SimCortex v2: Joint Cortical Surface Reconstruction with Near-Zero Collisions and Self-Intersections

Kaveh Moradkhani; Sylvain Bouix

cs.CVOct 5, 2026

SimCortex v2: Joint Cortical Surface Reconstruction with Near-Zero Collisions and Self-Intersections

Authors: Kaveh Moradkhani, Sylvain Bouix

Abstract

Reconstructing cortical WM and pial surfaces from structural magnetic resonance imaging (MRI) is a prerequisite for surface-based neuroanatomical analysis, yet remains challenging because the cortex is thin and tightly folded. Reconstruction methods can produce geometric artifacts such as mesh self-intersections and collisions between cortical surfaces, and although recent deep learning methods have reduced reconstruction time from hours to minutes, these artifacts persist. We propose SimCortex v2, a deep learning framework for simultaneous reconstruction of the left and right WM and pial surfaces from T1-weighted MRI. SimCortex v2 estimates topologically correct initial surfaces from a volumetric segmentation and refines all four jointly using multi-scale stationary velocity fields predicted by a ribbon-conditioned, U-Net-like network. We evaluated SimCortex v2 on 560 cases from 14 cohorts, thirteen of them unseen during training, spanning ages 6-89, healthy and clinical populations, and scanners from three vendors. SimCortex v2 matched the surface-distance accuracy of the strongest baseline (average symmetric surface distance 0.253 mm) while showing no detected inter-surface collision in 92.14% of cases and the lowest self-intersection fraction (0.044%) among learning-based methods, whereas every baseline produced at least one collision in every case. Source code, configuration files, pretrained weights, preprocessed data, and the exact evaluation splits are publicly released.

Figures & tables

Figure 1 : Overview of the SimCortex v2 pipeline. A T1w MRI is mapped to a common MNI152 space and passed to a 9-class segmentation network. The predicted anatomical labels are used to construct topology-corrected signed distance fields, from which subject-specific WM and pial initial surfaces and a cortical ribbon probability map are derived. A ribbon-conditioned deformation module then predicts multi-scale stationary velocity fields and jointly refines the four cortical surfaces in a shared deformation space.

Figure 2 : Volumetric segmentation network. The preprocessed T1w image is processed by a 3D U-Net encoder with four stride-2 downsampling stages, bottlenecked at $1/16$ resolution. Decoder stages upsample and fuse skip connections from each encoder level before a final classification head predicts voxel-wise logits over nine anatomical classes.

Figure 3 : Ribbon-conditioned deformation architecture. The preprocessed T1w image and cortical ribbon probability map are processed by separate encoders. Multi-scale features are fused through gated projections and decoded into stationary velocity fields, which are integrated by scaling and squaring and applied sequentially to the concatenated vertices of the four initialized cortical surfaces.

Dataset	Total subjects	Age range	Subjects used	Population	Scanner
CNP (ds000030)	272	21–50	40	Healthy / ADHD / Bipolar / Schizophrenia	Siemens Magnetom TrioTim 3T
ds000115	99	11–30	40	Healthy / Schizophrenia	Siemens Magnetom TrioTim 3T
ds000144	45	6–10	40	Anxious children	GE Discovery MR750 / Signa Excite
ds001486	195	8–15	40	Healthy	Siemens Magnetom TrioTim 3T
ds001748	62	10–35	40	Healthy	Siemens Magnetom TrioTim / Prisma 3T
ds002424	79	8–12	40	Healthy / ADHD	Siemens Magnetom TrioTim 3T

Table 1 : External datasets used exclusively for testing. Forty eligible subjects were randomly selected from each dataset for evaluation in this study.

Parameter	Value	Parameter	Value
Preprocessing		Deformation network
N4 shrink / spline	4 / 200	Input	$184\times 224\times 184$ , 2 ch.
Registration	affine to MNI152 1 mm	MRI encoder widths	$[8,16,32,64,128,128]$
Reference grid	$182\times 218\times 182$	Ribbon ratio $\rho$ / depth	0.5 / 6
Surface initialization		Norm / activation	GroupNorm / LeakyReLU(0.2)
Dilation gap $g$	1 voxel	Dropout	0.1 (3 enc., 2 dec.)

