Unified Brain Surface and Volume Registration
Authors: Mazdak Abulnaga
Andrew Hoopes
Malte Hoffmann
Robin Magnet
Maks Ovsjanikov
Lilla Zollei
John Guttag
Bruce Fischl
Adrian V Dalca
Venue: ICLR 2026 Poster (2026)
Keywords: neuroimaging
registration
sphere
cortex
mri
Primary area: applications to neuroscience & cognitive science
TL;DR: We present a machine learning model that leverages volumetric and spherical domains for unified registration of cortical and subcortical structures in brain MRI.

Abstract: Accurate registration of brain MRI scans is fundamental for cross-subject analysis in neuroscientific studies. This involves aligning both the cortical surface of the brain and the interior volume. Traditional methods treat volumetric and surface-based registration separately, which often leads to inconsistencies that limit downstream analyses. We propose a deep learning framework, UCS, that registers 3D brain MRI images by jointly aligning both cortical and subcortical regions, through a unified volume-and-surface-based representation. Our approach leverages an intermediate spherical coordinate space to bridge anatomical surface topology with volumetric anatomy, enabling consistent and anatomically accurate alignment. By integrating spherical registration into the learning, our method ensures geometric coherence between volume and surface domains. In a series of experiments on both in-domain and out-of-domain datasets, our method consistently outperforms both classical and machine learning-based registration methods--improving the Dice score by up to 7 points while maintaining regular deformation fields. Additionally, it is orders of magnitude faster than the standard method for this task, and is simpler to use because it requires no additional inputs beyond an MRI scan. Its superior accuracy, fast inference, and ease of use sets a new standard for joint cortical and subcortical registration.

Published as a conference paper at ICLR 2026
UNIFIED BRAIN SURFACE AND VOLUME REGISTRATION
S. Mazdak Abulnaga 1.3
Andrew Hoopes! Malte Hoffmann?
Robin Magnet
Maks Ovsjanikov' Lilla Zöllei
John Guttag' Bruce Fisch1
Adrian V. Dalca 1.2+ 1.2
MIT Computer Science and Artificial Intelligence Laboratory 2MGH, Harvard Medical School 8 Université Paris Cité, INRIA
*LIX, CNRS, École Polytechnique
abulnaga@csall
wwt.ssaaaam........mmmmmm......e mii. edu
ABSTRACT
Accurate registration of brain MRI scans is fundamental for cross-subject anal- ysis in neuroscientific studies. This involves aligning both the cortical surface of the brain and the interior volume. Traditional methods treat volumetric and surface-based registration separately, which often leads to inconsistencies that limit downstream analyses. We propose a deep learning framework, NeurAlign, that registers 3D brain MRI images by jointly aligning both cortical and sub- cortical regions through unified volume-and-ee waw-anddddee--uueeeeeeeee approach leverages an intermediate spherical coordinate space to bridge anatomical surface topology with volumetric anatomy, enabling consistent and anatomically accurate alignment. By integrating spherical registration into the learning, our method ensures geometric coherence between volume and surface domains. In a series of experiments on both in-domain and out-of-domain datasets, our method consistently outperforms both classical and machine learning-based registration methods methods-immprving the Dice score by up to 7 points while maintaining regular deformation fields. Additionally, it orders of magnitude faster than the standard method for this task, and is simpler to use because it requires no additional inputs beyond an MRI sean. With its superior accuracy, fast inference, and ease of use, NeurAlign sets a new standard for joint cortical and subcortical registration.
representation. Our
INTRODUCTION
Accurate alignment of both cortical and subcortical regions is essential for comprehensive and consistent whole-brain analysis in neuroimaging studies. For example, functional MRI (fMRI) measures brain activity by detecting blood oxygenation changes, with a key goal of localizing functional regions in the cerebral cortex. Mapping activation patterns to brain structure reveals functional organization and essential for quantifying how neurodegeneratiie diseases affect things such cognition (Fischl et al. 2008 Thompson et al. 2007 Ghosh et al. 2010).
Traditional deformable volumetric registration methods compute a three-dimensional (3D) displace- ment field to align brain images by maximizing intensity similarity (Avants et al. 2008 Balakrishnan ct al. 2019, Rueckert et al. 1999). While effective for aligning subcortical structures and global anatomy, volumetric deformable registration often fails in the cortex. The cortex is thin, highly curved surface with significant inter-subject variability in folding patterns that is difficult to align in Euclidean space (Fischl et al.) 1999). Accurate alignment is critical, since the cortex encodes many of the brain's 's high-level functions such as memory and language, and serves as a primary target for structural and functional neuroimaging studies (Fischl 2012). Surface-based methods address this challenge by projecting the cortex onto a sphere and aligning the cortex using pre-computed anatomical features such as sulcal depth and/or curvature. This facilitates registration by providing a common geometric space to preserve the topology of the cortex (Fischl et al. 1999: Yeo et al. 2009).
Using fundamentally different representations for surface and volume registration forces neuroscience researchers to tackle two disjoint problems and combine solutions ad hoc (Tucholka et al. 2012). This
"co-senior authors

---

Published as a conference paper at ICLR 2026
typically involves solving elastic partial differential equation to propagate the surface registration to the interior brain. However, interpolating the surface registration to the interior is not guaranteed to be consistent with the original volumetric registration. This sequential approach prevents computing a coherent registration that simultaneously satisfies both cortical and subcortical alignment objectives. This introduces errors, undermining whole-brain analyses by potentially misaligning anatomically and functionally connected areas (Joshi et al. 2009 Postelnicu et al. 2008 Ahmad et al. 2019).
In this work, we propose NeurAlign ing, machine learning framework for unified registration of cortical and subcortical structures. NeurAlign simultaneously trains a volumetric registration network and a spherical registration network using a shared framework that combines both domains. Unlike existing approaches, our model explicitly couples the two through loss function that encourages the volumetric deformation field on the cortical ribbon to match the spherical registration field. This promotes topologically correct and geometrically consistent alignment across cortical and subcortical regions. Crucially, because our method performs registration efficient and scalable whole-brain registration for large population studies. Further, NeurAlign does not require cortical meshes nor segmentations at inference, avoiding the computationally intensive preprocessing required by other methods. Our method, NeurAlign, achieves significantly improved cortical and subcortical alignment compared to the standard joint registration framework, CVS (Postelnicu et al., 2008), while reducing computation time by several orders of magnitude. In addition, Align substantially outperforms state-of-the-an volumetric machine learning-based registration approaches. To summarize our contributions:
single forward pass, it enables
We propose unified machine learning model that performs consistent registration of both cortical and subcortical structures using coupled spherical and volumetric networks.
We derive a cortical consistency loss that explicitly encourages agreement between the volumetric deformation field in the cortex and the spherical registration field, promoting anatomically coherent alignment across the entire brain.
Our proposed method leverages cortical meshes during training, but does not require them during inference, enabling accessible, rapid, and accurate registration.
We validate our method on four clinical neuroimaging datasets, showing substantially improved and rapid cortical and subcortical alignment compared to standard baselines.
Our code and model weights are available at https: wtt..cow.mmmaaaaaee http://ablnagga////m neuralign
com/
2 RELATED WORK
Volumetric Registration. Deformable registration estimates dense spatial mapping between pair of images. Classical methods (Rueckert et al. 1999; Ashburner 2007 Rohr et al. 2001 Modat et al. 2010) solve an optimization problem for each pair of images. This balances objective, often mean-squared error (MSE) or normalized cross correlation (NCC) (Avants et al.) 2008), between the warped image and the fixed image, with a regularization objective that encourages a smooth solution. Methods differ in their optimization strategy, choice of the objective function, and how they parameterize the deformation field.
mmage-similane larit
scarning-based methods fit the parameters of a neural network to a training dataset. The network learns nonlinear function that maps an input image pair an output transform, generally enabling much faster inference than classical methods. Supervised approaches (Sokooti et al.] [011 Rohé
al. 2017 Yang et al.) 2017) reproduce known simulated deformations or fields estimated by classical methods, whereas unsupervised approaches (De Vos et al.) 2017 Balakrishnan et al. 2019
Mok et al. [203)] Gizech et al. 2022 Abulnaga et al., 2025 Hoffmann et al. [2021] Rakie al.
2026) optimize an image-similarity loss term and a regularization loss term at training. analogous to classical registration.
Both optimization-base and machine learning-based volumetric approaches are highly effective at aligning subcortical structures. However, they struggle with cortical registration, since the op- timization landscape in Euclidean space often leads suboptimal local minima. This can lead to implausible solutions that, for example, move voxels from one gyrus to the next instead of following the cortical fold. Further, relying only image-based features cannot align the functional regions
2

