LUMINR: Intensity-conditioned Meta-learned INRs for Accelerated Medical Image Registration

Damian Rynczak; Marek Wodzinski

eess.IVOct 16, 2026

LUMINR: Intensity-conditioned Meta-learned INRs for Accelerated Medical Image Registration

Authors: Damian Rynczak, Marek Wodzinski

Organizations: AGH University of Krakow · Sano - Centre for Computational Personalised Medicine, International Research Foundation

Abstract

Implicit neural representations (INRs) have been applied to deformable image registration, where a lightweight network maps a spatial coordinate to a deformation vector. Because an INR encodes one specific signal in its parameters, a fresh network must be optimized for every image pair at test time, which is slow. Existing methods reduce this cost by meta-learning an initialization across a population of image pairs, and condition the weights of the INR globally, so the same conditioning applies at every coordinate while the deformation field it initializes varies across the domain. We propose LUMINR, a meta-learning framework that accelerates this per-pair fitting and in which the conditioning is local instead. LUMINR uses an INR that maps a coordinate, together with local intensity and gradient features, to a deformation vector, so the conditioning varies over the domain at the resolution of the field being modelled. Its objective is to find an initialization of the INR parameters from which the network can be fine-tuned to register any unseen pair in only a few optimization iterations. We evaluate LUMINR on 3D deformable registration of brain MRI from the OASIS dataset, where local conditioning and the meta-learned initialization prove complementary: early in fitting they reach a markedly higher accuracy than either does alone. Fine-tuned from that initialization, LUMINR matches the accuracy of the same conditioned INR fit from scratch in roughly a tenth of the gradient steps and a tenth of the wall-clock time, while the deformation fields stay smooth with negligible folding.

Figures & tables

Figure 1: LUMINR uses a multi-layer perceptron (MLP) that implicitly represents the function $\Phi$ , mapping an input feature vector from the moving image to its corresponding location in the fixed image. Using Reptile meta-learning, LUMINR finds an initialization $\theta^{*}$ from which $f_{\theta}$ can be fine-tuned to the correct correspondence for any unseen image pair in only a few optimization iterations.

Figure 2: Comparison of segmentation performance for the LUMINR (meta) and LUMINR (random) models ( $\alpha$ = 0.1) across 4 classes. We report the mean Dice score at each optimization iteration for a single pair of the MRI volumes. The meta-learned initialization leads to rapid convergence and achieves reasonable segmentation (Dice = 0.82) after 10 iterations.

Figure 3: Mean Dice score over all test pairs at each fitting iteration (

\alpha=0.1

), on the coarse 4-class (left) and the fine 35-class (right) labelling, background included; the grey dotted line is the pre-registration, affine-only Dice (

0.691

and

0.584

). LUMINR (meta) matches at 50 steps the Dice that LUMINR (random) reaches only at 500, and by two steps it already exceeds every point of both INR curves on DSC 4 ; on DSC 35 two steps match the INR baseline at 500 steps and ten steps clear INR (meta).

	LUMINR (meta)				LUMINR (random)
Iter.	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$
	[-]	[-]	[s]	[%]	[-]	[-]	[s]	[%]
2	0.764 [0.756, 0.771]	0.610 [0.598, 0.620]	0.27 [0.26, 0.27]	0.26 [0.06, 0.56]	0.471 [0.460, 0.481]	0.202 [0.189, 0.217]	0.28 [0.26, 0.29]	$0$ [0, 0]
10	0.825 [0.819, 0.832]	0.676 [0.664, 0.688]	1.32 [1.32, 1.33]	0.94 [0.00, 2.73]	0.640 [0.632, 0.647]	0.436 [0.421, 0.452]	1.31 [1.30, 1.33]	$0$ [0, 0]
50	0.843 [0.837, 0.849]	0.694 [0.683, 0.706]	6.55 [6.55, 6.56]	1.41 [0.46, 2.61]	0.734 [0.728, 0.740]	0.573 [0.562, 0.583]	6.50 [6.48, 6.52]	0.32 [0.00, 0.95]
100	0.844 [0.838, 0.850]	0.695 [0.683, 0.706]	13.12 [13.09, 13.19]	2.07 [0.48, 4.68]	0.774 [0.767, 0.780]	0.614 [0.602, 0.625]	12.98 [12.96, 13.00]	13.42 [0.13, 39.06]

