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Automatic Labeling of the Human Cerebral CortexBT Thomas Yeo, National University of Singapore, Singapore, Singapore; Duke-NUS Graduate Medical School, Singapore,Singapore; Massachusetts General Hospital, Charlestown, MA, USA

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Bra

Glossary‘fsaverage’ Subject FreeSurfer subject (Figure 1b and 1c)

obtained by averaging 40 subjects. This average subject

forms the basis of the FreeSurfer surface coordinate system

(Fischl, 2012).

Graphical Models The different algorithms in this article

can be summarized using graphical models. Graphical

models provide a general framework for representing

complex probabilistic models with explicit (conditional)

independence assumptions. See Figure 2 and ‘Summary’

section for more details.

Markov Random Field Markov Random Fields (MRFs)

provides a principal approach to impose a prior on the

spatial configuration of labels. One common prior is to

favor adjacent spatial locations to have the same labels. See

‘Spatially Dependent Priors: Markov Random Fields’

section for more details.

Mixture Models Registration-based labeling assumes the

availability of pre-existing labels. By contrast, mixture

modeling only requires that each label generate its own

unique image features. Given observed image features, there

are algorithms (e.g., Expectation-Maximization) that

simultaneously estimate the labels and the probabilistic

distribution of image features for each label. See ‘Mixture

Models’ section for more details.

MNI152 Template The International Consortium on Brain

Mapping (ICBM) average brain obtained by aligning and

averaging 152 subjects (Fonov et al., 2011).

Registration-based Labeling Registration is the process of

establishing spatial correspondences between images. The

resulting deformation can be used to transfer pre-existing

labels from an (single-subject or probabilistic) atlas to the

target brain. See ‘Registration-based Labeling’ section for

more details.

in Mapping: An Encyclopedic Reference http://dx.doi.org/10.1016/B978-0-12-39

Brain Mapping: An Encyclopedic Refere

Organization of the Cerebral Cortex

The human cerebral cortex is a highly folded 2D sheet of neural

tissue that possesses a mosaic of functionally distinct areas

oriented parallel to its surface (Figure 1). Information proces-

sing proceeds via the transformation of neural signals across

these areas (Felleman & Van Essen, 1991; Ungerleider &

Desimone, 1986). Accurate labeling of areal locations is there-

fore an important problem in systems neuroscience. There are

four main criteria for distinguishing cortical areas (Felleman &

Van Essen, 1991; Kaas, 1987): function, architectonics,

connectivity, and topography. Each of these criteria can be

interrogated in the human cerebral cortex using a broad

range of techniques (Figure 1).

Because (1) cortical folds are visible to the naked eye and in

anatomical Magnetic Resonance Imaging (MRI) and (2) some

cortical folds are indicative of certain underlying cortical areas

(Fischl et al., 2008; Van Essen, Glasser, Dierker, Harwell, &

Coalson, 2012; Yeo, Sabuncu, Vercauteren, Holt, et al.,

2010b), cortical folds are often used as macroanatomical

landmarks for comparison of results across brain imaging

studies. Consequently, methods that can accurately label cor-

tical folds across different subjects are important for studying

the human brain (Figure 1). The many types of cortical label-

ing criteria and data modalities are matched by the myriad of

published algorithms for estimating the labels. A comprehen-

sive survey is outside the scope of this article. Instead, we will

focus on a few popular approaches that have been effective

across multiple types of cortical labeling criteria and imaging

modalities.

Registration-Based Labeling

Suppose we want to label the cerebral cortex in a given brain

image (henceforth, referred to as target). The target brain could

be an image acquired from an individual subject or a model

that represents the population, for example, a template

obtained by averaging the brain images of multiple subjects.

The MNI152 template and FreeSurfer ‘fsaverage’ subject are

examples of the latter case. Assuming the existence of a brain

atlas containing the labels of interests, one simple strategy is to

employ an image registration algorithm to spatially align the

target image and the atlas and then use the registration result to

transfer the labels from the atlas coordinates to the target image

coordinates (Christensen, Joshi, & Miller, 1997; Collins,

Holmes, Peters, & Evans, 1995; Miller, Christensen, Amit, &

Grenander, 1993; Thompson & Toga, 1996).

