# On the Logic Elements Associated with Round-Off Errors and Gaussian Blur in Image Registration: A Simple Case of Commingling

arXiv: https://arxiv.org/abs/2502.11992 · HTML: https://mlsanity.com/paper/2502.11992/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 19 references that are in the map.
- First posted on arXiv 17 Feb 2025.

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

- [The Sliding Frank-Wolfe Algorithm and its Application to Super-Resolution Microscopy](https://mlsanity.com/paper/1811.06416/) (2018)
- [On Image Registration and Subpixel Estimation](https://mlsanity.com/paper/2405.12927/) (2024)
- [A Counterexample in Image Registration](https://mlsanity.com/paper/2410.10725/) (2024)
- [A Counterexample in Cross-Correlation Template Matching](https://mlsanity.com/paper/2410.19085/) (2024)
- [On Round-Off Errors and Gaussian Blur in Superresolution and in Image Registration](https://mlsanity.com/paper/2412.09741/) (2024)

## Abstract (arXiv)

Discrete image registration can be a strategy to reconstruct signals from samples corrupted by blur and noise. We examine superresolution and discrete image registration for one-dimensional spatially-limited piecewise constant functions which are subject to blur which is Gaussian or a mixture of Gaussians as well as to round-off errors. Previous approaches address the signal recovery problem as an optimization problem. We focus on a regime with low blur and suggest that the operations of blur, sampling, and quantization are not unlike the operation of a computer program and have an abstraction that can be studied with a type of logic. When the minimum distance between discontinuity points is between 1.5 and 2 times the sampling interval, we can encounter the simplest form of a type of interference between discontinuity points that we call ``commingling.'' We describe a way to reason about two sets of samples of the same signal that will often result in the correct recovery of signal amplitudes. We also discuss ways to estimate bounds on the distances between discontinuity points.