Uncertainty-Aware Cortical Surface Reconstruction and Spherical Registration for Heterogeneous Brain MRI

Jesper Duemose Nielsen; Karthik Gopinath; Andrew Hoopes; Adrian Dalca; Axel Thielscher; Juan Eugenio Iglesias; Oula Puonti

eess.IVOct 12, 2026

Uncertainty-Aware Cortical Surface Reconstruction and Spherical Registration for Heterogeneous Brain MRI

Authors: Jesper Duemose Nielsen, Karthik Gopinath, Andrew Hoopes, Adrian Dalca, Axel Thielscher, Juan Eugenio Iglesias, Oula Puonti

Organizations: Danish Research Centre for Magnetic Resonance, Department of Radiology and Nuclear Medicine, Copenhagen University Hospital – Amager and Hvidovre, Copenhagen, Denmark · Department of Health Technology, Technical University of Denmark, Kgs. Lyngby, Denmark · Athinoula A. Martinos Center for Biomedical Imaging, Massachusetts General Hospital, Charlestown, MA, USA · Computer Science and Artificial Intelligence Lab, Massachusetts Institute of Technology, Cambridge, MA, USA ·

Abstract

Surface-based cortical analysis is useful in many applications as it is a natural way to model the highly folded structure of the cerebral cortex, allowing quantities such as curvature and thickness to be easily calculated. Existing deep learning (DL) methods have focused on 1x1x1 mm3 T1-weighted (T1w) scans, thus replicating classical pipelines. Here we present a neural network that is trained exclusively on synthetic scans with random contrast and resolution. Consequently, it can be applied to almost any kind of magnetic resonance imaging (MRI) scan. In addition, our model provides vertex-wise uncertainty estimates of the predicted surface as well as a spherical registration to fsaverage space. Our model performs on par with other state-of-the-art DL methods on 1x1x1 mm3 T1w scans and outperforms the only other method capable of estimating cortical surfaces from low resolution, non-T1w scans. The predicted uncertainty, moreover, correlates with overall scan quality on low resolution scans and highlights areas of poor surface reconstruction on 1x1x1 mm3 T1w scans, suggesting that it can be used for quality control. Finally, the predicted spherical registrations prove comparable to other DL and classical registration methods. These qualities, when combined with the fast inference time, will provide the ability to analyze large, existing databases of clinical MRI scans, with the potential for finding disease-specific patterns that would otherwise be infeasible in a research setting.

Figures & tables

			t1w	synth	synth
		$p$	1mm	1mm	random
Select input image			x	x	x
	T1w		x
	Labeling			x	x
Sample intensities				x	x
Gamma transform		$0.33$		x	x

Table 1: Data augmentation steps for input scan when training the different models. FOV adjustment ensures that the data matrix is valid for processing with the CNN .

p

denotes the probability that an operation is applied (blank indicates that it is always applied). Indentation denotes a sub-step and x indicates that a step applies to this pipeline (if no sub-steps are marked, all sub-steps apply).

Figure 1: Examples of input data used to train the different models. The input template (blue) as well as the target WM (yellow) and GM (red) surfaces are overlaid on the input scans.

Figure 2: Overview of network training and inference. The input scan (here we show a single slice of a T1w image) is just an example; for the synth models this could be any contrast and for the synth-random model the resolution could be different. $\mathbf{f}$ is the image feature extractor (a UNet in our case) which extracts the features $\mathbf{F}$ . $g_{i}$ are the GCN blocks which predict the vectors used to deform the input template surface. Note that $V(7)$ from the WM pipeline is the final WM surface prediction and serves as the input for the GM pipeline. The predicted uncertainty is used to color the cortical surfaces as they evolve; the sphere is simply colored by vertices index to show its structure (we do not color by, for example, convexity or curvature since this is not used during training). $\mathcal{L}_{x}$ refers to the losses described in table 2 (the WM - GM loss is not shown).

Task	Loss	Weight
		0	20000	40000
WM	chamfer	$1.0$	$0.0$	$0.0$
	$-\mathcal{L}$	$0.0$	$0.5$	$0.5$
	Taubin	$40.0$	$40.0$	$40.0$
	edge	$5.0$	$2.0$	$1.0$
	quality	$2.5$	$1.0$	$0.5$

Table 2: Overview of the loss weights at each stage of the training process. The first number in the “weight” columns denotes the gradient step after which those weights apply. (w) indicates that it is weighted by the uncertainty estimate.

