Numerical Uncertainty in Linear MRI Registration

This repository contains the code and experimental setup for the project “Numerical Uncertainty in Linear Registration: An Experimental Study.”.

The goal of this work is to investigate how floating-point numerical perturbations affect the stability, reliability, and quality of commonly used linear MRI registration tools.

🚧 Under Active Refactoring 🚧 This repository is currently being refactored from research scripts into a production-ready Python package.

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🧠 Background & Motivation

Linear registration is a core step in most neuroimaging preprocessing pipelines. Despite its widespread use, its numerical stability—that is, sensitivity to small floating-point errors introduced by software, hardware, or compiler differences—has been largely understudied.

Even minor numerical perturbations can:

• Steer optimizers toward different local minima
• Cause sporadic registration failures
• Propagate uncertainty into downstream analyses

This project systematically quantifies these effects using Monte-Carlo Arithmetic (MCA).

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🔬 What This Project Does

We assess numerical uncertainty across:

• Registration software

  • SPM (spm_affreg)
  • FSL (FLIRT)
  • ANTs (antsRegistration)

• Similarity measures

  • SSD, NCC, CR, MI, NMI (tool-dependent)

• Templates

  • Symmetric and asymmetric MNI152 (1 mm resolution)

• Cohorts

  • Healthy controls (HC)
  • Parkinson’s disease (PD)

Each registration is run once using standard IEEE floating-point arithmetic and multiple times under MCA perturbations to quantify variability.

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📏 Numerical Uncertainty Metric

Numerical uncertainty is measured using the standard deviation of Framewise Displacement (FD) across perturbed runs.

FD provides a single, interpretable scalar that summarizes variability in affine registration parameters (translation, rotation, scale, and shear). Higher FD variability indicates greater numerical instability.

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📊 Key Findings

• SPM is the most numerically stable among the evaluated tools.
• FSL and ANTs show larger variability, with ANTs occasionally exhibiting catastrophic failures under perturbation.
• Similarity measure choice matters: NCC and CR are generally more stable than MI/NMI in FSL.
• In some cases, numerical variability reaches magnitudes comparable to voxel size or in-scanner head motion, making it practically significant.
• Cohort (HC vs PD) and template choice do not significantly affect numerical stability.
• MCA-derived variability metrics show promise as features for automated quality control (QC).

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🤖 Automated QC (Proof of Concept)

Subjects that fail visual QC consistently show higher numerical variability. This suggests that MCA-based uncertainty measures can support:

• Automated QC
• Anomaly detection
• More reproducible preprocessing pipelines

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🧰 Tools & Frameworks

• Monte-Carlo Arithmetic

  • Verificarlo (fuzzy-libm backend)
  • Verrou (validation experiments)

• Neuroimaging software

  • SPM12
  • FSL 6.x
  • ANTs 2.5+

• Infrastructure

  • Dockerized pipelines for reproducibility

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📁 Repository Structure

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├── docker/              # Dockerfiles for perturbed & unperturbed tools
├── scripts/             # Registration and execution scripts
├── analysis/            # FD computation and statistical analyses
├── qc/                  # QC labels and exploratory models
├── figures/             # Figures used in the manuscript
└── README.md