# Application and Evaluation of the Common Circles Method

arXiv: https://arxiv.org/abs/2602.17353 · HTML: https://mlsanity.com/paper/2602.17353/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 42 references that are in the map.
- First posted on arXiv 19 Feb 2026.

## Builds on (most cited first, 5 of 5)

- [Synchronizing Probability Measures on Rotations via Optimal Transport](https://mlsanity.com/paper/2004.00663/) (2020)
- [Parallelly Sliced Optimal Transport on Spheres and on the Rotation Group](https://mlsanity.com/paper/2401.16896/) (2024)
- [Fast rigid alignment of heterogeneous images in sliced Wasserstein distance](https://mlsanity.com/paper/2503.13756/) (2025)
- [Total variation-based reconstruction and phase retrieval for diffraction tomography](https://mlsanity.com/paper/2201.11579/) (2022)
- [Motion Detection in Diffraction Tomography by Common Circle Methods](https://mlsanity.com/paper/2209.08086/) (2022)

## Abstract (arXiv)

We investigate the application of the common circle method for estimating sample motion in optical diffraction tomography (ODT) of sub-millimeter sized biological tissue. When samples are confined via contact-free acoustical force fields, their motion must be estimated from the captured images. The common circle method identifies intersections of Ewald spheres in Fourier space to determine rotational motion. This paper presents a practical implementation, incorporating temporal consistency constraints to achieve stable reconstructions. Our results on both simulated and real-world data demonstrate that the common circle method provides a computationally efficient alternative to full optimization methods for motion detection.