Dataset	Subj.	Males	Diag.	Age	Scans
Train
ABIDE Di Martino et al. (2014)	$1112$	$1001$	$539$	$7-64$	$807$
ADHD200 Milham et al. (2012)	$947$	$575$	$362$	$7-26$	$820$
ADNI3 Weiner et al. (2017)	$331$	$170$	$199$	$61-97$	$284$
AIBL Ellis et al. (2009)	$668$	$294$	$668$	$55-96$	$627$
Buckner40 Fischl et al. (2002)	$40$	$19$	$0$	$18-93$	$38$

Table 3: Overview of training and test datasets. Datasets in the “train” section were used for training, validation, and testing (splits 0.8, 0.1, 0.1). Datasets in the “generalization” section were used to test on unseen subjects from unseen datasets (generalizability). The number in the “Diag.” (diagnosis) column refer to the number of subjects with any kind of diagnosis. “Scans” refers to the number of scans that passed quality control.

Figure 3: Illustration of the problem of correlating closest distance with uncertainty when the surface reconstruction error is large. The blue surface is reconstructed using FreeSurfer on a corresponding $1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}$ T1w scan (not shown) whereas the red and yellow surface is estimated from a $1\text{\times}1\text{\times}5\text{\,}\mathrm{mm}$ FLAIR scans (shown). Red and yellow indicate low and high uncertainty, respectively. The three encircled parts show examples of patches where the (closest) distance to the FreeSurfer surface is small even though the surface estimate is not correct thus warranting a high uncertainty. Spherical registration aligns the folding patterns of the surfaces and by resampling one surface onto the other, we hope to achieve a more appropriate alignment of the surfaces from which to calculate the distances.

Figure 4: Comparison of different surface reconstruction methods showing which cases are handled by the different methods. The ex vivo FLASH scan is from Edlow et al. (2019) . Its original resolution is $0.1\text{\times}0.1\text{\times}0.1\text{\,}\mathrm{mm}$ but downsampled to $1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}$ . N/A denotes that the model is not applicable to the given contrast-resolution combination.

		White matter					Gray matter					WM-GM
		ASSD	HD90	SIF	$\sigma(E)$	TQ	ASSD	HD90	SIF	$\sigma(E)$	TQ	IF
Test ( $n=490$ )
Ours
	T1w-1mm	0.143	$0.346$	0.001	$0.143$	$0.925$	$0.197$	$0.480$	$0.004$	0.202	$0.889$	0.005
	synth-1mm	$0.232$	$0.501$	0.001	$0.145$	$0.929$	$0.305$	$0.685$	0.001	$0.212$	0.894	$0.026$
	synth-random	$0.282$	$0.622$	0.001	0.142	0.930	$0.366$	$0.816$	0.001	$0.221$	$0.892$	$0.016$

Table 4: Evaluation on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans (except where noted) from the test and generalization sets. Metrics ASSD , HD90 , and

\sigma(E)

(standard deviation of edge lengths) are in mm; TQ (triangle quality; from eq. 16 ) is unitless; SIF and IF are in %. Please note that surfaces produced by RAC are postprocessed with FreeSurfer to, for example, remove SIF . The best value within each dataset is highlighted.

n

denotes the combined size of the datasets in each section.

Figure 5: Relationship between average uncertainty and surface reconstruction error for the generalization set using predictions from the T1w-1mm model. Pearson correlation cofficients are

r=0.16

( WM ) and

r=0.46

( GM ).

Figure 6: Relationship between average uncertainty and surface reconstruction error for the low resolution generalization set using predictions from the synth-random model. Pearson correlation cofficients are

r=0.67

( WM ) and

r=0.69

( GM ).

Figure 7: Correlation between uncertainty estimate and smoothed surface errors within subjects. The bar in the violin plot indicates the mean of the distribution.

Figure 8: Average uncertainty and error over subjects from the generalization set mapped to fsaverage . Surface predictions performed using the T1w-1mm model on $1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}$ T1w scans. The units are $\mathrm{mm}$ .

Figure 9: Average uncertainty and error over subjects from the ADNI -GO2 test set mapped to fsaverage . Surface predictions performed using the synth-random model on $1\text{\times}1\text{\times}5\text{\,}\mathrm{mm}$ FLAIR . The units are $\mathrm{mm}$ .

Figure 10: Boxplots of accuracy scores across all regions of the Desikan-Killiany atlas Desikan et al. (2006) . (left) Spherical registration of surfaces predicted on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans from the generalization set using the model T1w -1mm. (right) Spherical registration of surfaces predicted on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans from the ADNI GO-2 dataset using the model synth-random. The reference against which the accuracy score is compute is the default spherical registration pipeline from FreeSurfer. The method denoted “map” uses coordinates obtained by spherical registration of our template to fsaverage .