---

Published as a conference paper at ICLR 2026
of the cortex, geometric features must be employed from geometric representations (Fischl et al. 1999; Ségonne et al. 2007).
Spherical Registration. Cortical alignment the spherical domain is the standard approach in neuroscientific studies (Fischl 2012 Ghosh et al. 2010; Tucholka al. 2012). Mapping the cortex to the sphere simplifies the optimization, since the registration is guaranteed to preserve topology.
The registration is driven by geometric descriptors that measure the cortical shape and folding patterns (Fischl et al.] 1999; Yeo et al.] 2009] Conroy et al. [0033] iZhao et al. (019). Similar to volumetrie registration, spherical registration posed an optimization problem that balances geometric similarity objective with a regularization objective. Recent methods use deep learning to improve inference time (Li al. 2024 Zhao al. 2019 Cheng et al. 2020). The spherical mesh
is parameterized to the 2D plane using a stereographic projection. The registration is performed in 2D space using convolutional neural networks (Zhao al., 2019). Icosahedral CNNs (Zhao et al.. 2021) learn directly on the sphere but require rigid tessellation that is not produced natively by standard neuroimaging pipelines. These methods have achieved comparable accuracy to classical techniques with significant improvement in speed. We build on the planar parameterization methods to construct a spherical registration network and jointly model it with a volumetric network.
Surface Mesh Registration. Surface registration aligns two meshes or point clouds in 3D Euclidean space. Classical approaches typically frame the task as deformation problem, aiming to align two shapes by estimating a rigid or non-rigid transformation, that minimizes a distance metric (Besl & McKay 1992. Rusinkiewicz & Levoy 2001 Sorkine & Alexa 2007 Weischedel] 2012 Abulnaga et al. 2023). An alternative paradigm treats surface registration as a shape correspondence problem. focusing on establishing point-to-point correspondences based on intrinsic geometry (Deng et al.
2022). Functional maps (Ovsjanikov et al. 2012) and extensions (Sharp et al. [022] Donati et al.
2020 Cao al. 2023) have emerged as a powerful representation for such correspondences. enabling compact linear descriptions of dense mappings between shapes. However these methods, developed for graphics applications target moderate complexity meshes and scale poorly to high-curvature, high- resolution cortical surfaces, despite some efforts for memory-efficient variants (Magnet & Ovsjanikov 2024). Furthermore, because of the high curvature and topological consistency constraints of cortical surfaces, Euclidean 3D embeddings become unstable and less informative. Finally, these methods are unsuitable for registering volumetric structures as they are only defined for 2-dimensional surfaces. These reasons further motivate the use of spherical registration to align cortical surfaces.
Combined Volume and Surface Registration. Existing neuroscientific studies treat volumetric and cortical registration as two separate problems. The Combined Volume and Surface framework (CVS) (Postelnicu et al. 2008 Zöllei et al. (2100) is the standard method for jointly aligning cortical and subcortical anatomy in adult brains. CVS first aligns the cortical surface then propagates the resulting deformation into the volume using an elastic model, followed by intensity-based refinement. While effective, this sequential formulation decouples the surface and volumetric objectives, can introduce inconsistencies near the cortical-subcoriiall boundary, and requires surface meshes and long runtimes. Related work has also used cortical surface registration to supervise volumetric registration (Ahmad et al. 2019), though focused in the infant-brain domain. strength of these variational approaches is that they offer a principled way to propagate surface constraints into the volume using well-understood physical models. However, they remain impractical for large-scale datasets, as they require several hours of computation per pair and depend on extracting cortical surfaces and segmentation labelmaps.
To address these limitations, we introduce NeurAlign, which incorporates the established idea of surface-guided alignment into a single, unified learning-based diffcomorphic framework. NeurAlign jointly aligns cortical and subcortical structures through single forward pass, requires only 3D MRI at inference time (without surface meshes), and provides the speed and simplicity needed for high-th tgghthhooughput neuroimaging studies.
METHODS
We develop NeurAlign, a method for jointly aligning cortical and subcortical structures in 3D brain MRI. We jointly optimize volumetric and spherical deformation field and propose a soft constraint
3

---

Published as a conference paper at ICLR 2026
to encourage consistency between the two registration fields. We first propose the continuous formulation of the problem before deseribing the discrete case.
3.1 CONTINUOUS MODEL
Let M1, M2 C R be bounded brain volumes, with associated smooth cortical surfaces 0M1, aM2. We seek bijective map p M1 + M2 that aligns both the cortical and subcortical structures. Each volume equipped with an intensity sampling function R + R. The surfaces are also equipped with d geometric descriptor functions Di 0M; + R2, such as sulcal depth or mean curvature.
Finding &p amounts to finding a solution to the following optimization problem,
/
fi (Ix(x), 12 (xx(x)) (x S fs (91(x)) ds(x) + R(p), (I)
arg min PEP
M,
JaM,
with P denoting the feasible set of maps, enforcing for instance () C MM2
Here, fz measures image similarity, fs compares surface descriptors, dV and dS denote the volume and surface measures, and R[-] denotes a set regularization functionals.
Solving Eq. (1) is difficult: the joint matching of intensities and geometric features has nonconvex objective with degenerate solutions. Enforcing (0MM) S 0M₂ is especially challenging as the cortex is thin, highly folded, and has variable structure across subjects. Fine-grained boundary correspondence is poorly captured a Euclidean volumetric grid, and optimizers often only align subsets of folds while blurring or misaligning others (Ségonne al. 2007). Finally, finding unified representation that captures both the volumetric image and cortical surface difficult.
We joint representation, where cortical alignment performed the sphere, using topology- preserving maps and volumetric registration is performed in 3D. By enforcing consistency between the two, this learning-basse formulation efficiently registers both the cortical and subcortical structures.
3.2 SPHERICAL ALIGNMENT
We revise the optimization problem in Eq. by introducing spherical intermediate domain to help enforce the constraint set P. Let T; a., + Sa denote the (fixed) invertible spherical maps obtained via cortical inflation (Fiscll al. 1999 Hoopes et al. 2022) for each surface. The cortical alignment problem then computes a map v S S that displaces spherical coordinates (6, Φ). to align geometric descriptors. By optimizing the sphere, guarantee satisfaction of the constraint P. The revised optimization problem is then:
arg min / f1 v.vee J
/ Jonn
(ate)))))))(((((()))))) RR(p)
(2)
We decouple this optimization into two separate optimization problems: volumetric registration of subcortical regions using ş2, and cortical registration the sphere using v/. We introduce constraint set Q to encourage a consistent mapping below.
Cortical Alignment Consistency Constraint. Optimizing Eq. (2) independently can estimate maps and di that map the cortex to different locations in the volume. We therefore require consistency in
Euclidean space by composing maps to the sphere and back: Q {x((x) 72 o sb 77 (x(x) for aM1).
To keep the problem tractable, we soften this constraint using a coupling energy that encourages consistent alignment:
(eome(pp,)) Jan
f (((()) dS(x),
where f measures dissimilarity in the mapping by the squared error. We replace the hard constraint Q with the coupling energy (Eq. (3) to achieve a consistent mapping that accurately aligns both cortical and subcortical structures. This constraint only acts set of Lebesgue measure zero in R
4

---

Published as a conference paper at ICLR 2026
Moving Image
Moving
Spherical Inflation Paremntterization
Volumetric
Spherical Unet
C cons
π
sample ?p
L vol
sphere
Fixed
Fixed
Mesh
Image
Figure 1: Unified cortical and volumetric registration framework. We employ volumetric CNN to perform 3D image alignment, and 2D spherical CNN to align the cortical surfaces in the spherical domain. In training, the models require the MRI images, the cortical surface meshes, and the inflated spheres. The resultant deformation fields of both models are used in a loss term (Crons) that encourages cortical registration be consistent in the spherical and volumetric pathways. At inference time, the 3D model does not require meshes nor spheres to perform registration.
(the cortical surface iM)) and is therefore weak. In practice, however, our discrete implementation avoids this issue: the consistency loss samples the volumetric deformation mesh vertex locations via trilinear interpolation, distributing gradients to neighboring voxels. We also impose smoothness priors on the map, allowing the surface-derived updates to naturally propagate throughout the volume.
The remainder of this section focuses on the discretization and use of neural networks to model the registration problem.
3.3 DISCRETE MODEL
discretize the optimization problem Eq. (2). and use neural networks to parameterize the volumetric and spherical maps. Specifically, we formulate unsupervised learning problem where we jointly learn 3D and 2D U-Net convolutional neural networks (CNN) (Ronneberger et al. (0155). Given an image and surface, the networks output the 3D and 2D deformation fields ye, th, respectively. We propose consistency loss to obtain an accurate cortical surface registration in the volume. Figure]] presents overview of our framework.
Notation. Let /, 12 IR3 TR denote 3D brain MRI scans, where T (x) gives the intensity at spatial location x. Each image used in training the networks also has an associated triangular surface mesh C1, C2 R3 representing the cortical surface extracted from the respective anatomy. Vertex j of mesh i, v). is 3D coordinate in the image space of 4. Each cortical surface mesh has an associated mesh in the spherical domain denoted S1, where S тı (C1), with the same triangle connectivity. The vertices v are mapped the sphere by standard spherical inflation procedure and have an associated 8 representation (Fischl et al. 1999).
We employ neural network F, (1,, I2:we] to predict as function of the input images, where F, parameterized by w.. core 3D convolutional network first outputs a stationary velocity field (SVF), which we then integrate to obtain a diffeomorphic displacement field yo (Ashburner 2007 Dalca et al. 2019a). the deformation field y : R R33
Volumetric Registration Network.
each voxel in R is assigned displacement vector ut (p(x)) I + (xr).
Spherical Registration Network. We construct a 2D CNN registration network for the sphere. We parameterize the spherical meshes the Fuclidean plane using a stereographic projection use standard 2D CNN to learn a 2D diffcomorphic
82 + 2 By mapping to the plane, displacement field in the space of spherical angles (0, Φ).
To account for the nonuniform sampling of the spherical parameterization. where regions near the poles are stretched, we apply distortion correction in all surface-basee losses by weighting samples by sin(Ø), where 0 is the elevation angle (Cheng al. 2020 Li et al. 2024). We also handle the discontinuities at the image boundaries using the padding strategy of (Li et al. 2024), employing
circular padding along the left-right axis and 180 circular shift with reflection padding at the poles.
5