Single-Subject Atlas

In the simplest case, the atlas can be the labeled brain of a single

subject. This strategy has been used to transfer labels of cortical

folds or other macroanatomical brain structures from one

labeled subject to another (Lancaster et al., 2000; Sandor &

Leahy, 1997; Shen & Davatzikos, 2002; Tzourio-Mazoyer et al.,

2002). Cortical areas defined using architectonics can be trans-

ferred between histological slices and the MRI anatomical scan

of the same subject (Schormann & Zilles, 1998). Van Essen and

colleagues (Van Essen, 2004; Van Essen et al., 2012) had utilized

this strategy to transfer cortical areas derived from visuotopic

functional Magnetic Resonance Imaging (fMRI), task-based

7025-1.00306-7 357nce, (2015), vol. 1, pp. 357-363

http://dx.doi.org/10.1016/B978-0-12-397025-1.00306-7

0.2 1.0

7.6 12.5

(d)

(b)

(e)

(c)

(a)

hOc5Area 45

Area 2Area 6

Figure 1 Different types of cortical labels. (a) Cortical labels based on macroanatomy. Gyral-based regions of interest were labeled in a training set of 40subjects (Desikan et al., 2006), which were then used to train a Markov random field (MRF) classifier for labeling a new subject (Fischl et al., 2004)from the OASIS (Marcus et al., 2007) dataset. Section ‘Fusion of Registration-Based Labeling and Mixture Models’ discusses this general approach.(b) Cortical label based on cortical function. The cortical label was estimated from an automated ‘forward inference’ meta-analysis of the term ‘MT’ in MNIspace (Yarkoni, Poldrack, Nichols, Van Essen, & Wager, 2011) and projected to FreeSurfer (Fischl, 2012) ‘fsaverage’ surface space usinga nonlinear transformation estimated from 1000 subjects (Buckner, Krienen, Castellanos, Diaz, & Yeo, 2011). A high value indicates high likelihood thatstudies associated with the motion-sensitive area MT report activations at that spatial location. (c) Cortical labels based on architectonics. Areas 2 (Grefkes,Geyer, Schormann, Roland, & Zilles, 2001), 6 (Geyer, 2004), 45 (Amunts et al., 1999), and hOc5 (Malikovic et al., 2007) were delineated in ten postmortembrains based on observer-independent cytoarchitectonic analysis. These areas weremapped onto the FreeSurfer ‘fsaverage’ space to create prior probabilitymaps of different cytoarchitectonic areas (Fischl et al., 2008; Yeo et al., 2010b). Area hOc5may correspond to the region in (b). Section ‘Registration-BasedLabeling’ discusses this registration-based labeling approach. (d) Cortical labels based on resting-state functional connectivity MRI. Connectivity profiles ofevery vertex across both cerebral hemispheres of 1000 subjects were computed and averaged in FreeSurfer ‘fsaverage’ surface space. The averaged profileswere modeled with a mixture of von Mises–Fisher distributions and clustered into networks of regions with similar patterns of connectivity (Yeo et al.,2011). The resulting parcelation was projected to Caret (Van Essen & Dierker, 2007) ‘PALS-B12’ surface space for visualization. Section ‘Mixture Models’discusses this general approach. (e) Cortical labels based on functional topography. Topography of visual areas in a single subject was interrogated usingphase-encoded retinotopic mapping with a rotating angular wedge visual stimuli and spectral analysis (Adapted from Swisher, J.D., Halko, M.A., Merabet,L.B., McMains, S.A., & Somers, D.C. (2007). Visual topography of human intraparietal sulcus. The Journal of Neuroscience 27, 5326–5337). Red representsthe upper visual meridian, blue represents the contralateral horizontal meridian, and green represents the lower meridian.

358 INTRODUCTION TO METHODS AND MODELING | Automatic Labeling of the Human Cerebral Cortex


fMRI, or histology of individual subjects to the cortical mantle of

an average subject. This strategy can even be used to warp the

cortical areas of the macaque monkey to an average human

subject for comparative neuroanatomy (Orban, Van Essen, &

Vanduffel, 2004; Van Essen & Dierker, 2007).

Multisubject or Population Atlas

Using a brain atlas comprising a single subject is problematic

because macroanatomical registration cannot perfectly align

the cortical labels of the atlas and those of the target brain.

One reason is the high intersubject variability in cortical fold-

ing (Ono, Kubik, Abernathey, et al., 1990; Zilles, Armstrong,

Schleicher, & Kretschmann, 1988), so that the correct corre-

spondence is sometimes unclear even to a neuroanatomist.

Furthermore, macroanatomical features cannot fully predict

many cortical areas of interest (Amunts et al., 1999; Rajkowska

& Goldman-Rakic, 1995). This is especially problematic for

higher-order cortical areas (e.g., MTþ and Broca’s areas) com-

pared with lower-order areas, such as V1, whose alignment

accuracy can be as good as 2–3 mm using surface-based

Brain Mapping: An Encyclopedic Referen

registration (Fischl et al., 2008; Hinds et al., 2008; Yeo,

Sabuncu, Vercauteren, Ayache, et al., 2010a).