Figure 11: WM surface reconstructions (FreeSurfer and our synth-random model) on the subject from ISBI2015 with the highest reconstruction error. This illustrates that FreeSurfer (blue) is sensitive to WM lesions (hypointensities) whereas the synth-random model (red-yellow where red and yellow corresponds to low and high uncertainty as estimated by the model, respectively) is less so. Additionally, we see that the estimated uncertainty highlights these difficult or problematic areas (even if the surface prediction might be correct).

Panel of Figure 12 — Figure 12: Surface reconstructions on $1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}$ T1w scans with ( 12(a) ) no added noise, ( 12(b) ) low amount of local noise, or ( 12(c) ) high amount of local noise. Black (yellow/white) indicates low (high) values of uncertainty. Blue is the surface reconstruction from ( 12(a) ) with no overlay. Noise is sampled from a uniform distribution and added in a window of size $14\text{\times}14\text{\times}14\text{\,}\mathrm{v}\mathrm{o}\mathrm{x}\mathrm{e}\mathrm{l}\mathrm{s}$ .

Appendix figures & tables8 assets

Supplementary material from the paper’s appendix.

Appendix

	White matter					Gray matter
Contrast	T1w			synth		T1w			synth
Resolution	1 mm			1 mm	rand	1 mm			1 mm	rand
Model	DS	Ours	V2C	Ours	Ours	DS	Ours	V2C	Ours	Ours
ABIDE	$0.153$	$0.150$	$0.211$	$0.247$	$0.291$	$0.210$	$0.239$	$0.328$	$0.353$	$0.409$
ADHD200	$0.144$	$0.138$	$0.187$	$0.213$	$0.259$	$0.206$	$0.232$	$0.329$	$0.332$	$0.389$
ADNI3	$0.197$	$0.179$	$0.198$	$0.273$	$0.344$	$0.171$	$0.186$	$0.200$	$0.293$	$0.367$

Appendix

Table 1: Evaluation on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans from the test set (top) and generalization set (bottom) using ASSD in mm. DS (DeepSurfer), V2C (V2C-Flow). Contrast and resolution refers to the scans on which the models were trained.

Figure 1: White matter surface. The view shows a sulcus from below.

Figure 2: Gray matter surface. The view shows a sulcus from below.

Figure 3: Relationship between average uncertainty and surface reconstruction error for the test set using predictions from the T1w-1mm model. Pearson correlation coefficients are

r=0.22

( WM ) and

r=0.74

( GM ).

Figure 4: Average uncertainty and error over subjects from the test set mapped to fsaverage . Surface predictions performed using the T1w-1mm model on $1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}$ T1w scans. The units are $\mathrm{mm}$ .

	CAT	JOSA	ours (est)	ours (map)
Region
bankssts	$0.84$	$0.82$	$0.83$	$0.39$
caudalanteriorcingulate	$0.86$	$0.82$	$0.85$	$0.36$
caudalmiddlefrontal	$0.86$	$0.84$	$0.86$	$0.65$
cuneus	$0.87$	$0.75$	$0.82$	$0.70$
entorhinal	$0.73$	$0.65$	$0.73$	$0.32$

Appendix

Table 2: Classification accuracy per cortical region of the Desikan-Killiany atlas Desikan et al. (2006) . The results are computed using on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans from the generalization set (AOMIC-ID1000, COBRE, ISBI2015, MCIC). We use our model trained on

1\text{\times}1\text{\times}1\text{\,}\mathrm{mm}

T1w scans. The reference, against which the accuracy is computed, is the default spherical registration pipeline from FreeSurfer.

	CAT	JOSA	ours (est)	ours (map)
Region
bankssts	$0.81$	$0.82$	$0.79$	$0.57$
caudalanteriorcingulate	$0.84$	$0.83$	$0.87$	$0.49$
caudalmiddlefrontal	$0.87$	$0.85$	$0.86$	$0.57$
cuneus	$0.87$	$0.75$	$0.82$	$0.70$
entorhinal	$0.67$	$0.64$	$0.72$	$0.47$

Appendix

Table 3: Classification accuracy per cortical region of the Desikan-Killiany atlas Desikan et al. (2006) . The results are computed using

1\text{\times}1\text{\times}5\text{\,}\mathrm{mm}

FLAIR scans from the ADNI GO-2 dataset. We use our model trained on synthetic scans (random contrast, random resolution). The reference, against which the accuracy is computed, is the default spherical registration pipeline from FreeSurfer.

Panel of Figure 5 — Figure 5: ( 5(a) ) Original white matter surface from FreeSurfer’s recon-all pipeline. ( 5(b) ) White matter surface resampled to fsaverage . Sheared triangles are clearly visible.

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Ω

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