Table 1: Mean Dice score, cumulative fitting time, and fraction of folding voxels across fitting iterations for the LUMINR (meta) and LUMINR (random) models. DSC 4 and DSC 35 are Dice on the coarse (4-class) and fine (35-class) labellings respectively; fitting time and folding are independent of the labelling and are therefore reported once. Each entry is the mean over all test pairs with its 95% confidence interval in brackets. Both models are the same architecture: the left one is fitted from the meta-learned initialization, the right one from a random initialization.

Figure 4: Mean Dice score over all test pairs at each evaluated fitting iteration (

\alpha=0.1

), on the coarse 4-class (left) and the fine 35-class (right) labelling, background included; the grey dotted line is the pre-registration, affine-only Dice (

0.691

and

0.584

). At 50 steps LUMINR (meta) comes within

0.002

of the Dice that LUMINR (random) reaches only at 500, and by two steps it already exceeds every point of both INR GS curves on DSC 4 ; on DSC 35 two steps match INR GS at 50 steps and ten steps clear both curves.

Figure 5: Mean Dice over all test pairs at each fitting iteration for LUMINR at three regularization strengths (

\alpha\in\{0.01,0.1,1.0\}

); 4-class and 35-class and background labelling. The choice of

\alpha

barely affects the converged score: the settings agree by 50 steps and plateau together at 500, differing only in the first few iterations where weaker regularization (

\alpha=0.01

) starts slightly higher.

	INR (meta)				INR (random)
Iter.	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$
	[-]	[-]	[s]	[%]	[-]	[-]	[s]	[%]
2	0.665 [0.657, 0.674]	0.528 [0.512, 0.544]	0.35 [0.32, 0.39]	$0$ [0, 0]	0.640 [0.631, 0.648]	0.471 [0.456, 0.487]	0.75 [0.59, 0.95]	$0$ [0, 0]
10	0.689 [0.681, 0.697]	0.573 [0.560, 0.586]	1.53 [1.49, 1.57]	$0$ [0, 0]	0.688 [0.680, 0.695]	0.575 [0.562, 0.587]	2.34 [2.10, 2.61]	$0$ [0, 0]
50	0.723 [0.716, 0.730]	0.630 [0.619, 0.641]	7.50 [7.44, 7.55]	$0$ [0, 0]	0.667 [0.658, 0.675]	0.525 [0.509, 0.540]	9.42 [8.98, 9.89]	$0$ [0, 0]
100	0.726 [0.718, 0.733]	0.638 [0.627, 0.649]	15.00 [14.93, 15.08]	$0$ [0, 0]	0.678 [0.670, 0.686]	0.550 [0.535, 0.564]	18.17 [17.59, 18.77]	$0$ [0, 0]

Table 2: Mean Dice score, cumulative fitting time, and fraction of folding voxels across fitting iterations for the baseline INR (meta) and INR (random) models. DSC 4 and DSC 35 are Dice on the coarse (4-class) and fine (35-class) labellings respectively; fitting time and folding are independent of the labelling and are therefore reported once. Each entry is the mean over all test pairs with its 95% confidence interval in brackets. Both models are the same architecture: the left one is fitted from the meta-learned initialization, the right one from a random initialization.

Appendix figures & tables3 assets

Supplementary material from the paper’s appendix.

