SIAM Undergraduate Research Online
Volume 18
In This Volume
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Applications of Automatic Differentiation in Image Registration
Published electronically July 28, 2025DOI: 10.1137/24S1710917
Authors
Warin Watson (Corresponding author – Colorado Mesa University), Cash Cherry (Colorado School of Mines), Rachelle Lang (University of Wisconsin – Madison)
Project Advisors
Lars Ruthotto (Emory University)
Abstract
We demonstrate that automatic differentiation (AD), which has become commonly available in machine learning frameworks, is an efficient way to explore ideas that lead to algorithmic improvement in multi-scale affine image registration and affine super-resolution problems. In our first experiment on multi-scale registration, we implement an ODE predictor-corrector method involving a derivative with respect to the scale parameter and the Hessian of an image registration objective function, both of which would be difficult to compute without AD. Our findings indicate that exact Hessians are necessary for the method to provide any benefits over a traditional multi-scale method; a Gauss-Newton Hessian approximation fails to provide such benefits. In our second experiment, we implement a variable projected Gauss-Newton method for super-resolution and use AD to differentiate through the iteratively computed projection, a method previously unaddressed in the literature. We show that Jacobians obtained without differentiating through the projection are poor approximations to the true Jacobians of the variable projected forward map and explore the performance of other approximations in the problem of super-resolution. By addressing these problems, this work contributes to the application of AD in image registration and sets a precedent for further use of machine learning tools in this field.
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Integrating Local Learning into the Two-Stage Markov Task to Separate Model-Based from Model-Free Learning
Published electronically July 11, 2025 -
Generative Modeling with Diffusion
Published electronically June 27, 2025 -
Bernstein Polynomials: A Bridge Between the Weierstrass Theorem and a Landau Temperature Fluctuation Problem
Published electronically June 10, 2025 -
An Agent-based Approach to the Gravity Model of Linguistic Diffusion
Published electronically May 28, 2025 -
Spatio-Temporal Analysis for Modeling High-Demand Events in European Private Aviation
Published electronically May 7, 2025 -
Analyzing Mortar Baseplate Movement Using Differential Equations
Published electronically April 29, 2025 -
Counting the Eigenvalues of the Laplace Operator on Some Convex Domains
Published electronically April 14, 2025 -
A Probabilistic Approach to the Enumeration of Bounded Motzkin Paths via the Gambler's Ruin
Published electronically March 19, 2025 -
A Comprehensive Study of Covid-19 in Florida
Published electronically March 12, 2025 -
Training Implicit Networks for Image Deblurring using Jacobian-Free Backpropagation
Published electronically February 26, 2025 -
Controlling Ball Progression in Soccer
Published electronically February 20, 2025 -
A Laplace Equation on a Rectangle With Mixed Boundary Conditions
Published electronically February 5, 2025 -
Modeling Traffic Conditions to Determine Shortest Path
Published electronically January 10, 2025
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