Table 2: Preprocessing, surface initialization, and training hyperparameters. Loss-weight superscripts (

0

) denote target weights reached after a 25-epoch linear warm-up of all non-Chamfer terms.

Class	Region	FreeSurfer aparc+aseg labels
0	Background / non-target tissue	all labels not listed below
1	Left inner cerebrum / WM	2, 5, 10, 11, 12, 13, 26, 28, 30, 31 (+77/80 if left)
2	Right inner cerebrum / WM	41, 44, 49, 50, 51, 52, 58, 60, 62, 63 (+77/80 if right)
3	Left cortical ribbon	3, 1000–1003, 1005–1035
4	Right cortical ribbon	42, 2000–2003, 2005–2035
5	Left hippocampus–amygdala	17, 18

Table 3 : Mapping from FreeSurfer aparc+aseg labels to the nine segmentation classes used by SimCortex v2. Voxels whose label is not listed are assigned to background. FreeSurfer WM hypointensity labels 77 and 80 carry no hemisphere and are split into the left (class 1) or right (class 2) inner-cerebrum class using filled.mgz (255

\rightarrow

left, 127

\rightarrow

right).

Method	ASSD (mm)	HD90 (mm)	Chamfer (mm)	Thickness abs. err. (mm)	SIF (%)	Coll union (%)	Coll (%)
V2C - Flow	$\underline{0.255\pm 0.095}$	$\underline{0.600\pm 0.290}$	$\underline{0.534\pm 0.082}$	$\mathbf{0.105\pm 0.065}$	$2.843\pm 0.890$	$1.423\pm 0.171$	$100.00$
CFPP	$0.358\pm 0.189$	$0.837\pm 0.612$	$0.621\pm 0.173$	$0.219\pm 0.158$	$0.343\pm 0.265$	$0.944\pm 0.208$	$100.00$
CF	$0.435\pm 0.144$	$1.070\pm 0.558$	$0.670\pm 0.132$	$0.271\pm 0.156$	$0.770\pm 0.298$	$\underline{0.762\pm 0.143}$	$100.00$
V2C	$0.482\pm 0.155$	$1.245\pm 0.516$	$0.699\pm 0.142$	$0.400\pm 0.170$	$1.116\pm 0.533$	$0.910\pm 0.091$	$100.00$
CortexODE	$1.124\pm 1.570$	$3.663\pm 6.052$	$1.346\pm 1.548$	$0.296\pm 0.255$	$0.217\pm 0.138$	$1.403\pm 0.796$	$100.00$
FreeSurfer	–	–	–	–	$\mathbf{0.003\pm 0.004}$	$6.667\pm 0.584$	$100.00$

Table 4 : Overall cortical surface reconstruction performance across 560 evaluation cases. Continuous metrics are reported as mean

\pm

SD and lower values are better. Coll (%) is the percentage of cases with at least one union collision. Union collision is the mean, over the four cortical surfaces, of the percentage of each surface’s faces that intersect any of the other three surfaces, with intersections evaluated across all six surface pairs. Because the FreeSurfer surfaces serve as the silver-standard reference for surface-distance and thickness metrics, FreeSurfer is not included in those comparisons; its SIF and collision values describe the intrinsic geometric validity of the reference surfaces themselves. Best results are in bold and second-best results are underlined.

Figure 4 : Distributions of ASSD for SimCortex v2 against each competing learning-based method. Each column shows a paired comparison over the same 560 evaluation cases: the left half of each violin represents SimCortex v2 and the right half represents the competing method indicated on the horizontal axis. Inner boxes show the median and interquartile range, and black dots indicate the means. Columns are ordered by the competing method’s median ASSD. For visual readability, the displayed range is clipped to the 0.5th–99.5th percentiles of the pooled plotted values; clipping affects visualization only, and all summary statistics shown in the figure are computed from the full, unclipped data. Lower ASSD values are better.

