SIAM Undergraduate Research Online

Volume 18

In This Volume

  • DOI: 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.

  • Generative Modeling with Diffusion

    Published electronically June 27, 2025
  • A Comprehensive Study of Covid-19 in Florida

    Published electronically March 12, 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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