major property is that of providing a compact representation of the input data, preserving the features that characterize the data itself. In this presentation, I will cover my contribution in developing computational tools for the analysis of both scalar fields and multivariate data. We will describe in detail our compact representation for the Forman gradient defined on simplicial complexes and how it can be adapted to the n-dimensional case. Moreover, I will introduce the multiscale interactive tools I have developed for terrain and volume data analysis.
Dr. Federico Iuricich received his Ph.D. in Computer Science from the University of Genova in 2014 defending a thesis on "Multi-resolution shape analysis based on discrete Morse decompositions". The same year he started his post-doctoral work at the University of Maryland focusing on efficient dimension-independent representations for Topological Data Analysis. In 2016 he moved to the Department of Geographical Sciences, at the University of Maryland, where he was working on topological methods for the analysis and visualization of geographical and environmental data. Currently, he his a postdoctoral fellow at the City University of New York working on applications of computational topology to machine learning.
Friday, February 16 at 2:30pm to 3:30pm
McAdams Hall, 119
821 McMillan Rd., Clemson, SC 29634, USA