---

Published as a conference paper at ICLR 2026
We use neural network (1)) (( w.) = v predict v, by first predicting SVF that integrated. The network outputs a displacement field u, such that ((p) = + up()), where P (8, is discrete location in pixel coordinates the parameterized grid.
(
3.3.1 UNIFIED TRAINING AND CORTICAL ALIGNMENT
Cortical Consistency Loss. We maximize alignment of the cortex and subcortical structures between pair of images while maintaining smooth map.
We discretize the proposed consisteney loss in Eq. B and use it to jointly train the volumetric and spherical registration networks. The consistency loss penalizes disagreement between the predicted 3D displacement on the cortex, and the 3D displacement computed from the predicted 2D warp:
1 Σ (o()))) (vb (v)))). No vEC.
Loma (,,,,,
(4)
where N2 is the number of vertices in C1. (()) is the projection of the plane, and f(..)) is similarity metric; we use the mean squared error in our experiments. We implement x with trilinear interpolation over the mapped planar parameterizations v. Maps yp and & are the outputs of the 3D and 2D CNN, respectively.
Image Similarity Loss. Both networks are trained by minimizing an unsupervised loss that balances image-similarity and field regularity. The similarity loss the volume matches MRI intensities and the loss on the sphere matches geometric descriptors. We pre-compute geometric descriptors on the cortical meshes, 0 : C IR2. As is standard in spherical registration,
the sulcal depth
and mean curvature (Fischl et al. 1999 Cheng et al. 2020). The similarity loss is Csim (4,, vi) Ssim (I2. (Iz) + Laim (g (ι (S2)) )) db g TT (s)))) (p)) Here, w(p) is a weighting to correct for area distortion introduced by the stereographic projection. The similarity loss measures pairwise similarity between the fixed image and sphere /2, S2 and the mapped image and sphere, s0(1), (S)) We the local normalized cross correlation function as similarity measure (Avants 2010).
Regularization. We regularize the displacement fields to be smooth to encourage well-behaved map. Our regularization loss Creg(y: 15) = [| 2 [V where V.p is the Jacobian of map y.
Auxiliary structural loss. The use of anatomical label maps during training of learning- based registration often improves substructure alignment (Balakrishnan et al. 2019). When segmentation maps are available for some pairs of images, we use this information to supervise by structural alignment. Let seg[/]] indicate the segmentation labelmap of the K brain substructures for image I. We add an additional loss to align these structures, Letrue v/) = (strue (p(seg((s) Cetrue (T (seg[Sy] T( ((ees (S2)))) In practice, we use the soft Dice loss function, which captures volume overlap the warped subcortical structures on one image warped the second.
Joint training loss. Combining all loss terms provides our joint optimization problem:
Clg, b Lxim (1p, 10 + "ooon (p,, v) + ACreg (v,, 3) + &. (F,,)) v),
(5)
where X, y, and i. are hyperparameters.
EXPERIMENTS
We evaluate NeurAlign using 3D brain MRI scans from multiple datasets comprising healthy subjects and subjects with cognitive disorders. We compare our method against CVS, the state-of-hhe art combined cortical surface-voluma registration framework (Postelnicu et al.) 2008) and against learning-bast methods that emphasize structural alignment. We test the ability of our method to generalize datasets unseen in training.

---

Published as a conference paper at ICLR 2026
4.1 EXPERIMENTAL SETUP
Data. We train our model using two public 3D brain MRI datasets: OASIS-1 (Mareus et al. 2007 and ADNI (Mueller et al. 2005). Both datasets are obtained from large population studies focused on Alzheimer's s disease (AD). OASIS-1 (Marcus et al. 2007) includes We-weighted (T) scans of 416 subjects aged 18-96. We use a random subset of 100 ADNI subjects aged 56-90, half of whom were diagnosed with AD. For each ADNI subject, we use data from two sessions, two years apart.
For each dataset, we hold out 20% of the subjects for testing, stratified by gender, age, and disease state. The remaining subjects are split into 85% for training and 15% for validation using the same stratification. In training, we randomly sample pairs from both datasets. In our test set, we create 123 non-overlapping pairs for registration: 83 pairs aligning OASIS-1 1 and OASIS- 20 pairs aligning ADNI and ADNI, and 20 pairs aligning O and ADNI.
Held-out datasets. We use two additional held-out datasets for testing model generalization. The IXI dataset contains MRI scans from healthy subjects acquired in 3 London hospitals (IXI Consortium). We randomly select Tlw scans from 115 subjects for evaluation. We also hold out 80 TIw scans from the Mindboggle-109 101 dataset (Klein et al. 2017). collection of manually labeled brain MRI volumes and surfaces. We exclude all OASIS-1 subjects from the Mindboggle dataset.
All evaluations are performed on Tlw MRI, which is the modality that enables reliable cortical surface extraction. TIw MRI has the strongest gray-white matter contrast and supports reliable delineation of white and pial surfaces (Fischl et al. 1999 Fischl 2012; Hoopes et al. 2022).
Processing. We use FreeSurfer (Fischl 2012) to perform all image preprocessing. FreeSurfer is an open-source, widely used toolkit in neuroimaging that supports cortical surface analysis, longitudinal workflows, and population-scale MRI studies. We first perform affine alignment of each image the Talairach template (Tlairach & Tournoux] 1990).. We crop all images to roughly 10 mm margin around the brain. To prepare our training data, we generate anatomical segmentations, white matter (internal) and pial (external) cortical surface reconstructions, and spherically inflated surfaces with parameterized curvature maps. For evaluation, we use both volumetric segmentations of subcortical brain regions, computed on the volume, as well parcellations of the cortical ribbon, computed on the surface mesh. Surface parcellations are rasterized as volumetric segmentations. We emphasize that our method does not require surface meshes, spheres, nor segmentation labelmaps at inference.
Implementation Details. We train using the Adam optimizer (Kingma & Ba 2014) with learning rate of 10-4 We set the field regularization hyperparameter to A = 1.0, the segmentation loss weight to 10.0, and the cortical consistency weight to y 0.05. These were chosen using a grid search over the validation set. We train for 300, 000 iterations, using the best performing model on the validation set. All models are trained on single A100 GPU. All CVS experiments are done on an (ntel(R) Xeon(R) Gold 5218 CPU, as there is no GPU implementation.
Baselines. We select state-of -fthe-of baselines that emphasize structural alignment. We evaluate CVS (Postelnicu et al.) 20088) Zöllei al. 2010), the most widely used joint volume-cortical alignment registration method, which is integrated in the FreeSurfer software suite. CVS performs sequential spherical to volumetric alignment using a biomechanical model and image intensity registration.
We evaluate uGradICoN (Tian et al. 2024), a modern foundation model for medical image reg- istration that generalizes well to unseen data. UniGradICON employs test-time optimization to improve pairvise-registattinn accuracy. We also use the uGradI CON-seg variant that performs loss function masking using the segmentation labelmaps to improve cortical structure alignment.
We test hMrrph (Hoffmann et al. 2023 2024). a seate-of-the-are registration tool trained exclusively on images synthesized from label maps. Since this tool optimized the overlap of standard FreeSurfer labels in training, which include only two large cortical structures, also retrain it with extended label sets, optimizing overlap of the "a2009s" set of 196 labels that include finer Destrieux parcels of the cortex (Destrieux et al. 2010) (SynthMorph-wm)
We evaluate Voxe1Morph (Dalca et al., 2019b). an unsupervised diffeomorphic registration model. We use the same size UNet as our model and train on our training set. We also evalu- ate FireANTs (Jena et al., 2025), a library for fast medical image registration using Riemannian optimization. We use the SyN transformation for symmetric diffeomorphic registration.
7

---

Published as a conference paper at ICLR 2026
uGradICON
uGradICON-seg
SM
SM-wm
VXM
FireANTs
80
90
70
Subcortical Dice
Cortical Dice
80
60
50
70
40
30
OAS/ADNI
IXI
MB-101
OAS/ADNI
MB-101
Figure 2: Violin plot of distributions of Dice score across all subjects in each dataset. Our method (blue) consistently achieves the highest mean Dice for cortical structures, with mass centered near the mean. We preserve subcortical performance while delivering much stronger cortical alignment.
Evaluation. To evaluate registration accuracy, we compute Dice scores between anatomical struc- tures in the warped and target images. We report overlap for 43 subcortical structures and for cortical regions obtained by parcellating the cortical ribbon into 34 regions per hemisphere. We assess field regularity and topology by computing the determinant of the Jacobian of the map, det J (p) = det (Vp (p)) at each voxel p. Locations where det (p( < 0 represent folded regions. We report the percentage of folds (% folds). We measure the smoothness of the warp fields using the standard deviation of log det J] (SDlogJ) (Leow et al. 2007
4.2 RESULTS
Table and Figure present results on the 3 datasets. Our method, NeurAlign, consistently achieves the highest cortical Dice score, often by large margin. For example, improves by up Dice points on the held-out Mindboggle dataset. NeurAlign also achieves the highest subcortical Dice score on OASIS-1 & ADNI and Mindboggle. We obtain slightly lower subcortical Dice on IXI (1.5 points at worse), though the difference is not substantial. Across all datasets, NeurAlign achieves statistically better cortical Dice scores (p- 0.01) and in many cases a substantial increase (up to 7.5 points over the next best method). We also outperform baselines on whole cerebral cortex alignment (see Suppl. A.2). Finally, NeurAlign produces regular deformation fields with negligible folding. These results demonstrate that we are able to greatly improve cortical structure alignment while maintaining strong performance in substructure alignment and field regularity.
CVS was the slowest method, requiring 2.5 + 0.5 hours per pair. uGradICON required minutes to perform test-time optimization. NeurAlign and all other baselines converged in milliscconds.
Figure 3 visualizes example registrations and corresponding warps. Our method yields accurate alignments with smooth and regular deformation fields.
4.3 ABLATIONS
To study important aspects NeurAlign, we conduct two ablation experiments. In the first, we quantify the effect of different model components: label map supervision in training and including the spherical alignment loss. In the second, we quantify the effect K, the Dice loss weight parameter.
Results. Table 2 presents ablations of model components. trained with = 1.0 and = 0.05, on the IXI dataset. We train a base VoxeIMorph model (Dalca et al. 2019a), called Base, and extensions testing components of NeurAlign. We compare the performance when training with supervision of segmentations of subcortical structures, Base+Dice (subcort), training with segmentations of all structures, Base-Da -Diee-iie ce (all), training with only the spherical consistency loss, baseeSSheere and training with all proposed components, Base+Dice (all) +Sphere. We selected 1.0, it achieved the best performance for Diseuuiicesu
8

