Mathematical and Data-driven Pattern Representation with Applications in Image Processing, Computer Graphics, and Infinite Dimensional Dynamical Data Mining

Series
Dissertation Defense
Time
Friday, April 9, 2021 - 10:00am for 1.5 hours (actually 80 minutes)
Location
Online
Speaker
Yuchen (Roy) He – School of Math, Georgia Institute of Technology – yhe306@gatech.eduhttps://yuchenhephd.wixsite.com/academic
Organizer
Yuchen He

Patterns represent the spatial or temporal regularities intrinsic to various phenomena in nature, society, art, and science. From rigid ones with well-defined generative rules to flexible ones implied by unstructured data, patterns can be assigned to a spectrum. On one extreme, patterns are completely described by algebraic systems where each individual pattern is obtained by repeatedly applying simple operations on primitive elements. On the other extreme, patterns are perceived as visual or frequency regularities without any prior knowledge of the underlying mechanisms. In this presentation, we aim at demonstrating some mathematical techniques for representing patterns traversing the aforementioned spectrum, which leads to qualitative analysis of the patterns’ properties and quantitative prediction of the modeled behaviors from various perspectives. We investigate lattice patterns from material science, shape patterns from computer graphics, submanifold patterns encountered in point cloud processing, color perception patterns applied in underwater image processing, dynamic patterns from spatial-temporal data, and low-rank patterns exploited in medical image reconstruction. For different patterns and based on their dependence on structured or unstructured data, we introduce suitable mathematical representations using techniques ranging from group theory to deep neural networks.

Join Zoom Meeting

https://zoom.us/j/97642529845?pwd=aS9aTGloQnBGVVNQMHd6d0I4eGFNQT09

Meeting ID: 976 4252 9845

Passcode: 42PzXb