ACMD Seminar: Higher Order and Non-Smooth Optimization of Shells with Applications in 3D Imaging and Micro Fluids

Stephan Schmidt
Humboldt University, Berlin

Tuesday, March 2, 2021, 3:00 PM EST (1:00 PM MST)

A video of this talk is available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page.

Abstract: We discuss the use of geometric flows as an edge preserving regularizer in inverse problems, where the geometry is the unknown to be found. Such problems arise not only in tomography and 3D imaging, but also as geometric in-painting while scanning concave objects.  To this end, we study the total generalized variation (TGV) of the normal. This is a special multi-stage total variation (TV) approach originally developed for pixel images. Compared to classical TV, TGV develops much fewer staircasing effects.  Seeing that computing the TGV of a geometry is in itself an optimization problem, we also present a modified split Bregman iteration between manifolds to compute these optimal shapes.

Bio: Stephan Schmidt is a lecturer in the Department of Mathematics at Humboldt University Berlin.  His habilitation thesis topic at Würzburg University was “Geometric Inverse Problems, Images and SQP Methods Based on Weak Shape Hessians”.

Host: Günay Doğan

Note: This talk will be recorded to provide access to NIST staff and associates who could not be present to the time of the seminar. The recording will be made available in the Math channel on NISTube, which is accessible only on the NIST internal network. This recording could be released to the public through a Freedom of Information Act (FOIA) request. Do not discuss or visually present any sensitive (CUI/PII/BII) material. Ensure that no inappropriate material or any minors are contained within the background of any recording. (To facilitate this, we request that cameras of attendees are muted except when asking questions.)