---

Published as a conference paper at ICLR 2026
Table 1: Performance across three datasets. The proposed method (NeurAlign) substantially improves
cortical dice and consistently matches or improves subcortical Dice, and produces smooth deformation fields with negligible folding. Mean + standard deviation across subjects are indicated.
Dice (t)
Dice (f)
Dataset
Method
% folds (1)
SD log det J (L)
cortical
subcortical
uGradICON
0.58 + 0.028
0.701 + 0.032
0.647 0.105
0.408 + 0.127
OASIS-I & ADNI
uGradICON-eeg
0.583 + 0.028
0.701 = 0.031
0.688 = 0.101
0.41 0.126
SynthMorph
0.511 + 0.033
0.673 + 0.034
0.0 0.0
0.197 + 0.1
Synth-Mrph-wm
0.525 1 0.032
0.682 + 0.031
0.0 0.0
0.188 1 0.1
VoxeIMorph
0.551 + 0.039
0.756 + 0.026
0.001 1 0.001
0.233
FireANTss
0.554 +:: 0.038
0.684 + 0.041
1.319 0.171
0.137
CVS
0.681 + 0.035
0.715 0.041
1.73 = 0.321
177773.477 3.475
NeurAlign (Ours)
0.698 + 0.032
0.747 = 0.026
0.169 = 0.037
0.829 = 0.281
uGradICON
0.631 + 0.021
0.824 + 0.022
0.489 + 0.1
0.382 + 0.121
uGradICON-seg
0.639 + 0.021
0.825 + 0.022
0.602 + 0.109
0.399 + 0.125
SynthMorph
0.577 0.03
0.811 + 0.021
0.0 0.0
0.177 + 0.069
IXI
SynthMorph-wwr -mm
0,599 + 0.025
0.817 0.019
0.0 0.0
0.167
VoxelMorph
0.566 + 0.045
0,816 0.038
0.001 = 0.001
0.465 0.17
FireANTs
0.601 + 0.037
0.8 = 0.04
1.382 = 0.183
0.501 + 0.133
CVS
0.582 0.039
0.814 0.038
1.863 = 0.382
7.591 + 4.115
NeurAlign (Ours)
0.683 + 0.029
0.81 + 0.036
0.081 0.023
0.712 0.24
uGradICON
0.618 + 0.038
0,821 + 0.023
0.85 + 0.404
0.436 + 0.199
uGradICON-ser
0.626 1 0.038
0.822 1 0.023
0.958 0.4
0.445 0.188
Mindboggle
SyrthMMorh
0.577 + 0.054
0.806 = 0.065
0.0 0.0
0.185 + 0.071 0.071
SynthMorph-wm
0.596 + 0.048
0.811 = 0.059
0.0 0.0
0.173 0.062
VoxeIMorph
0.573
0.827 0.09
0.002 = 0.002
0.51 +
FireANT's
0.597 + 0.07
0.79 + 0.09
1.604 0.3/17
0.53 + 0.169
CVS
0.535 0.07
0.766 + 0.081
2.164 + 0.652
7.429 + 1.654
NeurAlign (Ours)
0.703 + 0.06
0.823 + 0.086
0.174 + 0.034
0.831 + 0.261
As expected, training with subcortical supervision improved the Dice (subcortical) score compared to the Base model. However, interestingly, training with supervision of all brain structures did not lead to a substantial improvement in the Dice (cortical) score. Only when including our proposed spherical consistency loss (Base+Diccaal)+Shheee
did we observe substantial increase in the Dice (cortical) score while maintaining the Dice (subcortical) score. Training with just the spherical loss without structural supervision did not improve results, indicating that also require volumetric structure supervision. This ablation study demonstrates the benefit of our anterical-volumetti consistency constraint in obtain accurate alignment of fine-gree greegga cortical structures.
We assess the impact of K, the weighting hyperparameter for the Dice loss term (see Suppl. Table A. Fig. A.I. As expected, increasing ς improves Dice performance at test time, yielding higher structural overlap. In some regions, however, this comes at the expense of deformation field regularity. Overall, setting x >>> produces models that outperform baselines across most metrics. Consistent with prior work (Dalca et al. 2019b Hoopes et al.) (02T). the optimal choice of к depends on the intended downstream application: for atlas-based segmentation propagation, higher Dice weighting is advantageous, whereas for longitudinal studies, smoother deformation fields may be preferable. Hypernetorrss can be considered to select hyperparameters at test-time (Hoopes et al. 202T).
Table 2: Ablations over training settings on IXI. The proposed spherical alignment consistency loss is necessary to obtain high cortical structure alignment while maintaining strong subcortical alignment.
Dice (f) cortical
Dice (1) subcortical
Ablation
% folds (L)
SD log det J (L)
Base
U.582 0.045
0.789 + 0.049
0.003 + 0.003
0.446 0.172
Bise+Dice (subcort)
0.553 0.045
0.815 0.038
0.002 1 0.001
0.494 1 0.185
Bise+Dice (all)
0.562 +: 0.044
0.812 + 0.041
0.001 1 0.001
0.462 + 0.168
Basc+Sphere
0.56 0.03
0.736 + 0.047
0.004 + 0.002
0.421 = 0.152
Base+ Diceallicelll
0.633 : 0.028
0.799 +: 0.038
0.006 4 0.003
0.432 + 0.137

---

Published as a conference paper at ICLR 2026
Moving
Fixed
Warped Image
Warp Field
uGadICON SynthMrph FirAANTs
CVS
Ours
GGodlCON Morth FIGANTT
CVS
Chura
Figure 3: Example registrations for three image pairs. Columns show the moving and fixed images, followed by warped images produced by uGradlCON-seg. SynthMorph-wm, FireANTs, CVS, and our method. Corresponding deformation fields are visualized the right. Our method (NeurAlign) yields accurate alignments with smooth and regular warp fields.
DISCUSSION
Limitations and Future Work. We presented NeurAlign, a model for unified cortical and subcorti- cal neuroimage registration, evaluated primarily on adult Tlw MRI from healthy and Alzheimer's disease populations. As with any diffeomorphic registration framework, NeurAlign cannot accurately accommodate topology-alces -altriingg pathologies. This limitation can be partially mitigated by incorporat- ing pathology masks during training (Brett et al., 200T). It also remains unclear how well the model can generalize to lower-quality clinical scans or to pediatric populations. Extending NeurAlign to these more challenging settings is an important direction for future work.
Training our model requires cortical surface extraction and spherical inflation. This preprocessing pipeline may fail on challenging seans. A simple approach for quality control could be to discard failed cases, for example surfaces with many self-intersecting faces, or to use robust, learning- -baee extraction methods (Hoopes et al., 2022; Bongratz et al. 2022). In practice, we did not observe any failures our training data.
Our model was also only tested on the Tlw modality. Tlw is the most widely used imaging modality for structural imaging studies (Bhalerao et al. 2024), and it is currently the primary modality from which cortical surfaces can be reliably reconstructed (Fischl Hoopes et al. (022)) An interesting future direction is extending NeurAlign to multimodal acquisitions. Additional contrasts such as T2w, FLAIR, or DWI could provide complementary information for subcortical tissue segmentation or characterization. Incorporating these modalities would require multimodal training with all contrasts aligned to the TI lw image so that the cortical surfaces remain consistent across channels. Importantly, inference time, the surfaces would no longer be required, potentially reducing the current dependence on Tlw imaging for surface extraction.
benefit of our formulation is that can be easily extended to include additional structures with genus-0 topology. For example, this can improve alignment of the hippocampus by providing additional supervision through surface alignment. Further, our consistency loss in Eq. (3) can be adopted for non-spherical surface registration, implicit surfaces, or to perform cortical alignment directly on the surface mesh using frameworks such as Deep Functional Maps (Donati et al. 2020). Representations beyond spheres can be used, provided there is a one-to-one map the cortical mesh.
Conclusion. We introduced NeurAlign, deformable registration method that achieves accurate cortical and subcortical alignment. NeurAlign parameterizes the deformation field through coupled spherical and volumetric alignment, promoting topological consistency the cortex.
Our model outperforms state-of-the-art deep learning and foundational models trained or fine-tuned using cortical segmentation label maps. Compared to CVS, the most widely used method in large- scale neuroimaging pipelines, our method achieves substantially better alignment and deformation field regularity on held-out datasets, while running orders of magnitude faster. Further, method does not require additional inputs (cortical meshes, segmentations) as inputs. This positions our method as a practical alternative to CVS for many neuroimaging applications.
10

