P. Thomas Fletcher

Also known as Tom Fletcher

Tom Fletcher is a researcher who brings differential geometry and statistics to medical image analysis, computer vision and, more recently, deep generative models. A mathematics B.A. at the University of Virginia in 1999 led to a computer science Ph.D. at UNC Chapel Hill in 2004, the year principal geodesic analysis, a generalization of principal component analysis to nonlinear spaces, appeared in IEEE Transactions on Medical Imaging. A 2007 ICCV paper on population shape regression, written while Fletcher was at the University of Utah, won the Marr Prize, and a National Science Foundation CAREER Award followed in 2012. Papers on the geometry of deep generative models appeared in 2017 and 2025, and the co-edited book Riemannian Geometric Statistics in Medical Image Analysis was published in 2019. As of October 2026, Fletcher is an associate professor of electrical and computer engineering and of computer science at the University of Virginia.

Now at: University of Virginia
Badges: Boomerang

Timeline

1999–2004

Degrees at Virginia and UNC

Fletcher earns a B.A. in mathematics at the University of Virginia in 1999, then an M.S. in computer science in 2002 and a Ph.D. in computer science in 2004 at the University of North Carolina at Chapel Hill. The UNC thesis, "Statistical Variability in Nonlinear Spaces: Application to Shape Analysis and DT-MRI," is advised by Stephen Pizer.
2004

Principal geodesic analysis

In August 2004, Fletcher and three coauthors, including Sarang Joshi and Stephen Pizer, publish "Principal Geodesic Analysis for the Study of Nonlinear Statistics of Shape" in IEEE Transactions on Medical Imaging. A 2004 ECCV workshop paper with Joshi extends principal geodesic analysis, a generalization of principal component analysis, to symmetric spaces and applies it to the variability of diffusion tensor data.
2007

Marr Prize at ICCV

At ICCV in 2007, "Population Shape Regression From Random Design Data" by Bradley Davis, Fletcher, Elizabeth Bullitt and Sarang Joshi wins the Marr Prize, which goes to the best paper at the conference. Fletcher and Joshi are at the University of Utah, and the research is part of Davis's PhD work at UNC Chapel Hill.
2010–2012

A most-cited paper and NSF CAREER

In 2010, the journal Signal Processing names "Riemannian Geometry for the Statistical Analysis of Diffusion Tensor Data," by Fletcher and Sarang Joshi, its most-cited paper among articles published from 2007 to 2009. In 2012, as a USTAR assistant professor in Utah's School of Computing, Fletcher receives a National Science Foundation CAREER Award to develop nonlinear statistical models and classification procedures for time-varying shape. The research combines statistics and differential geometry to solve problems in medical image analysis and computer vision.
2013

Papers at NeurIPS, ICML and ISBI

In 2013, "Probabilistic Principal Geodesic Analysis" and "Adaptive Sparsity in Gaussian Graphical Models," both coauthored by Fletcher, appear at Neural Information Processing Systems and the International Conference on Machine Learning, respectively. A paper by Nikhil Singh, Jacob Hinkle, Sarang Joshi and Fletcher, "A Vector Momenta Formulation of Diffeomorphisms for Improved Geodesic Regression and Atlas Construction," wins Best Student Paper at ISBI 2013.
2017

Geometry of deep generative models

In 2017, Fletcher coauthors "The Riemannian Geometry of Deep Generative Models" with Hang Shao and Abhishek Kumar. The paper develops algorithms for geodesic curves and parallel translation on the manifolds that deep generative models parameterize, and finds on real image data that these manifolds are surprisingly close to zero curvature.
2019

Co-editing a Riemannian statistics book

With Xavier Pennec and Stefan Sommer, Fletcher co-edits Riemannian Geometric Statistics in Medical Image Analysis, published by Elsevier in September 2019. The book is a reference on statistics on Riemannian manifolds and other nonlinear spaces, with applications in medical image analysis.
As of October 2026

Associate professor at Virginia

Fletcher is an associate professor in both the Department of Electrical and Computer Engineering and the Department of Computer Science at the University of Virginia. In October 2025, "A Likely Geometry of Generative Models," coauthored with Frederik Möbius Rygaard, Shen Zhu, Yinzhu Jin and Søren Hauberg, appears on arXiv; the paper constructs a general geometry for analyzing generative models without additional training.