Appendix

	INR GS (meta)				INR GS (random)
Iter.	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$	DSC 4	DSC 35	$t$	det( $J$ ) $<$ 0 $\times 10^{-5}$
	[-]	[-]	[s]	[%]	[-]	[-]	[s]	[%]
2	0.701 [0.694, 0.709]	0.598 [0.586, 0.610]	0.17 [0.14, 0.22]	$0$ [0, 0]	0.603 [0.594, 0.612]	0.399 [0.383, 0.415]	0.15 [0.12, 0.18]	$0$ [0, 0]
10	0.730 [0.723, 0.737]	0.642 [0.631, 0.653]	0.74 [0.68, 0.83]	$0$ [0, 0]	0.671 [0.663, 0.679]	0.530 [0.516, 0.544]	0.66 [0.62, 0.72]	$0$ [0, 0]
50	0.736 [0.729, 0.743]	0.655 [0.644, 0.666]	3.61 [3.49, 3.75]	$0$ [0, 0]	0.709 [0.701, 0.716]	0.611 [0.599, 0.623]	3.22 [3.14, 3.32]	$0$ [0, 0]
100	0.737 [0.730, 0.744]	0.655 [0.644, 0.665]	7.35 [7.17, 7.54]	$0$ [0, 0]	0.717 [0.709, 0.724]	0.624 [0.612, 0.635]	6.36 [6.26, 6.48]	$0$ [0, 0]

Appendix

Table 3: Mean Dice score, cumulative fitting time, and fraction of folding voxels across fitting iterations for the baseline INR GS (meta) and INR GS (random) models. DSC 4 and DSC 35 are Dice on the coarse (4-class) and fine (35-class) labellings respectively; fitting time and folding are independent of the labelling and are therefore reported once. Each entry is the mean over all test pairs with its 95% confidence interval in brackets. Both models are the same architecture: the left one is fitted from the meta-learned initialization, the right one from a random initialization.

Figure 6: Comparison of segmentation performance for the LUMINR (meta), LUMINR (random), INR (meta), INR (random), INR GS (meta), and INR GS (random) models ( $\alpha$ = 0.1) across 4 classes. We report the mean Dice score at each optimization iteration. The meta-learned initialization leads to rapid convergence and achieves reasonable segmentation after 10 iterations.

Figure 7: Comparison of segmentation performance for the LUMINR (meta), LUMINR (random), INR (meta), INR (random), INR GS (meta), and INR GS (random) models ( $\alpha$ = 0.1) across 35 classes. We report the mean Dice score at each optimization iteration. The meta-learned initialization leads to rapid convergence and achieves reasonable segmentation after 10 iterations.

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Medical Image Registration Deformable Image Registration Implicit Neural Representations

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Deformable image registration models implicitly encode deformation priors through their parametrization and optimization. In this work, we conduct a validation study on continuous registration methods to examine how these implicit priors affect performance across different registration tasks. Classic B-Spline transformations impose locality, smoothness, and scale through their control-point structure, whereas recent INR-based methods impose different priors through neural parameterization and optimization. We compare INR-Dense (IDIR), which directly models a dense displacement field using a SIREN-based INR; INR-BSCP (SINR), which predicts B-Spline control points with an INR; D-BSCP, which directly optimizes single-scale B-Spline control points; and MR-D-BSCP, which adds a multiresolution coarse-to-fine scheme. Experiments on inter-subject brain MR registration (OASIS) and intra-subject exhale-to-inhale lung CT registration (DIR-LAB 4DCT) reveal different behavior across deformation regimes. On OASIS, where deformations are moderate but locally complex, D-BSCP matches or slightly outperforms INR-BSCP, suggesting that the B-Spline parameterization accounts for much of INR-BSCP's effectiveness. On DIR-LAB 4DCT, where respiratory motion is larger and more coherent, single-scale B-Spline methods (D-BSCP and INR-BSCP) are less suitable, while INR-Dense and MR-D-BSCP are more effective. Across both tasks, MR-D-BSCP achieves the best performance among the tested continuous parameterizations. These findings highlight that registration accuracy depends strongly on matching the induced deformation prior to the target motion pattern, and support prior-deformation matching as a practical design principle for medical image registration. Our code will be available at https://github.com/HengjieLiu/RightPriorDIR.

Abstract

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