---

Published as a conference paper at ICLR 2026
REPRODUCIBILITY STATEMENT
Our model is summarized in Section 3.3
including descriptions of the 3D and 2D models used and
loss functions in training. We provide implementation details including all hyperparameters used, and data processing details in Section 4.1 upon acceptance.
Complete code for full reproducibility will be made public
ACKNOWLEDGMENTS
We thank Neel Dey for helpful discussions. Support for this research was provided in part by Quanta Computer Inc., the BRAIN Initiative Cell Atlas Network (BICAN) grants U01MH117023. UMIMH1348 12 and UMIMH1 the Brain Initiative Brain Connects con- sortium (UOINSI32)) 131181, JUMINS132358-01 the National Institute for Biomedical Imaging and Bioengineering (ROI EB033773, 2R01EB023281. R21EB018990 ROIEBO1995 1956, P41EB030006), the National Institute on Aging AG22220,,,,,, IR01AG064027, ROLAGO0 6495, 1R01 AG070988),
the National Institute of Mental Health UMMIMH13091,, RO1 MH123195, RO1 MH121885, IRFIMH123195), the National Institute for Neurological Disorders and Stroke, (IU24NS) 33561- 01, RO1 NS070963, 2R01 150835053534, ROINS105820, R25NS1225999 the National Insititute for Child Health and Human Development (RO1HD 109436, ROOHD1015510 and was made possible by the resources provided by Shared Instrumentation Grants 1S10RR023401, 1S10RR019307, and IS 1S1ORR023043 Additional support was provided by the NIH Blueprint for Neuroscience Research (5001-MH937655) part of the multi-instiuutional Human Connectome Project. Parts of this work were also supported by the ERC Starting Grant 758800 (EXPROTEA), ERC Consolidator Grant 101087347 (VEGA), as well as gifts from Ansys and Adobe Research. Much of the computation resources required for this research was performed on computational hardware generously provided by the Massachusetts Life Sciences Center is an advisor to DeepHealth, company whose medical pursuits focus on medical imaging and measurement technologies. AD an advisor to Radence and DeepHealth, BF's and AD's s interests were reviewed and are managed by Massachusetts General Hospital and Mass. General Brigham in accordance with their conflict of interest policies.
In addition, BF
REFERENCES
S Mazdak Abulnaga, Oded Stein, Polina Golland, and Justin Solomon. Symmetric volume maps: Order-invariant volumetric mesh correspondence with free boundary. ACM Transactions on Graphics, 42(3):1-20, 2023. 3
S. Mazdak Abulnaga, Andrew Hoopes, Neel Dey, Malte Hoffmann, Bruce Fischl, John Guttag, and Adrian Dalca. Multimorph: On-demand atlas construction. In Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 20906-30917, June 2025. 2
Sahar Ahmad, Zhengwang Wu, Gang Li, Li Wang, Weili Lin, Pew-Thian Yap, and Dinggang Shen. Surface-constraineed volumetric registration for the early developing brain. Medical Image Analysis, 58:101540, 2019.
2
John Ashburner. A fast diffeomorphic image registration algorithm. Neuroimage, 38(1)955-113 2007. 5
Brian B Avants, Charles L Epstein, Murray Grossman, and James C Gee. Symmetric diffeomorphic image registration with cross-correlation. evaluating automated labeling of elderly and neurode- generative brain. Medical image analysís, 12(1):26 2008
Brian B Avants, Paul Yushkevich, John Pluta, David Minkoff, Mare Korczykowski, John Detre, and James C Gee. The optimal template effect in hippocampus studies of diseased populations. Neuroimage, 49(3):2457-2466, 2010.
6
Guha Balakrishnan, Amy Zhao, Mert R Sabuneu, John Guttag, and Adrian V Dalca. Voxelmorph: a learning framework for deformable medical image registration. IEEE transactions on medical imaging, 38(8): 1788))788-1180 2019.

---

Published as a conference paper at ICLR 2026
Paul J. Besl and Neil D. McKay. A Method for Registration of 3-D Shapes. IEEE Trans. Pattern Anal. Mach. Intell., 1992. 3
Gaurav Bhalerao, Grace Gillis, Mohamed Dembele, Sana Suri, Klaus Ebmeier, Johannes Klein, Michele Hu, Clare Mackay, and Ludovica Griffanti. Automated quality control of t1-weighted brain mri scans for clinical research: methods comparison and design of a quality prediction classifier. medRxiv, pp. 2024-04, 2024. 10
Fabian Bongratz, Anne-Maric Rickmann, Sebastian Pölsterl, and Christian Wachinger. Vox2cortex: Fast explicit reconstruction of cortical surfaces from 3d mri scans with geometric deep neural networks. In Proceedings of the IEEE/CVF conference on computer vision and pattern recognition, pp. 20773-20782, 2022. 10
Matthew Brett, Alexander Leff, Chris Rorden, and John Ashburner. Spatial normalization of brain images with focal lesions using cost function masking. Neuroimage, 14(2):486 500, 2001. TO
Dongliang Cao, Paul Roetzer, and Florian Bernard. Unsupervised Learning of Robust Spectral Shape Matching. ACM Transactions on Graphics, 42(4)::32:1-133::55 July 2023. B
Jieyu Cheng, Adrian V Dalca, Bruce Fischl, Lilla Zöllei, Alzheimer's Disease Neuroimaging Initiative, et al. Cortical surface registration using unsupervised learning. Neurolmage, 221: 171611 2020.
Bryan R Conroy, Benjamin D Singer, J Swaroop Guntupalli, Peter J Ramadge, and James V Haxby. Inter-subject alignment of human cortical anatomy using functional connectivity. Neurolmage, 81: 400-411, 2013.
Adrian Dalca, Marianne Rakic, John Guttag, and Mert Sabuncu. Learning conditional deformable templates with convolutional networks. Advances in neural information processing systems, 32,
2019a. 5
Adrian V Dalca, Guha Balakrishnan, John Guttag, and Mert R Sabuneu. Unsupervised learning of probabilistic diffeomorphic registration for images and surfaces. Medical image analysis, 57: 226-236 2019b. 7
Bob D De Vos, Floris F Berendsen, Max Viergever, Marius Staring, and Ivana Išgum. End-to- end unsupervised deformable image registration with convolutional neural network. In Deep Learning in Medical Image Analysis and Multimodal Learning for Clinical Decision Support: Third International Workshop. DLMIA 2017. and 7th International Workshop, ML-CDS 2017, Held in Conjunction with MICCAI 2017, Québec City, QC, Canada, September 14, Proceedings
pp. 204 212. Springer, 2017. 2
Bailin Deng, Yuxin Yao, Roberto M. Dyke, and Juyong Zhang. A Survey of Non-Rigid 3D Registra- tion. Computer Graphics Forum, 41(2):559-558 589, 2022. 3
Christophe Destrieux, Bruce Fischl, Anders Dale, and Eric Halgren. Automatic parcellation of human cortical gyri and sulci using standard anatomical nomenclature. Neuroimage, 53(1):1-15, 2010.
Nicolas Donati, Abhishek Sharma, and Maks Ovsjanikov. Deep Geometric Functional Maps: Robust Feature Learning for Shape Correspondence. 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 8589-8598, Seattle, WA, USA, June 2020. IEBE. ISBN
978-1-72817-168-
10
Bruce Fischl. Freesurfer. Neuroimage, 62(2):774-781, 2012. 1
10
Bruce Fischl, Martin I Sereno, and Anders M Dale. Cortical surface-basse analysis: li: inflation, flattening, and a surface-based coordinate system. Neuroimage, 992):195-077, 1999.
Bruce Fischl, Niranjini Rajendran, Evelina Busa, Jean Augustinack, Oliver Hinds, BT Thomas Yeo, Hartmut Mohlberg, Katrin Amunts, and Karl Zilles. Cortical folding patterns and predicting cytoarchitecture. Cerebral cortex, 1873))197311990 2008.
12

