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

TL;DR
This paper explores how logic can model round-off errors and Gaussian blur in 1D image registration, revealing conditions for accurate signal recovery amidst interference and proposing bounds estimation methods.
Contribution
It introduces a logical framework to analyze the effects of blur and round-off errors on signal recovery, focusing on the commingling interference phenomenon.
Findings
Identifies conditions where signal discontinuities can be correctly recovered.
Describes a logical approach to analyze sample interference.
Proposes methods to estimate bounds on discontinuity distances.
Abstract
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 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…
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Taxonomy
TopicsMedical Image Segmentation Techniques · Image and Object Detection Techniques
MethodsFocus