Method	Surface generation inference (s)	End-to-end reconstruction (s)
V2C - Flow	$6.792\pm 0.155$	$138.259\pm 26.927$
CFPP	$3.491\pm 0.135$	$140.536\pm 29.644$
CF	$5.386\pm 0.047$	$162.448\pm 22.419$
V2C	$\underline{0.685\pm 0.016}$	$\underline{133.994\pm 21.164}$
CortexODE	$0.784\pm 0.102$	$\mathbf{24.150\pm 0.829}$
SimCortex v2	$\mathbf{0.594\pm 0.005}$	$174.248\pm 18.746$

Table 5 : Runtime comparison across 28 cases comprising two subjects from each of the 14 evaluation datasets. Values are mean

\pm

SD in seconds and correspond to generation of all four cortical surfaces. Surface-generation inference measures the GPU-synchronized model computation required to generate all four cortical surfaces from model-ready inputs. End-to-end reconstruction measures total time through each method’s required preprocessing and reconstruction pipeline to the four final surfaces. Benchmarks were run on one NVIDIA RTX A6000 GPU (48 GB) on a workstation with an Intel Xeon Gold 5218R CPU at 2.10 GHz (20 cores/40 threads) and 128 GiB RAM. Best results are shown in bold and second-best results are underlined.

	V2C - Flow		CFPP		CF		V2C		CortexODE		FreeSurfer		SimCortex v2
Dataset	ASSD	Coll.	ASSD	Coll.	ASSD	Coll.	ASSD	Coll.	ASSD	Coll.	ASSD	Coll.	ASSD	Coll.
cnp	$\mathbf{0.188}$	1.409	0.244	0.838	0.324	$\underline{0.713}$	0.407	0.900	0.504	1.606	–	6.770	$\underline{0.218}$	$\mathbf{0}$
ds000115	$\mathbf{0.185}$	1.340	0.225	0.746	0.311	$\underline{0.615}$	0.357	0.901	0.490	1.219	–	6.754	$\underline{0.206}$	$\mathbf{0}$
ds000144	$\mathbf{0.274}$	1.362	0.295	0.962	0.451	$\underline{0.855}$	0.513	0.889	0.982	1.301	–	6.397	$\underline{0.282}$	$\mathbf{5.09\times 10^{-5}}$
ds001486	$\underline{0.294}$	1.511	0.325	0.816	0.422	$\underline{0.671}$	0.469	0.908	0.929	2.028	–	6.865	$\mathbf{0.287}$	$\mathbf{2.98\times 10^{-5}}$
ds001748	$\mathbf{0.233}$	1.365	0.253	0.944	0.387	$\underline{0.758}$	0.425	0.983	0.653	0.854	–	6.548	$\underline{0.244}$	$\mathbf{9.76\times 10^{-5}}$

Table 6 : ASSD and union collision percentage for each method per dataset. For each case, ASSD is averaged across the four cortical surfaces, and union collision is the mean of the four per-surface union collision percentages. Dataset-level values are averaged over 40 cases. The out of domain ( OOD overall ) row pools the 520 cases from the 13 external datasets, whereas the in distribution ID overall row contains the 40 held-out HCP-YA/OASIS-1 cases in hcp_oasis . FreeSurfer provides the reference surfaces for ASSD and is therefore excluded from the ASSD comparison. Lower values are better for both metrics. Best and second-best values are shown in bold and underlined, respectively. Very small nonzero collision percentages are reported in scientific notation.