---

Published as a conference paper at ICLR 2026
Satrajit S Ghosh, Sita Kakumoori, Jean Augustinack, Alfonso PietoCaastanon, loulia Kovelman, Nadine Gaab, Joanna A Christodoulou, Christina Triantafyllou, John DE Gabrieli, and Bruce Fischl. Evaluating the validity of volume-based and srfface-based brain image registration for developmental cognitive neuroscience studies in children 4 to 11 years of age. Neuroimage, 53(1):
85-93, 2010. 13
Daniel Grzech, Mohammad Farid Azampour, Ben Glocker, Julia Schnabel, Nassir Navab, Bernhard Kainz, and Loic Le Folgoe. A variational Bayesian method for similarity learning in non-rigid image registration. In Proceedings of the IEEE/CVF Conference Computer Vision and Pattern Recognition, pp. 119-128, 2022. 2
Malte Hoffmann, Benjamin Billot, Douglas N Greve, Juan Eugenio Iglesias, Bruce Fischl, and Adrian V Dalca. Synthmorph: learning IEEE transactions on medical imaging, 41 413)5543-5558 2021. 2
registration without acquired images.
Malte Hoffmann, Andrew Hoopes, Bruce Fischl, and Adrian V Dalca. Anatomy-specific acquisition- agnostic affine registration learned from fictitious images. In Medical Imaging 2023: Image Processing, volume 12464, pp. 1246402. SPIE, 2023. 7
Malte Hoffmann, Andrew Hoopes, Douglas N Greve, Bruce Fischl, and Adrian Dalca. Anatomy- aware and acquisition-agnostic joint registration with SynthMorph. Imaging Neuroscience, 2:1-33,
2024. 7
Andrew Hoopes, Malte Hoffmann, Bruce Fischl, John Guttag, and Adrian Dalca. Hypermorph: Amortized hyperparameter learning for image registration. In International conference informa- tion processing in medical imaging, pp. 3-17. Springer, 2021. 9
Andrew Hoopes, Juan Eugenio Iglesias, Bruce Fischl, Douglas Greve, and Adrian Dalca. Topofit: rapid reconstruction of topologically-coreee cortical surfaces. Proceedings of machine learning research, 172:508, 2022.
10
IXI Consortium. IXI dataset.
URL
Rohit Jena, Pratik Chaudhari, and James C Gee. Deep implicit optimization enables robust learnable
features for deformable image registration. Medical Image Analysis, 103:103577, 2025. 7
Anand Joshi, Richard Leahy, Arthur W Toga, and David Shattuck. A framework for brain registration via simultancous surface and volume flow. In International Conference on Information Processing in Medical Imaging, pp. 576-588- Springer, 2009. 2
Diederik P Kingma and Jimmy Ba. Adam: method for stochastic optimization. arXiv preprint 14Xiv:1412.6980 2014. 7
Amo Klein, Satrajit S Ghosh, Forrest S Bao, Joachim Giard, Yrjö Häme, Eliezer Stavsky, Noah Lee, Brian Rossa, Martin Reuter, Elias Chaibub Neto, al. Mindboggling morphometry of human brains. PLoS computational biology, 13(2)=e1003350 2017. 7
Alex D Leow, Igor Yanovsky,
Chiang, Agatha D Lee, Andrea D Klunder, Allen Lu, James T Becker, Simon W Davis, Arthur W Toga, and Paul M Thompson. Statistical properties of jacobian maps and the realization of unbiased large-deformation nonlinear image registration. IEEE transactions on medical imaging, 26(6):822-32, 2007. g
Jian Li, Greta Tuckute, Evelina Fedorenko, Brian L Edlow, Adrian V Dalca, and Bruce Fischl. Josa: Joint surface-based registration and atlas construction of brain geometry and function. Medical Image Analysis, 1031032, 2024.
Robin Magnet and Maks Ovsjanikov. Memory-Scalable and Simplified Functional Map Learning. In 2024 IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR), pp. 4041-4050, Seattle, WA, USA, June 2024. IEEE. ISBN 9798350353006.
13

---

Published as a conference paper at ICLR 2026
Daniel S Marcus, Tracy H Wang. Jamie Parker, John G Csemansky, John C Morris, and Randy L Buckner. Open access series of imaging studies (oasis): cross-sections mri data in young. middle aged, nondemented, and demented older adults. Journal of cognitive neuroscience, 19(9):1498- 1507, 2007.
Mare Modat, Gerard R Ridgway, Zeike A Taylor, Manja Lehmann, Josephine Barnes, David Hawkes, Nick C Fox, and Sébastien Ourselin. Fast free-form deformation using graphics processing units. Computer methods and programs in biomedicine, 98(3):278-285) 2010. 2
Tony CW Mok, Zi Li, Yingda Xia, Jiawen Yao, Ling Zhang, Jingren Zhou, and Le Lu. Deformable medical image registration under distribution shifts with neural instance optimization. In In- ternttional Workshop Machine Learning in Medical Imaging, pp. 126-136. Springer, 2023.
Susanne G Mueller, Michael W Weiner, Leon J Thal, Ronald C Petersen, Clifford Jack, William Jagust, John Q Trojanowski, Arthur W Toga, and Laurel Beckett. Ways toward an early diagnosis in alzheimer's 's disease: the alzheimer's 's disease neuroimaging initiative (adni). Alzheimer's 's & dementia, 1(1):55-66, 2005. 7
Maks Ovsjanikov, Mirela Ben-Chen, Justin Solomon, Adrian Butscher, and Leonidas Guibas. Func- tional maps: A flexible representation of maps between shapes. ACM Transactions Graphics, 31(4):1-11, August 2012. 3
Gheorghe Postelnicu, Lilla Zollei, and Bruce Fischl. Combined volumetric and surface registration. IEEE transactions on medical imaging, 2884):508-5 2008. 2
Marianne Rakie, Andrew Hoopes, Mazdak S. Abulnaga, Mert R. Sabuneu, John V. Guttag, and Adrian V. Dalca. Atlasmorph: Learning conditional deformable templates for brain mri. Medical Image Analysis, 110 103893, 2026. ISSN 1361-8415, 2
Mare-Miche Rohé, Manasi Datar, Tobias Heimann, Maxime Sermesant, and Xavier Pennec. Svf-net: learning deformable image registration using shape matching. In Medical Image Computing and Computer Assisted Intervention- MICCAI 2017: 20th International Conference, Quebec City, QC, Canada, September 1 1-13, 2017, Proceedings, Part 20, pp. 266-274. Springer, 2017. 2
Karl Rohr, H Siegfried Stiehl, Rainer Sprengel, Thorsten M Buzug, Jürgen Weese, and MH Kuhn. Landmark-baad based elastic registration using approximating thin-plate splines. IEEE Transactions on medical imaging. 20(6):526 534, 2001.
Olaf Ronneberger, Philipp Fischer, and Thomas Brox. U-net: Convolutional networks for biomedical image segmentation. In Medical image computing and computer-assisted intervention-MICCA. 2015: 18th international conference, Munich, Germany, October 5-9, 2015, proceedings, part III 18, pp. 234 241. Springer, 2015. 5
Daniel Rueckert, Luke Sonoda, Carmel Hayes, Derek LG Hill, Martin O Leach, and David J Hawkes. Nonrigid registration using free-form deformations: application to breast mr images. IEEE transactions on medical imaging, 18(8):712-721, 1999. 1
S. Rusinkiewicz and M. Levoy. Efficient variants of the ICP algorithm. In Proceedings Third International Conference on 3-D Digital Imaging and Modeling, pp. 145-152, May 2001.
Florent Ségonne, Jenni Pacheco, and Bruce Fischl. Geometrically accurate topology-correett correction of cortical surfaces using nonseparating loops. IEEE transactions on medical imaging, 26(4): 518-529, 2007.
4
Nicholas Sharp, Souhaib Attaiki, Keenan Crane, and Maks Ovsjanikov. DiffusionNet: Discretization Agnostic Learning on Surfaces. ACM Transactions on Graphics, 41(3):1-16, June 2022. 3
Hessam Sokooti, Bob De Vos, Floris Berendsen, Boudewijn PF Lelieveldt, Ivana lšgum, and Marius Staring. Nonrigid image registration using multi-scale 3d convolutional neural networks. In Medical Image Computing and Computer Assisted Intervention- MICCAI 2017: 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings. Part 20, pp.
232-239. Springer, 2017. 2
14

---

Published as a conference paper at ICLR 2026
Olga Sorkine and Mare Alexa. As-rigid-as-possiee surface modeling. In Proceedings of the Fifth Eurographics Symposium on Geometry Processing, SGP '07. pp. 109-116, Goslar, DEU, July 2007. Eurographics Association. ISBN 978-3- 378-3-905673-44-33 3
(Jean) Talairach and Pierre Tournoux. Co-planar stereotaxic atlas of the human brain- dimensional proportional system: An approach to cerebral imaging. Clinical Radiology, 41: 219, 1990.
Paul M Thompson, Kiralee M Hayashi, Rebecca Dutton, MING-CHANG CHIANG, Alex D Leow, Elizabeth R Sowell, Greig De Zubicaray, James T Becker, Oscar L Lopez, Howard J Aizenstein, et al. Tracking alzheimer's disease. Annals of the New York Academy of Sciences, 1097()):183-214, 2007. 0
Lin Tian, Hastings Greer, Roland Kwitt, Francois-Xavier Vialard, Raúl San José Estépar, Sylvain Bouix, Richard Rushmore, and Marc Niethammer. unigradicon: A foundation model for medical image registration. In International Conference on Medical Image Computing and Computer-
Assisted Intervention, pp. 749-760. Springer, 2024. 7
Alan Tucholka, Virgile Fritsch, lean-Baptist Poline, and Bertrand Thirion. An empirical comparison of surface-based and volume-based group studies neuroimaging. Neuroimage, 6333):1443-1453,
2012. 0
Clarisse Weischedel. A Discrete Geometric View on Shear-Deformable Shell Models. PhD thesis, Georg-August-Univerisin Göttingen, August 2012.
Xiao Yang. Roland Kwitt, Martin Styner, and Mare Niethammer. Quicksilver: Fast predictive image registration-a deep learning approach. Neurolmage, 158:378-396, 2017. 2
Thomas Yeo, Mert R Sabuneu, Tom Vercauteren, Nicholas Ayache, Bruce Fischl, and Polina Gol- land. Spherical demons: fast diffeomorphic landmark-free surface registration. IEEE transactions
on medical imaging. 29(3):650-66 2009.
3
Fenqiang Zhao, Shunren Xia, Zhengwang Wu, Dingna Duan, Li Wang, Weili Lin, John H Gilmore, Dinggang Shen, and Gang Li. Spherical u-net cortical surfaces: methods and applications. In Information Processing in Medical Imaging: 26th International Conference, IPMI 2019, Hong Kong, China, June 2-7, 2019, Proceedings 26, pp. 855-866. Springer, 2019.
Fenqiang Zhao. Zhengwang Wu, Li Wang, Weili Lin, John H Gilmore, Shunren Xia, Dinggang Shen, and Gang L.. Spherical deformable u-net: Application to cortical surface parcellation and development prediction. IEEE transactions on medical imaging, 1014):111712228, 2021.
Lilla Zöllei, Allison Stevens, Kristen Huber, Sita Kakunoori, and Bruce Fischl. Improved tractography alignment using combined volumetric and surface registration. Neuroimage, 51(1):206-211 221:21,,,111 2010.
15

