Joint Reconstruction and Parcellation of Cortical Surfaces Anne-Marie Rickmann12 Fabian Bongratz2 Sebastian P olsterl1 Ignacio

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Joint Reconstruction and Parcellation of

Cortical Surfaces

Anne-Marie Rickmann1,2∗, Fabian Bongratz2∗, Sebastian P¨olsterl1, Ignacio

Sarasua1,2, and Christian Wachinger1,2

1Ludwig-Maximilians-University, Munich, Germany

2Technical University of Munich, Germany

Lab for Artiﬁcial Intelligence in Medical Imaging

Abstract. The reconstruction of cerebral cortex surfaces from brain

MRI scans is instrumental for the analysis of brain morphology and the

detection of cortical thinning in neurodegenerative diseases like Alzhei-

mer’s disease (AD). Moreover, for a ﬁne-grained analysis of atrophy pat-

terns, the parcellation of the cortical surfaces into individual brain re-

gions is required. For the former task, powerful deep learning approaches,

which provide highly accurate brain surfaces of tissue boundaries from

input MRI scans in seconds, have recently been proposed. However, these

methods do not come with the ability to provide a parcellation of the re-

constructed surfaces. Instead, separate brain-parcellation methods have

been developed, which typically consider the cortical surfaces as given,

often computed beforehand with FreeSurfer. In this work, we propose two

options, one based on a graph classiﬁcation branch and another based on

a novel generic 3D reconstruction loss, to augment template-deformation

algorithms such that the surface meshes directly come with an atlas-

based brain parcellation. By combining both options with two of the lat-

est cortical surface reconstruction algorithms, we attain highly accurate

parcellations with a Dice score of 90.2 (graph classiﬁcation branch) and

90.4 (novel reconstruction loss) together with state-of-the-art surfaces.

1 Introduction

The reconstruction of cerebral cortex surfaces from brain MRI scans remains an

important task for the analysis of brain morphology and the detection of cor-

tical thinning in neurodegenerative diseases like Alzheimer’s disease (AD) [28].

Moreover, an accurate parcellation of the cortex into distinct regions is essen-

tial to understand its inner working principles as it facilitates the location and

the comparison of measurements [13,9]. While voxel-based segmentations are

useful for volumetric measurements of subcortical structures, they are merely

suited to represent the tightly folded and thin (thickness in the range of few

millimeters [24]) geometry of the cerebral cortex.

∗Equal contribution

arXiv:2210.01772v1 [q-bio.NC] 19 Sep 2022

2 Rickmann and Bongratz et al.

The traditional software pipeline FreeSurfer [10], which is commonly used

in brain research, addresses this issue by oﬀering a surface-based analysis in

addition to the voxel-based image processing stream. More precisely, the voxel

stream provides a voxel-based segmentation of the cortex and subcortical struc-

tures, whereas the surface-based stream creates cortical surfaces and a cortex

parcellation on the vertex level. To this end, FreeSurfer registers the surfaces to

a spherical atlas. Cortical thickness can be computed from these surfaces with

sub-millimeter accuracy and diﬀerent regions of the brain can easily be analyzed

given the cortex parcellation. Yet, the applicability of FreeSurfer is limited by

its lengthy runtime (multiple hours per brain scan).

Recently, signiﬁcantly faster deep learning-based approaches for cortical sur-

face reconstruction have been proposed [1,4,20,23]; they reconstruct cortical sur-

faces from an MRI scan within seconds. To date, however, these methods do not

come with the ability to provide a parcellation of the surfaces. At the same

time, recent parcellation methods [5,14] usually rely on FreeSurfer for the ex-

traction of the surface meshes. A notable exception is [15], which, however, is

not competitive in terms of surface accuracy.

In this work, we close this gap by augmenting two state-of-the-art corti-

cal surface reconstruction (CSR) methods [1,20] with two diﬀerent parcellation

approaches in an end-to-end trainable manner. Namely, we extend the CSR net-

works with a graph classiﬁcation network and, as an alternative, we propagate

template parcellation labels through the CSR network via a novel class-based

reconstruction loss. Both approaches are illustrated in Figure 1. We demonstrate

that both approaches yield highly accurate cortex parcellations on top of state-

of-the-art boundary surfaces.

2 Related Work

In the following, we will brieﬂy review previous work related to corical surface

reconstruction and cortex parcellation. While we focus on joint reconstruction

and parcellation, the majority of existing methods solves only one of these two

tasks at a time, i.e., cortex parcellation or cortical surface reconstruction.

Convolutional neural networks (CNNs) remain a popular choice for med-

ical image segmentation and they have been applied successfully to the task

of cortex parcellation. For example, FastSurfer [16] replaces FreeSurfer’s voxel-

based stream by a multi-view 2D CNN. Similar approaches [17,3] have been pro-

posed based on 3D patch-based networks. However, the computation of cortical

biomarkers based on fully-convolutional segmentations is ultimately restricted

by the image resolution of the input MRI scans and the combination with the

FreeSurfer surface stream is not eﬃcient in terms of inference time.

Deep learning-based parcellation methods operating on given surface meshes

(typically pre-computed with FreeSurfer) have also been presented in the past.

For example, the authors of [5] investigate diﬀerent network architectures for the

segmentation of two brain areas. They found that graph convolution-based ap-

proaches are more suited compared to multi-layer perceptrons (MLPs). Similarly,

Joint Reconstruction and Parcellation of Cortical Surfaces 3

Fig. 1. Overview of surface reconstruction networks with our extensions for learning

cortex parcellation. Bottom left: A classiﬁcation network is added after the deformation

network and trained with a classiﬁcation loss on the vertex-wise class predictions.

Right: The deformation network takes surface templates with parcellation labels (from

a population atlas) as input and the reconstruction loss is computed separately for

each class.

the method presented in [8] parcellates the whole cortex using graph attention

networks. In contrast, the authors of [14] utilize spherical graph convolutions,

which they ﬁnd to be more eﬀective than graph convolutions in the Euclidean

domain. All of these vertex classiﬁers consider the surface mesh as given.

To avoid the lengthy runtime of FreeSurfer for surface generation, deep

learning-based surface reconstruction approaches focus on the fast and accurate

generation of cortical surfaces from MRI. These approaches can be grouped into

implicit methods [4], which learn signed distance functions (SDFs) to the white-

to-gray-matter and gray-matter-to-pial interfaces, and explicit methods [1,20],

which directly predict a mesh representation of the surfaces. The disadvan-

tage of implicit surface representations is the need for intricate mesh extrac-

tion, e.g., with marching cubes [21], and topology correction. This kind of post-

processing is time-consuming and can introduce anatomical errors [10]. In con-

trast, Vox2Cortex [1] and CorticalFlow [20] deform a template mesh based on

geometric deep learning. More precisely, Vox2Cortex implements a combina-

tion of convolutional and graph-convolutional neural networks for the template

deformation, whereas CorticalFlow relies on the numerical integration of a de-

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JointReconstructionandParcellationofCorticalSurfacesAnne-MarieRickmann1;2,FabianBongratz2,SebastianPolsterl1,IgnacioSarasua1;2,andChristianWachinger1;21Ludwig-Maximilians-University,Munich,Germany2TechnicalUniversityofMunich,GermanyLabforArticialIntelligenceinMedicalImagingAbstract.Thereconstruc...

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Joint Reconstruction and Parcellation of Cortical Surfaces Anne-Marie Rickmann12 Fabian Bongratz2 Sebastian P olsterl1 Ignacio

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