	L WM		L Pial
Method	ASSD (mm)	Coll. (%)	ASSD (mm)	Coll. (%)
V2C - Flow	$\mathbf{0.206\pm 0.085}$	$1.295\pm 0.167$	$\underline{0.296\pm 0.097}$	$1.580\pm 0.228$
CFPP	$0.277\pm 0.147$	$0.804\pm 0.196$	$0.388\pm 0.198$	$1.011\pm 0.226$
CF	$0.351\pm 0.129$	$\underline{0.643\pm 0.127}$	$0.512\pm 0.215$	$\underline{0.753\pm 0.151}$
V2C	$0.347\pm 0.093$	$0.973\pm 0.113$	$0.626\pm 0.248$	$0.755\pm 0.118$
CortexODE	$0.878\pm 1.644$	$1.128\pm 0.639$	$1.111\pm 1.561$	$1.310\pm 0.641$

Table 7 : ASSD and union collision percentage for each surface type across 560 evaluation cases (mean

\pm

SD; lower is better). For each surface, the collision percentage reflects its union of overlaps with the other three cortical surfaces. FreeSurfer, used as the reference for ASSD, is excluded from that comparison. L and R denote left and right hemispheres. Best results are in bold; second-best are underlined.

Figure 5 : Distributions of ASSD for SimCortex v2 and the five competing learning-based methods. Within each competitor group, the four columns correspond to the left WM (LW), left pial (LP), right WM (RW), and right pial (RP) surfaces. Each split violin represents a paired comparison over the same 560 evaluation cases: the left half (green) shows SimCortex v2 and the right half shows the competing method. Inner boxes indicate the median and interquartile range, and black dots indicate arithmetic means computed in the original metric units. The vertical axis is logarithmic to accommodate the larger ASSD range of CortexODE while preserving visibility of the distributions of the other methods. Lower ASSD is better.

	V2C - Flow		CFPP		CF		V2C		CortexODE		FreeSurfer		SimCortex v2
Dataset	ASSD	SIF	ASSD	SIF	ASSD	SIF	ASSD	SIF	ASSD	SIF	ASSD	SIF	ASSD	SIF
cnp	$\mathbf{0.188}$	2.111	0.244	0.253	0.324	0.629	0.407	0.662	0.504	0.290	–	$\mathbf{0.002}$	$\underline{0.218}$	$\underline{0.041}$
ds000115	$\mathbf{0.185}$	2.396	0.225	0.221	0.311	0.651	0.357	0.861	0.490	0.163	–	$\mathbf{0.001}$	$\underline{0.206}$	$\underline{0.039}$
ds000144	$\mathbf{0.274}$	2.923	0.295	0.384	0.451	0.977	0.513	1.546	0.982	0.166	–	$\mathbf{0.008}$	$\underline{0.282}$	$\underline{0.054}$
ds001486	$\underline{0.294}$	3.488	0.325	0.442	0.422	0.824	0.469	1.454	0.929	0.250	–	$\mathbf{0.004}$	$\mathbf{0.287}$	$\underline{0.052}$
ds001748	$\mathbf{0.233}$	2.177	0.253	0.122	0.387	0.578	0.425	0.890	0.653	0.140	–	$\mathbf{0.001}$	$\underline{0.244}$	$\underline{0.035}$

Table 8 : ASSD and SIF for each method per dataset. For each case, both metrics are averaged across the four cortical surfaces and then averaged across cases within each dataset. The out of domain OOD overall row pools the 520 cases from the 13 external datasets, whereas the in distribution ID overall row contains the 40 held-out HCP-YA/OASIS-1 cases in hcp_oasis . Because the FreeSurfer surfaces serve as the reference for ASSD, a FreeSurfer ASSD value is not reported. Lower values are better for both metrics. Best and second-best values are shown in bold and underlined, respectively.

Panel of Figure 6 — Figure 6 : Joint distributions of reconstruction accuracy and geometric validity across the six learning-based methods, with 560 cases per method. (a) ASSD versus union collision percentage. (b) ASSD versus SIF. Small markers represent individual cases, large markers indicate method means, and contours enclose 80% of each method’s cases; marginal densities are shown along the corresponding axes. The ASSD axis and the positive-valued collision and SIF axes are shown on logarithmic scales, with densities and contours fitted in log space. In panel (a), union collision is exactly zero for 92.14% of SimCortex v2 cases and for no case of any competing method. Because zero values cannot be represented on a logarithmic axis, collision-free cases are shown separately in the shaded band at the bottom of the panel. No density contour is drawn for SimCortex v2 in panel (a) because its collision distribution is dominated by the mass at exactly zero; for the same reason, its mean collision percentage lies below its smallest non-zero case. Together, the two panels show that similar surface-distance accuracy can be associated with markedly different geometric validity. Lower values are better for all metrics.