---

Published as a conference paper at ICLR 2026
A SUPPLEMENTARY MATERIAL
A.1 ABLATION OVER DICE Loss WEIGHT
In this section, we conduct ablations over the Dice loss weight R. We use the IXI dataset and a sphere loss weight 7 0.05. As demonstrated on T the inclusion of the soft Dice loss on cortical and subcortical structures in combination with our proposed spherical alignment loss is necessary to produce accurate cortical and subcortical aligmments. However, this comes the cost of field regularity. Table A.1 presents the results. Consistent increases in Dice (cortical) are observed with increasing K, but Dice (subcortical) starts saturate for >> This comes at the expense field regularity, as measured by the % of folds and SDlog det. J.
Figure A.1 presents example images and warps varying K. As expected, deformation fields become more irregular with increasing si, though presented ranges are reasonable. The optimal choice of depends on the intended downstream application. The user has control over the desired strength of structural alignment over field regularity and smoothness. We note however that our model produces accurate matchings with regular fields for large range x values.
Table A.1: Ablations over Dice loss weight on the IXI dataset.
Dice (t) cortical
Dice (f) subcortical
Dice loss weight
% folds (L)
SD log det J (4)
0.5
0.613 + 0.029
0.787 0.041
0.014 # 0.005
0.459 + 0.15
K = 1.0
0.633 + 0.028
0.799 = 0.038
0.006 = 0.003
0.432 0.137
A 2.0
0.637 + 0.03
0.793 0.037
0.016 + 0.006
0.462 0.141
K = 5
0.653 + 0.029
0.796 + 0.039
0.046 0.015
0.597 + 0.188
K 10
0.683 = 0.029
0.81 0.036
0.081 = 0.023
0.712 0.24
K = 50
0.691 + 0.028
0.799 0.038
0.848 = 0.135
1.294 + 0.414
Warped image
Warp field
Moving
Fixed
K = 1
==
= 10
== 1
== 5
= 10
Figure A.1: Example registrations for one image while varying k. Columns show the moving and fixed images, followed by warped images and corresponding deformation fields are visualized on the right. Deformation fields become more irregular with increasing however all demonstrated values produce accurate and smooth alignments.
A.2 WHOLE CEREBRAL CORTEX ALIGNMENT PERFORMANCE
Our evaluation on Table and Fig. focused on quantifying performance of aligning cortical parcellations within the cerebral cortex. We hypothesized that the spherical alignment signal will be most important for aligning the homologous folds the image intensity information is unable to capture the functional regions within the cortex. To test this hypothesis, we compared Dice score in aligning cortical parcellations (Dice cortical) with Dice score aligning the entire cerebral cortex (Dice CC), which groups all parcellations as one class. Table A.2 presents the results.
On two the three datasets, our model achieves the highest Dice (CC) performance, while CVS outperforms our method by 1.2 Dice points on the OASIS- & ADNI test set. Interestingly, all baseline methods show improved performance in aligning the cerebral cortex and differences across baselines smaller. This indicates that purely volumetric approaches may be sufficient capturing the whole cerebral cortex structure. However, when trying to align the cortical parcellations, the benefit of our formulation is immediate, obtain 1.9 7.5 point Dice increases over the next best
16

---

Published as a conference paper at ICLR 2026
Table A.2: Performance all methods across three datasets, focusing on structural alignment on the graymatter. Dice (CC) indicates the dice score in aligning the entire cerebral cortex, while Dice cortical refers to the parcellated substructures within the cerebral cortex. The benefit of our method in aligning substructures within the cortex (Dice cortical) is immediately apparent, as consistently achieve the highest score, including up to 7.5 dice score improvement over the next method. When considering the cerebral cortex as one structure, performance differences decrease, though our method still performs the strongest on the datasets. The benefit the spherical registration is immediately apparent it is necessary to align functional regions in the cortex where image-only approaches fail. Mean + standard deviation across subjects are indicated.
Dice (CC) (t) left
Dice (CC) (t) right
Dice (f) cortical
Dataset
Method
% folds (L)
OASIS- & ADNI
uGradICON
0.711 + 0.029
0.71 = 0.026
0.58 + 0.58 0.028
0.647 0.105
uGradICON-seg
0.712 + 0.03
0.711 = 0.027
0.583 + 0.028
0.688 + 0.101
SynthMorph
0.626 1 0.035
0.628 + 0.032
0.511 + 0.033
0.0 0.0
SynthMorph-wm
0.617 0.035
0.62 0.031
0.525 + 0.032
0.0 0.0
VoxelMorph
0.72 0.031
0.72 0.03
0.551 0.039
0.001 0.001
FireANTss
0.703
0.703 0.033
0.554 0.038
CVS
0.777
0.775 0.03
0.681 + 0.035
1.73 + 0.321
NeurAlign (Ours)
1.765:0.003
0.764 0.025
0.698 + 0.032
0.169 0.037
uGradICON
0.74 0.02
0.746 + 0.017
0.631 + 0.021
0.489 + 0.1
uGradICON-seg
0.749 0.02
0.755 + 0.017
0.639 0..02
0.602 0.109
SynthMorph
0.691
0.693 0.02
0.577 0.03
0.0
IXI
SyathMorph-wm
0.683 1 0.021
0.684 + 0.021
0.599 1 0.025
0.0
VoxeIMorph
0.736 1 0.033
0.737 1 0.032
0.566 + 0.045
0.001 + 0.001
FireANT's
0.754 0.024
0.601 = 0.037
1.382 0.183
CVS
0.748 + 0.041
0.754 0.036
0.582 0.039
1.865 0.382
NeurAlign (Ours)
0.758 + 0.023
0.758 = 0.021
0.683 + 0.029
0.081 0.023
uGradICON
0.722 1: 0.051
0.731 0.044
0.618 0.038
+ 0.404
Mindboggle
uGradICON-see
0.73 0.049
0.738 = 0.045
0.626 0.038
0.958 + 0.4
SyuthMorph
0.697 = 0.03
0.701 = 0.036
0.577 + 0.054
0.0 0.0
SynthMorph-win
0.685 0.031
0.688 = 0.038
0.596 0.048
0.0
VoxelMorph
+ 0.736 0.055
0.744 0.055
0.573 0.072
0.002 0.002
FireANTss
0.742 0.05
0.748 + 0.051
0.597 0.07
1.604 0.347
CVS
0.689 + 0.091
0.693 + 0.088
0.535 0.07
2.164 0.652
NeurAlign (Ours)
0.782 1: 0.04
0.785 + 0.041
0.703 - 0.06
0.173 + 0.034
method across all datasets. The purely volumetric approaches show substantially lower performance than our method, as well.
17


