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Interpretable Unsupervised Deformable Image Registration via Confidence-bound Multi-Hop Visual Reasoning

Zafar Iqbal, Anwar Ul Haq, Srimannarayana Grandhi

TL;DR

This work tackles unsupervised deformable image registration by introducing a confidence-bound, multi-hop Visual Chain of Reasoning (VCoR) that progressively refines the deformation field $\mathbf{u}$ through three hops. Each hop combines Localized Spatial Refinement and Cross-Reference Attention to produce interpretable intermediate representations and attention maps, while a theoretical confidence–uncertainty bound links iterative refinements to increasing reliability. The method demonstrates competitive accuracy on DIR-Lab 4D CT and IXI brain MRI, achieving lower Target Registration Error and fewer negative Jacobians, with hop-wise DVFs and Jacobian visualizations providing transparent insights into the alignment process. These interpretability affordances and reliability guarantees aim to enhance clinical trust and facilitate deployment for longitudinal studies, surgical planning, and atlas construction. Overall, IMVCoR advances unsupervised DIR by marrying accurate, plausible deformations with explicit reasoning trails and uncertainty estimates.

Abstract

Unsupervised deformable image registration requires aligning complex anatomical structures without reference labels, making interpretability and reliability critical. Existing deep learning methods achieve considerable accuracy but often lack transparency, leading to error drift and reduced clinical trust. We propose a novel Multi-Hop Visual Chain of Reasoning (VCoR) framework that reformulates registration as a progressive reasoning process. Inspired by the iterative nature of clinical decision-making, each visual reasoning hop integrates a Localized Spatial Refinement (LSR) module to enrich feature representations and a Cross-Reference Attention (CRA) mechanism that leads the iterative refinement process, preserving anatomical consistency. This multi-hop strategy enables robust handling of large deformations and produces a transparent sequence of intermediate predictions with a theoretical bound. Beyond accuracy, our framework offers built-in interpretability by estimating uncertainty via the stability and convergence of deformation fields across hops. Extensive evaluations on two challenging public datasets, DIR-Lab 4D CT (lung) and IXI T1-weighted MRI (brain), demonstrate that VCoR achieves competitive registration accuracy while offering rich intermediate visualizations and confidence measures. By embedding an implicit visual reasoning paradigm, we present an interpretable, reliable, and clinically viable unsupervised medical image registration.

Interpretable Unsupervised Deformable Image Registration via Confidence-bound Multi-Hop Visual Reasoning

TL;DR

This work tackles unsupervised deformable image registration by introducing a confidence-bound, multi-hop Visual Chain of Reasoning (VCoR) that progressively refines the deformation field through three hops. Each hop combines Localized Spatial Refinement and Cross-Reference Attention to produce interpretable intermediate representations and attention maps, while a theoretical confidence–uncertainty bound links iterative refinements to increasing reliability. The method demonstrates competitive accuracy on DIR-Lab 4D CT and IXI brain MRI, achieving lower Target Registration Error and fewer negative Jacobians, with hop-wise DVFs and Jacobian visualizations providing transparent insights into the alignment process. These interpretability affordances and reliability guarantees aim to enhance clinical trust and facilitate deployment for longitudinal studies, surgical planning, and atlas construction. Overall, IMVCoR advances unsupervised DIR by marrying accurate, plausible deformations with explicit reasoning trails and uncertainty estimates.

Abstract

Unsupervised deformable image registration requires aligning complex anatomical structures without reference labels, making interpretability and reliability critical. Existing deep learning methods achieve considerable accuracy but often lack transparency, leading to error drift and reduced clinical trust. We propose a novel Multi-Hop Visual Chain of Reasoning (VCoR) framework that reformulates registration as a progressive reasoning process. Inspired by the iterative nature of clinical decision-making, each visual reasoning hop integrates a Localized Spatial Refinement (LSR) module to enrich feature representations and a Cross-Reference Attention (CRA) mechanism that leads the iterative refinement process, preserving anatomical consistency. This multi-hop strategy enables robust handling of large deformations and produces a transparent sequence of intermediate predictions with a theoretical bound. Beyond accuracy, our framework offers built-in interpretability by estimating uncertainty via the stability and convergence of deformation fields across hops. Extensive evaluations on two challenging public datasets, DIR-Lab 4D CT (lung) and IXI T1-weighted MRI (brain), demonstrate that VCoR achieves competitive registration accuracy while offering rich intermediate visualizations and confidence measures. By embedding an implicit visual reasoning paradigm, we present an interpretable, reliable, and clinically viable unsupervised medical image registration.
Paper Structure (16 sections, 1 theorem, 15 equations, 4 figures, 4 tables, 1 algorithm)

This paper contains 16 sections, 1 theorem, 15 equations, 4 figures, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Proposed Methodology
  4. Feature Extraction
  5. Visual Chain of Reasoning (VCoR)
  6. VCoR Hop-1: Coarse Alignment
  7. VCoR Hop-2: Intermediate Alignment
  8. VCoR Hop-3: Fine Alignment
  9. Confidence–Uncertainty Bounds in Multi-Hop Registration
  10. Experiments and Evaluation
  11. Loss Function
  12. Evaluation Metrics
  13. Results and Discussion
  14. Ablation Experiments
  15. Limitations and Future Work
  16. ...and 1 more sections

Key Result

Lemma 1

Let $I, J : \Omega \to \mathbb{R}$ be an image pair on domain $\Omega \subset \mathbb{R}^D$. At hop $h \in \{0, \dots, H\}$, let $\Phi_h, \Psi_h : \Omega \to \mathbb{R}^D$ denote the deformation fields produced by a coarse-to-fine refiner. Let $S_h \in \mathbb{R}$ be a similarity score between the w Confidence and Uncertainty. Define confidence as a smooth, strictly increasing function of similar

Figures (4)

  • Figure 1: The proposed VCoR architecture performs three progressive reasoning hops, each combining a Localized Spatial Refinement (LSR) and Cross-Reference Attention (CRA) block. This design ensures anatomically consistent alignment while providing interpretability through hop-wise intermediate outputs.
  • Figure 2: Confidence and uncertainty evolution across VCoR hops. (a) DIR-Lab: empirical weighting shows greater confidence gains (0.472→0.571) and lower uncertainty than constant weighting (0.452→0.549). (b) IXI: similar trends confirm the robustness of empirical weighting within the VCoR framework.
  • Figure 3: Interpretable visualization of folding reduction across VCoR hops. Three orthogonal slices (axial, coronal, sagittal) are shown per step, with the last column presenting Jacobian determinant maps that enhance explainability: blue highlights folding (negative determinants), green near 1 indicates local volume preservation, and bright colours mark regions of expansion. Jacobian maps in the last column enhance interpretability by localizing folding artifacts.
  • Figure 4: Interpretable visualization for IXI brain MRI showing progressive reduction of folding artifacts across VCoR hops. Three orthogonal slices (axial, coronal, sagittal) are displayed at each step. The last column shows Jacobian determinant maps: blue indicates folding (negative), green near 1 denotes volume preservation, and bright colours highlight expansion. Jacobian maps in the last column enhance interpretability by localizing folding artifacts.

Theorems & Definitions (1)

  • Lemma 1: Confidence–Uncertainty Bounds Across Multi-Hop Registration