ACMD Seminar: Geometric data analysis: a Riemannian perspective

Nicolas Charon
Assistant Professor, Dept. of Applied Mathematics & Statistics, Johns Hopkins

Tuesday, May 2, 2023, 3:00-4:00 PM ET (1:00-2:00 PM MT)

A video of this talk will be made available to NIST staff in the Math channel on NISTube, which is accessible from the NIST internal home page. It will be taken down from NISTube after 12 months at which point it can be requested by emailing the ACMD Seminar Chair.

Abstract: Extending statistical analysis and machine learning methods to geometric data, such as datasets of curves or surfaces, is a challenging task due to the intricate structure of these objects and the specific set of group invariances that are involved. This talk will present two of the mainstream frameworks to endow spaces of submanifolds with Riemannian metrics: the intrinsic (elastic) model based on quotient Sobolev metrics and the extrinsic diffeomorphic approach derived from Grenander's shape space formalism. Despite their different characteristics, both of these provide effective settings for the comparison and interpolation of shapes and, by extension, for the generalization to geometric data of concepts and methods such as atlas estimation, parallel transport, tangent PCA and LDA, clustering... The presentation will focus specifically on the variational and optimal control formulation of such problems, and notably the use of tools from geometric measure theory for that purpose, as well as the numerical aspects of the implementation on discrete shapes. I will also discuss some extensions of those models, in particular to tackle the issue of partial data observations. Lastly, the talk will conclude with a few perspectives on ongoing and future research directions.

Bio: Nicolas is an Assistant Professor in the Department of Applied Mathematics and Statistics and the Center of Imaging Sciences at Johns Hopkins University. Prior to this position, he obtained my PhD in Mathematics from Ecole normale supérieure de Cachan in 2013 under the supervision of Pr. Alain Trouvé , and worked as a post-doctoral researcher at University of Copenhagen in Denmark. His main research interests are in morphological shape analysis and geometric methods for applications to medical imaging and computational anatomy. Specifically, mathematical and numerical models for the representation, registration and statistical analysis of geometric structures occurring in the anatomy and in biology.

Host: Gunay Dogan

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.)

Note: Visitors from outside NIST must contact Lochi Orr at least 24 hours in advance.