Reviews:
[{"review_id": "RDMd0b9Fcy", "reviewer": "Reviewer_57Lz", "summary": "This paper proposes UCS, a unified learning framework that trains a 3D diffeomorphic registration network and a 2D spherical registration network jointly, with a cortical-consistency loss that ties the cortical ribbon deformation in the volume to the sphere-space deformation.\nThe writing is clear and the experiments are sufficient. But still, some weakness exists.\n\nI am inclined to give a score of around 5, but since that option isn't available, I will select 4 for now.", "questions": "- Discuss licensing/availability of FreeSurfer usage. Many ICLR readers are not neuroimaging specialists.", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "- This paper proposes a real and valuable challenge in MRI registration: current pipelines split surface vs volume.\n- Key technical idea (soft consistency energy on cortical surface) is simple, plausible, and seems to explain gains; ablation supports this. \n- Sufficient comparison to the right classical joint method (CVS) and to current learning baselines (SynthMorph variants, uniGradICON).\n- It is great to test on two additional held-out datasets.", "weaknesses": "- The author claims, \"Unlike other methods that require additional inputs (cortical meshes, segmentations) at inference, our method requires only structural MRI images.\" However, they also mention, \"For each image, we use FreeSurfer to generate anatomical segmentations\" in the experiment setup. Therefore, it is not truly \"only structural MRI images\" as input. If you plan to integrate this with your model as a complete pipeline, do you include the time spent on segmentation when comparing to CVS?\n- Why this task cannot be done by “3D reg + surface reg, then post-hoc propagation” process? Compared to some baseline methods, they did missing one modality in registration. It is quite nature to think more modality for cross-validation is better. The reviewer would like to see a discussion or clarification on this part", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "TA135FHz8Y", "reviewer": "Reviewer_7rxY", "summary": "This paper presents UCS, a deep learning framework for brain MRI registration that combines volumetric and surface-based approaches. UCS employs a coupled architecture with spherical coordinate mappings and a consistency loss to enforce geometric coherence, using surface mesh registration results as additional supervision for volumetric registration. The method achieves state-of-the-art performance across multiple datasets.", "questions": "I don't have questions to ask because the paper is clearly written and the approach is straightforward to understand.", "limitations": "", "rating": 2, "confidence": 5, "soundness": 3, "presentation": 3, "contribution": 1, "strengths": "1. UCS couples volumetric and spherical registration networks, promoting anatomical consistency across domains.\n\n2. UCS outperforms classical (CVS) and modern deep learning methods (SynthMorph, uniGradICON) in both cortical and subcortical Dice scores.", "weaknesses": "1. The authors claim that their approach provides a unified solution for the registration of cortical and subcortical structures. And the key idea is to use correspondence between surface areas as additional supervision signal. This idea is not novel; a similar approach was presented in https://doi.org/10.1016/j.media.2019.101540\n\n2. From the title, I had the expectation that the proposed approach would have some special designs for the registration of subcortical structures. However, such designs were not found.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "Z8MfY41XQR", "reviewer": "Reviewer_rb9L", "summary": "The paper proposes a deep learning framework called UCS that aligns both cortical and subcortical structures in in-vivo neuroimaging by using volume based dense registration combined with surface-based registration of the cortical surface. The paper posits the limitations of volumetric registration methods for registering the cortex despite its success in registering the subcortical structures and global anatomy. The problem with incorporating intensity and surface based registration is that the 2D surface registration has a gradient with a Lebesgue measure of 0 on the ambient 3D space, and to avoid this problem the paper proposes training a 2D and 3D registration network for the surface and volume respectively, and add a consistency term between the losses. Results are shown on four clinical MRI datasets (OASIS, ADNI, IXI, Mindboggle).", "questions": "1. 2D registration has to be performed on a sphere where the coordinate $\\phi$ wraps around from 0 to $2\\pi$. how is this circular nature considered in the spherical registration? appropriate citations or derivations in the supplementary material can be useful \n2. What is the performance of the method without the segmentation loss? This might be used for hippocampus or MTL registration for example where only the registration of a single surface might be of interest without registering other structures. \n3. In many other clinical or research scenarios pertinent to neuroimaging studies, the surface mesh is typically available (using a segmentation algorithm or manually) and accurate registration of the surface and volume might be desired. However, collecting training data across many subjects might be infeasible. In such a scenario, can UCS be used in an online optimization fashion? \n\nI would like the authors to address some of the weaknesses of the paper followed up by the questions in this section.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "1. The mathematical formulation is very well defined, easy to follow, and technically sound. Usual papers in this topic are rather sloppy with overloaded notation or hand wavy definitions, but this paper is much clearer in that sense.\n2. Most of the formulation is consistent with a typical deep learning registration framework, and the coupling term is the major technical novelty in the paper, which is easy to undeerstand.\n3. Results are shown on a few popular clinical MRI datasets", "weaknesses": "1. The premise of the paper \"While effective for aligning subcortical structures and global anatomy, volumetric deformable registration often fails in the cortex. The cortex is a thin, highly curved surface with significant inter-subject variability in folding patterns that is difficult to align in Euclidean space\" is not substantiated in any way except for the experiments in the paper. Most methods trained on SynthSeg or Freesurfer labels (e.g. OASIS dataset) have achieved overall dice scores in the order of 0.88, almost to the point of overfitting on the labelmaps. Two of the labelmaps in freesurfer / synthseg labels are the cerebral cortex for each hemisphere. It would greatly strengthen the premise of the paper to show the performance of pre-trained optimization and deep learning methods on these datasets or labelmaps on only the cortical label registration.\n2. Exaggerated narrative about slowness of optimization methods - \"Moreover, because of its reliance on classical optimization techniques, CVS is computationally expensive, requiring several hours per subject pair, making it impractical for large-scale datasets.\" and other statements imply classical methods being very slow which has been shown to be false with newer implementations - particularly in the Oncoreg Learn2Reg challenge (where Syndeeds and ConvexAdam perform very well with no or little learning), and FireANTs which shows real-time registration on various clinical datasets.  \n3. Equation 2 is not a coupled optimization - coupling is only achieved with Equation 3. This is problematic because the objective (integral) in Equation 3 is only defined on the boundary of the surface $dS$ , which has a Lebesgue measure of 0 on the 3D ambient space. This suffers from the same problem as joint optimization of the volumetric and surface registration using a single volumetric displacement grid. The paper does not justify why Equation 3 does not suffer from the same problem that direct optimization on the surface matching objective using a volumetric displacement does. This is a major issue in the paper - since the whole idea behind not performing direct optimization of the cortical surface was the measure 0 gradient of the surface loss. Since this is the only proposed technical novelty in the paper (coupling the surface and volume registration), proper empirical (showing the gradient propagation with and without the coupling term) or theoretical (proofs) justification is needed.\n4. \"All CVS experiments are done on an Intel(R) Xeon(R) Gold 5218 CPU. (There is no GPU-based implementation of CVS.)\" - Use FireANTs or ConvexAdam for GPUs. These baselines have existed for more than a year now, and are very efficient for the scale of clinical datasets. \n5. Baselines are not adequate. Voxelmorph with segmentation loss should be compared with UCS. Synthmorph and unigradICON are general purpose registration tools like ANTs, but since the method assumes access to a training dataset, at least a few baselines should be trained with the same data. \n6. Line 424: \"Including our proposed sphere loss (Base+Dice(all)+Sphere) produces a clear increase in Dice (cortical) while preserving a high Dice(subcortical) score.\" - this is not the right ablation to run. The correct ablation here is to add the cortical surface loss directly in the training / inference objective instead of the roundabout way (i.e. consistency between network outputs).\n\nMinor issues: \n1. The geometric descriptors used in the surface registration are not mentioned. This hinders reproducibility of the paper.\n2. to my knowledge, loss masking in unigradicon does not explicitly align the structures themselves but only registers within the provided masks. im not sure why this baseline is used in that case\n3. Line 469 - \"Unlike other methods that require additional inputs (cortical meshes, segmentations) at inference, our method requires only structural MRI images.\"  - This is a partially false statement - since all methods considered in the paper (except unigradICON with masking) do not require additional labels at inference. This is only true for classical iterative methods that do not learn any label-aware features.\n4. Another potential weakness in the evaluation setup is that the considered datasets are possibly overfit to in the long run. There are other high resolution, high quality datasets (e.g. Ultracortex 9.4T) that have higher than 1mm resolution (i.e. 0.6mm)  and manual labellings of the cortical surface - providing a challenging evaluation setup for the exact problem tackled in the paper", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "jFYZCbTkGA", "reviewer": "Reviewer_L2kZ", "summary": "This paper proposes a unified deep learning framework for brain MRI registration that jointly aligns cortical surfaces and volumetric subcortical structures using spherical + volumetric CNNs coupled by a consistency loss. The work aims to overcome limitations of existing methods (e.g., CVS) that treat the two domains sequentially.", "questions": "Surface preprocessing dependency\nYour method requires cortical meshes and spherical inflation during training. How sensitive is performance to inaccuracies or failures in this preprocessing? Could UCS be trained without spherical meshes (e.g., using synthetic or implicit surfaces)?\n\nInference on challenging scans\nSince no surface information is used at inference, how well does the model perform on:\n\nlow-resolution or motion-corrupted clinical MRIs?\n\nsubjects with pathology altering cortical shape (e.g., tumors, resections)?\nAny preliminary results or failure analyses?\n\nConsistency loss mechanics\nCould you elaborate on the interpolation needed to map spherical displacement back to 3D mesh vertices? How does sampling density on the sphere affect gradient stability?\n\nSubcortical performance variability\nYour method slightly underperforms baselines on IXI subcortical alignment.\nWhy might IXI behave differently? (acquisition style? age distribution?)\nWould modest segmentation supervision balance this out?\n\nJacobian regularity vs. Dice trade-off\nAblations show increasing κ improves Dice but degrades regularity.\nDo you have guidance on selecting κ for different applications (e.g., longitudinal studies)? Could adaptive balancing be learned?\n\nTopology enforcement\nWhile spherical alignment preserves cortical topology, volumetric deformation can still introduce folding. Would incorporating diffeomorphic constraints on the spherical path reduce the remaining ~0.1–0.2% folds?\n\nSphere parameterization distortion\nStereographic projection introduces sampling and area distortion.\nHow does this influence fine-scale folding alignment? Any alternatives considered (e.g., icosahedral CNNs)?\n\nTraining pairs\nRegistration direction is arbitrary. Did you augment by swapping moving/fixed pairs? Any asymmetry observed in deformation field quality?\n\nRuntime comparison fairness\nSince CVS requires spherical meshes at inference, did timing exclude preprocessing?\nCould UCS runtime remain competitive if including preprocessing of spheres during training on real pipelines?\n\nScalability to groupwise registration\nCould your framework support joint template estimation or atlas building?\nWhat changes would be required to extend UCS to multi-subject alignment?", "limitations": "", "rating": 8, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "Clear contribution: A unified model bridging spherical and volumetric registration is well-motivated.\n\nTechnical novelty: The cortical consistency loss connecting domains is elegant and addresses a real limitation in current pipelines.\n\nStrong results: Substantial gains in cortical Dice (up to +7 points) on multiple datasets, with very fast inference vs. CVS.\n\nGeneralization: Tested on multiple held-out datasets including IXI and Mindboggle.\n\nSolid ablation studies isolating effects of proposed components.", "weaknesses": "Dependence on spherical preprocessing at training: Requires surface extraction and inflation (FreeSurfer), which can be slow and may fail on challenging scans; more discussion on robustness would help.\n\nSubcortical performance not universally better: Slight drop vs. uniGradICON/SynthMorph on IXI subcortical structures.\n\nLimited modality / population scope: All training on adult T1-weighted datasets (OASIS/ADNI). No fetal/pediatric/clinical robustness experiments.\n\nAblations could explore more consistency-loss formulations (e.g., geodesic metrics on the sphere).\n\nClarity: Some math sections are dense; figure captions could better explain preprocessing needed.\n\n\nNo code availabel.\n\nThe paper is a bit dense I think more figure would help.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Decision: Accept (Poster)