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Unbalanced optimal transport for robust longitudinal lesion evolution with registration-aware and appearance-guided priors

Melika Qahqaie, Dominik Neumann, Tobias Heimann, Andreas Maier, Veronika A. Zimmer

TL;DR

This work reframes longitudinal lesion correspondence as unbalanced optimal transport (UOT) to allow lesions to appear or disappear, enabling robust matching even when topology changes occur. It augments UOT with registration-trust from deformation fields and patch-based appearance consistency, plus a tumor-load–aware asymmetry prior to adapt to global burden changes. The resulting transport plan yields a lesion-evolution graph that encodes persistent, new, disappearing, merging, and splitting events without retraining. Across synthetic and clinical lung-CT data, the approach improves edge-detection, lesion-state recall, and topology fidelity over distance-based baselines, especially in complex scenarios with merges and splits. This principled, interpretable framework supports more accurate and reliable longitudinal tumor assessment with potential clinical impact.

Abstract

Evaluating lesion evolution in longitudinal CT scans of can cer patients is essential for assessing treatment response, yet establishing reliable lesion correspondence across time remains challenging. Standard bipartite matchers, which rely on geometric proximity, struggle when lesions appear, disappear, merge, or split. We propose a registration-aware matcher based on unbalanced optimal transport (UOT) that accommodates unequal lesion mass and adapts priors to patient-level tumor-load changes. Our transport cost blends (i) size-normalized geometry, (ii) local registration trust from the deformation-field Jacobian, and (iii) optional patch-level appearance consistency. The resulting transport plan is sparsified by relative pruning, yielding one-to-one matches as well as new, disappearing, merging, and splitting lesions without retraining or heuristic rules. On longitudinal CT data, our approach achieves consistently higher edge-detection precision and recall, improved lesion-state recall, and superior lesion-graph component F1 scores versus distance-only baselines.

Unbalanced optimal transport for robust longitudinal lesion evolution with registration-aware and appearance-guided priors

TL;DR

This work reframes longitudinal lesion correspondence as unbalanced optimal transport (UOT) to allow lesions to appear or disappear, enabling robust matching even when topology changes occur. It augments UOT with registration-trust from deformation fields and patch-based appearance consistency, plus a tumor-load–aware asymmetry prior to adapt to global burden changes. The resulting transport plan yields a lesion-evolution graph that encodes persistent, new, disappearing, merging, and splitting events without retraining. Across synthetic and clinical lung-CT data, the approach improves edge-detection, lesion-state recall, and topology fidelity over distance-based baselines, especially in complex scenarios with merges and splits. This principled, interpretable framework supports more accurate and reliable longitudinal tumor assessment with potential clinical impact.

Abstract

Evaluating lesion evolution in longitudinal CT scans of can cer patients is essential for assessing treatment response, yet establishing reliable lesion correspondence across time remains challenging. Standard bipartite matchers, which rely on geometric proximity, struggle when lesions appear, disappear, merge, or split. We propose a registration-aware matcher based on unbalanced optimal transport (UOT) that accommodates unequal lesion mass and adapts priors to patient-level tumor-load changes. Our transport cost blends (i) size-normalized geometry, (ii) local registration trust from the deformation-field Jacobian, and (iii) optional patch-level appearance consistency. The resulting transport plan is sparsified by relative pruning, yielding one-to-one matches as well as new, disappearing, merging, and splitting lesions without retraining or heuristic rules. On longitudinal CT data, our approach achieves consistently higher edge-detection precision and recall, improved lesion-state recall, and superior lesion-graph component F1 scores versus distance-only baselines.
Paper Structure (15 sections, 4 equations, 2 figures, 1 table)

This paper contains 15 sections, 4 equations, 2 figures, 1 table.

Table of Contents

  1. Introduction
  2. Methods
  3. Problem setup
  4. Unbalanced Optimal Transport
  5. Cost function for lesion matching
  6. Asymmetric marginal weighting
  7. Graph extraction
  8. Experiments and Results
  9. Datasets
  10. Evaluation
  11. Results on synthetic data
  12. Results on clinical data
  13. Conclusion
  14. Compliance with ethical standards
  15. Acknowledgments

Figures (2)

  • Figure 1: Overview of our Unbalanced Optimal Transport framework for lesion matching.
  • Figure 2: Classification of topology classes on the synthetic dataset (row A) and clinical test set (row B).