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Fast Rigid Alignment of Heterogeneous Images in Sliced Wasserstein Distance
Yunpeng Shi1, Amit Singer2,3, Eric J Verbeke3
1Department of Mathematics, University of California at Davis, Davis, CA 95616 USA.
SIAM Journal on Imaging Sciences
|August 12, 2026
Summary
This study introduces a fast algorithm for aligning heterogeneous images using optimal transport. The method efficiently computes image alignment, proving robust against various image transformations.
Area of Science:
- Computer Vision
- Image Processing
- Computational Geometry
Background:
- Image alignment is crucial for many computer vision applications.
- Aligning similar but non-identical images presents a significant challenge.
- Existing methods may lack speed or robustness.
Purpose of the Study:
- To develop a fast and robust algorithm for aligning heterogeneous images.
- To leverage optimal transport theory for efficient image alignment.
- To demonstrate the algorithm's effectiveness against image transformations.
Main Methods:
- Utilized optimal transport theory for image alignment.
- Combined fast Fourier methods with sliced probability metrics.
- Employed the sliced 2-Wasserstein distance for computation.
- Achieved an operational complexity of O(L^2 log L) for L x L images.
Main Results:
- Developed a computationally efficient algorithm for image alignment.
- Demonstrated robustness against translations, rotations, and deformations.
- The algorithm achieves alignment in O(L^2 log L) operations.
Conclusions:
- The proposed algorithm offers a fast and robust solution for heterogeneous image alignment.
- Optimal transport provides an effective framework for addressing this computer vision task.
- The method has potential applications in various image analysis scenarios.