Panel of Figure 7 — Figure 7 : Qualitative comparison of cortical surface reconstruction in a complex, highly folded cortical region for a randomly selected evaluation subject. The colored contours show the pial and white cortical surfaces on the displayed MRI slice. In every panel, SimCortex v2 is shown in black and the FreeSurfer reference in yellow; the remaining colored contour corresponds to the comparison method named above the panel. All panels show the same anatomical location and field of view, allowing visual comparison of surface localization in deep sulcal regions.

Panel of Figure 8 — Figure 8 : Qualitative examples of left–right pial-surface collisions for the same randomly selected evaluation subject. Each top-row panel shows the pial and white surface contours produced by the indicated method, zoomed around a location where the left and right pial surfaces intersect; red arrows indicate the selected collision points. The bottom row shows the corresponding SimCortex v2 reconstruction at the exact same anatomical location and field of view. In the SimCortex v2 reconstructions, the corresponding left and right pial surfaces remain separated.

Variant	ASSD (mm)	HD90 (mm)	Chamfer (mm)	SIF (%)	Union collision (%)	Coll. (%)
SimCortex v2 (full)	$0.253\pm 0.067$	$0.586\pm 0.228$	$0.529\pm 0.060$	$0.044\pm 0.014$	$9.04\times 10^{-5}\pm 6.47\times 10^{-4}$	$7.86$
Remove architectural components
Dedicated ribbon encoder and gated fusion	$0.273\pm 0.079$	$0.639\pm 0.253$	$0.541\pm 0.069$	$0.038\pm 0.013$	$4.41\times 10^{-5}\pm 2.08\times 10^{-4}$	$5.71$
$\Delta$	$+0.020$	$+0.053$	$+0.012$	$-0.006$	$-4.63\times 10^{-5}$	$-2.15$
Residual, normalized backbone	$0.313\pm 0.062$	$0.715\pm 0.211$	$0.568\pm 0.058$	$0.034\pm 0.013$	$1.77\times 10^{-5}\pm 1.20\times 10^{-4}$	$2.68$
$\Delta$	$+0.060$	$+0.129$	$+0.039$	$-0.010$	$-7.27\times 10^{-5}$	$-5.18$

Table 9 : Ablation results across the 560 evaluation cases. The full model is the reference; each block below removes one or more component from it and reports the resulting change (

\Delta

, ablated minus full). Values are mean

\pm

SD across cases, except the collision rate. Lower values are better for all metrics, so a positive

\Delta

indicates a loss. Deltas are computed from unrounded values. Because the variants are diagnostic probes rather than competing methods, no best-in-column marking is used; the accuracy–validity tradeoff visible among the architectural variants is discussed in Section 5.2 .

Figure 9 : Case-level relationship between reconstruction accuracy and geometric validity for the SimCortex v2 ablation variants across the 560 evaluation cases. Columns compare the full model with, from left to right, the Vanilla U-Net, early-fusion residual, shallow dual-encoder, MRI-only (without ribbon probability), and no-separation/nesting variants. The top row shows ASSD versus self-intersecting-face percentage (SIF), and the bottom row shows ASSD versus union inter-surface collision percentage. Gray points represent SimCortex v2 and colored points represent the corresponding ablated variant; large markers indicate arithmetic means. In the SIF panels, black and colored contours enclose 80% of the cases for the full and ablated models, respectively. ASSD, SIF, and positive-valued collision measurements are displayed on logarithmic scales. Because exact zero collision cannot be represented on a logarithmic axis, collision-free cases are shown separately in the shaded bands in the bottom row. The first three columns group architectural ablations, whereas the final two columns examine removal of the ribbon input and the separation/nesting losses. Lower values are better for all displayed metrics.

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