Consequently, a more accurate approach should reflect this

residual spatial variability in cortical areas after image registra-

tion. Given a training set of subjects with ‘ground-truth’ labels,

we can register the subjects to the atlas and estimate the prior

probability of a cortical label at every spatial location. A target

subject that has been registered into atlas space inherits this

prior probability (Evans, Kamber, Collins, & MacDonald,

1994; Mazziotta et al., 1995).

This strategy has been used to compute a probabilistic

labeling of cortical folds (Collins, Zijdenbos, Baare, & Evans,

1999; Shattuck et al., 2008; Smith et al., 2004) and cortical

areas based on architectonics (Amunts et al., 1999; Eickhoff

et al., 2005; Fischl et al., 2008; Van Essen et al., 2012).

Mixture Models

The registration-based approach (Section ‘Registration-Based

Labeling’) assumes the availability of other labeled subjects.

ce, (2015), vol. 1, pp. 357-363

INTRODUCTION TO METHODS AND MODELING | Automatic Labeling of the Human Cerebral Cortex 359


However, in many situations, an atlas with prior information

might not be available. Therefore, an orthogonal approach is

to directly model the relationship between image features and

cortical labels in the absence of previously labeled training

subjects.

More formally, suppose there are N cortical locations. Let

x¼{xn} denote the set of cortical locations: n2{1, . . .,N}. Let

y¼{yn} and L¼{Ln} denote the image features and cortical

labels, respectively, at locations {xn}. We assume there are K

cortical labels of interest, so Ln2{1, . . .,K}. Our goal is to

estimate L.

One common approach is to assume the observed features

{yn} are generated from a mixture model. In particular, the

model assumes each cortical label Ln is independently drawn

from a probability distribution, that is, p(L)¼Pnp(Ln). This is a

key difference with Section ‘Multisubject or Population Atlas,’

where the prior came from the training data. Assuming identi-

cal distributions across spatial locations, p(Ln) is parameterized

by the vector m ¼ m1; . . . ;mK½ �;Pk mk ¼ 1.

Conditioned on the cortical label Ln at spatial location xn,

the observed features yn are assumed to be generated from the

distribution p(yn|Ln). We assume that p(yn|Ln) is parameterized

by y¼{y1, . . .,yK}. For example, if p(yn|Ln) is a Gaussian distri-

bution, then yk might correspond to the mean and variance of

the k-th Gaussian distribution and the entire model is known

as a Gaussian mixture model.

A common way to solve for L is to maximize the likelihood

or posterior probability of the parameters m and y assuming the

observation of the image features y. This can be achieved via

numerical optimization schemes, such as the expectation–

maximization (EM) algorithm (Dempster, Laird, & Rubin,

1977). These types of methods essentially perform a data-

driven clustering and thus identify clusters of voxels or vertices

that are assigned a label. The well-known k-means clustering

algorithm (MacQueen et al., 1967) can be interpreted as a

special case of this mixture modeling approach.

This clustering (mixture model or k-means) strategy was

used for the segmentation of different tissue types in anatom-

ical MRI data (Kapur, Grimson, Wells, & Kikinis, 1996; Teo,

Sapiro, & Wandell, 1997; Wells, Grimson, Kikinis, & Jolesz,

1996). The same approach has been applied to cortical labels

based on task-based fMRI (Flandin, Kherif, Pennec,

Malandain, et al., 2002; Flandin, Kherif, Pennec, Riviere,

et al., 2002; Goutte, Toft, Rostrup, Nielsen, & Hansen, 1999;

Penny & Friston, 2003), connectivity measured by diffusion

MRI (Anwander, Tittgemeyer, von Cramon, Friederici, &

Knosche, 2007; Beckmann, Johansen-Berg, & Rushworth,

2009; Klein et al., 2007; Mars et al., 2011; Nanetti, Cerliani,

Gazzola, Renken, & Keysers, 2009; Tomassini et al., 2007),

connectivity measured by resting-state fMRI (Bellec, Rosa-

Neto, Lyttelton, Benali, & Evans, 2010; Cauda et al., 2011;

Chang, Yarkoni, Khaw, & Sanfey, 2013; Deen, Pitskel, &

Pelphrey, 2011; Golland, Golland, Bentin, & Malach, 2008;

Kahnt, Chang, Park, Heinzle, & Haynes, 2012; Kelly et al.,

2012; Kim et al., 2010; Yeo et al., 2011), and activation coor-

dinates from meta-analysis of functional studies (Cauda et al.,

2012; Kelly et al., 2012).

