Fast algorithms for nonlinear optimal control of geodesic flows of diffeomorphisms
Oct 14, 2022, 10:00 AM - 12:00 PM
Room: Expl. 4106
In this talk, we will discuss optimal control formulations for diffeomorphic registration and efficient algorithms for their solution. Our contributions are in the design of numerical methods and computational kernels that scale on heterogeneous, high-performance computing platforms. Diffeomorphic registration is an infinite-dimensional, nonlinear inverse problem. The inputs are two views of the same object. Given these views, we seek a spatial transformation $y$ that relates points in one view to its corresponding points in the other. We formulate the problem as a constrained optimization problem with dynamical systems as constraints. We introduce a pseudo-time variable $t$ and parameterize the sought-after mapping $y$ by its velocity $v$. Prescribing suitable regularity requirements for $v$ allows us to ensure that $y$ is a diffeomorphism. We will explore different formulations and discuss various numerical solution strategies.
Our solvers are based on state-of-the-art algorithms to enable fast convergence and short runtime. We will showcase results on real and synthetic data to study the rate of convergence, time-to-solution, numerical accuracy, and scalability of our solvers. As a highlight, we will showcase results for a GPU-accelerated implementation termed CLAIRE that allows us to solve clinically relevant 3D image registration problems with 50 million unknowns to high accuracy in under 5 seconds on a single GPU, and scales up to 100s of GPUs.
This is joint work with George Biros, Miriam Schulte, and others.
Speaker: Andreas Mang
Affiliation: University of Houston (Room: Expl. 4106)
For questions please contact Harbir Antil (firstname.lastname@example.org).