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FireANTs: Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching

Rohit Jena, Pratik Chaudhari, James C. Gee

TL;DR

FireANTs tackles the core challenges of dense diffeomorphic registration by removing the need for training and harnessing a multi-scale Adaptive Riemannian optimization on the group of diffeomorphisms. The method uses a Jacobian-free Eulerian descent that exploits the Lie group structure to obtain fast, scalable updates without parallel transport, enabling high-resolution registration on GPUs and rapid hyperparameter tuning. Across fourteen datasets spanning brains, lungs, abdomen, and microscopy, FireANTs achieves state-of-the-art performance, strong cross-domain generalization, and substantial runtime/memory advantages over ANTs and many deep learning baselines. The approach supports scalable atlas generation and real-world deployments, providing a practical, modular tool for high-throughput, multi-modal image registration in biomedical science. Overall, FireANTs delivers a fast, robust, training-free framework that scales to mesoscale and microscale imaging while preserving diffeomorphic integrity and enabling rapid experimentation.

Abstract

The paper proposes FireANTs, a multi-scale Adaptive Riemannian Optimization algorithm for dense diffeomorphic image matching. Existing state-of-the-art methods for diffeomorphic image matching are slow due to inefficient implementations and slow convergence due to the ill-conditioned nature of the optimization problem. Deep learning methods offer fast inference but require extensive training time, substantial inference memory, and fail to generalize across long-tailed distributions or diverse image modalities, necessitating costly retraining. We address these challenges by proposing a training-free, GPU-accelerated multi-scale Adaptive Riemannian Optimization algorithm for fast and accurate dense diffeomorphic image matching. FireANTs runs about 2.5x faster than ANTs on a CPU, and upto 1200x faster on a GPU. On a single GPU, FireANTs performs competitively with deep learning methods on inference runtime while consuming upto 10x less memory. FireANTs shows remarkable robustness to a wide variety of matching problems across modalities, species, and organs without any domain-specific training or tuning. Our framework allows hyperparameter grid search studies with significantly less resources and time compared to traditional and deep learning registration algorithms alike.

FireANTs: Adaptive Riemannian Optimization for Multi-Scale Diffeomorphic Matching

TL;DR

FireANTs tackles the core challenges of dense diffeomorphic registration by removing the need for training and harnessing a multi-scale Adaptive Riemannian optimization on the group of diffeomorphisms. The method uses a Jacobian-free Eulerian descent that exploits the Lie group structure to obtain fast, scalable updates without parallel transport, enabling high-resolution registration on GPUs and rapid hyperparameter tuning. Across fourteen datasets spanning brains, lungs, abdomen, and microscopy, FireANTs achieves state-of-the-art performance, strong cross-domain generalization, and substantial runtime/memory advantages over ANTs and many deep learning baselines. The approach supports scalable atlas generation and real-world deployments, providing a practical, modular tool for high-throughput, multi-modal image registration in biomedical science. Overall, FireANTs delivers a fast, robust, training-free framework that scales to mesoscale and microscale imaging while preserving diffeomorphic integrity and enabling rapid experimentation.

Abstract

The paper proposes FireANTs, a multi-scale Adaptive Riemannian Optimization algorithm for dense diffeomorphic image matching. Existing state-of-the-art methods for diffeomorphic image matching are slow due to inefficient implementations and slow convergence due to the ill-conditioned nature of the optimization problem. Deep learning methods offer fast inference but require extensive training time, substantial inference memory, and fail to generalize across long-tailed distributions or diverse image modalities, necessitating costly retraining. We address these challenges by proposing a training-free, GPU-accelerated multi-scale Adaptive Riemannian Optimization algorithm for fast and accurate dense diffeomorphic image matching. FireANTs runs about 2.5x faster than ANTs on a CPU, and upto 1200x faster on a GPU. On a single GPU, FireANTs performs competitively with deep learning methods on inference runtime while consuming upto 10x less memory. FireANTs shows remarkable robustness to a wide variety of matching problems across modalities, species, and organs without any domain-specific training or tuning. Our framework allows hyperparameter grid search studies with significantly less resources and time compared to traditional and deep learning registration algorithms alike.
Paper Structure (59 sections, 1 theorem, 24 equations, 33 figures, 1 table, 1 algorithm)

This paper contains 59 sections, 1 theorem, 24 equations, 33 figures, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Results
  3. Experiment Setup
  4. In-vivo brain mapping challenges klein2009evaluationoasisdataset
  5. PRIMatE Data Exchange (PRIME-DE) primate
  6. Ultracortex ultracortex
  7. Waxholm Rat Brain and Allen CCFv3 mouse brain datasets kleven2023waxholmwang2020allen
  8. Lung CT mapping challenges murphy2011evaluationnlst
  9. RnR ExM Mouse Isocortex Dataset rnrexm
  10. AZBA and ZBrain datasets azbazbrain
  11. BICCN Mouse Dataset
  12. Learn2Reg Abdomen MRCT registration hering2022learn2reg
  13. Results on generalization to long-tail of modalities
  14. Results on state-of-the-art biomedical benchmarks
  15. In-vivo brain MRI mapping
  16. ...and 44 more sections

Key Result

Theorem 1

For a $C^\infty(\Omega, \mathbb{R}^d)$ velocity field $v_0$ with compact support on $\Omega$ such that $v_0(x) = 0$ on $x \in \partial \Omega$, the transform $\varphi = id + \epsilon v_0$ is a diffeomorphism for $|\epsilon| < 1/LP(v_0)$, where $LP(v_0)$ is the Lipschitz constant of $v_0$.

Figures (33)

  • Figure 1: Overview of datasets used in the paper.
  • Figure 2: Normalized performance of state-of-the-art registration algorithms across a wide range of datasets and benchmarks. FireANTs achieves asymptotically best normalized performance across various datasets and evaluation criteria.
  • Figure 3: Raw performance (measured by Dice Score, Mutual Information of Labelmap and Intensity, Landmark Distance) of state-of-the-art registration algorithms across various datasets. In all datasets except NLST, higher scores are better. Colorbars are shown in \ref{['fig:radarchart']} with lightgray denoting zero displacement (baseline).
  • Figure 5: Following the evaluation setup of Klein et al. paper, we validate registration performance using the average volume overlap of all anatomical label maps between the fixed and warped label maps. We consider ANTs (the winner of the challenge), and Diffeomorphic Demons as state-of-the-art optimization algorithms, and Voxelmorph and Synthmorph as state-of-the-art unsupervised deep learning baselines. Evaluation is shown for five metrics with $\uparrow$ denoting a higher score is better, and $\downarrow$ signifying a lower score is better. For deep learning baselines, appropriate preprocessing (intensity normalization, alignment, and resampling to 1mm isotropic) is performed to ensure a fair comparison, whereas no such preprocessing is required for optimization methods, including FireANTs. FireANTs shows significant gains in performance that are consistent across all four datasets, with the median overlap scores outperforming the third quartile of all other methods for IBSR18 and CUMC12 datasets. Comparison of overlap metrics by specific anatomical regions are in \ref{['fig:regionwise-dice-brain']}. For the overlap aggregation mentioned in klein2009evaluation, results are shown in \ref{['fig:braintable_klein']}.
  • Figure 6: FireANTs achieves substantially lower inter-quartile range of fissure errors, defined as the percentage of marked pixels that are registered to points on the opposite side of the fissure boundary.
  • ...and 28 more figures

Theorems & Definitions (2)

  • Theorem 1
  • proof