In the context of cortical labeling, other popular clustering

approaches in the neuroimaging literature include hierarchical

clustering (Bellec et al., 2010; Cauda et al., 2011; Cieslik et al.,


2012; Eickhoff et al., 2011; Kelly et al., 2012), spectral cluster-

ing (Craddock, James, Holtzheimer, Hu, & Mayberg, 2012;

Thirion et al., 2006; van den Heuvel, Mandl, & Pol, 2008),

and fuzzy clustering (Cauda et al., 2011; Lee et al., 2012).

Unlike mixture modeling, these approaches do not enjoy a

simple generative modeling interpretation.

Fusion of Registration-Based Labeling and MixtureModels

In Section ‘Mixture Models,’ we assumed simple forms of the

prior p(L|m) and likelihood p(yn|Ln,y), which we estimated

from the subjects we are labeling, using the EM algorithm. In

this section, we consider more complex priors p(L|m) and

likelihood p(yn|Ln,y).

Spatially Varying, Spatially Independent Priors

In Section ‘Mixture Models,’ we assumed p(L|m) to be param-

eterized by the vector m¼ [m1, . . .,mK], whereP

kmk¼1. There-

fore, such a model assumes that the prior probability of

observing different label classes is the same throughout the

cortex. However, we can reasonably expect this prior probabil-

ity to vary across the brain (e.g., Figure 1(c)). Therefore, a

spatially varying prior probability of observing different corti-

cal labels can constrain and improve the cortical labeling.

As discussed in Section ‘Multisubject or Population Atlas,’

we can obtain a prior for our target brain by registering to an

atlas constructed from other subjects that have been labeled. In

this case, m becomes a function of spatial location xn, so that if

we also assume spatial independence, we get

p Ljmð Þ ¼Y

np Lnjm xnð Þð Þ ¼

YnmLn xnð Þ [1]

where mLn xnð Þ is the prior probability of observing label Ln at

spatial location xn;P

kmk(xn)¼1 for all locations {xn}.

Spatially Dependent Priors: Markov Random Fields

In Section ‘Spatially Varying, Spatially Independent Priors,’

we assumed the prior probability of cortical labels to be inde-

pendent across spatial locations. However, for many cortical

labels, the number of spatial locations along their boundaries

is significantly less than the number of spatial locations within

the labels. In other words, adjacent spatial locations are more

likely to have the same label than different labels. As another

example, we might expect adjacent vertices along the fundus of

a sulcus are more likely to have the same sulcal labels (Fischl

et al., 2004).

We can impose this kind of neighborhood spatial prior

using Markov random field (MRF) theory (Dobruschin,

1968; Spitzer, 1971). In an MRF, the labels L¼{Ln} are related

to each other within a neighborhood system

N ¼ N xn , xn 2 xf g where N xn are the neighboring locations

of xn, xn=2N xn and xn 2 N xm , xm 2 N xn :

In the brain imaging context, the neighborhood N of a

location xn is often the surrounding voxels (Fischl et al.,

2002; Held et al., 1997; Van Leemput, Maes, Vandermeulen,

& Suetens, 1999; Zhang, Brady, & Smith, 2001) or vertices

nce, (2015), vol. 1, pp. 357-363



(Fischl et al., 2004; Yeo, Sabuncu, Desikan, Fischl, & Golland,

2008). Furthermore, the following simple MRF model is com-

monly used:

p Lð Þ ¼ 1

Z Uð Þ exp ð�U Lð ÞÞ [2]

where Z(U) ensures p(L) is a valid probability distribution and

U(L) is an energy function of the form

U Lð Þ ¼X

nW Lnð Þ þ

Xxn

Xxm2N xn

V Ln; Lmð Þ [3]

and so we can write

p Lð Þ ¼ 1

Z Wð Þ exp �X

nW Lnð Þ

� �

� 1

Z Vð Þ exp �X

xn

Xxm2N xn

V Ln; Lmð Þ� �

[4]

p Lð Þ ¼Y

n

1

Znexp �W Lnð Þð Þ

� 1

Z Vð Þ exp �X

xn

Xxm2N xn

V Ln; Lmð Þ� �

[5]

The local clique potential W is commonly set by equating

1/Znexp(�W(Ln)) with the prior probability mLn xnð Þ from Sec-

tion ‘Spatially Varying, Spatially Independent Priors’ (Fischl

et al., 2002, 2004; Yeo et al., 2008). The clique potentials V can

be estimated from data, such as by iterative proportional fitting

(Jirousek & Preucil, 1995). However, they are often set manu-

ally. For example, setting V(Ln,Lm)¼bd(Ln�Lm) (b>0)

encourages neighboring labels to be the same (Zhang et al.,

2001). Fischl et al. (2004) learned an anisotropic neighbor-

hood potential to reflect the observation that changes in sulcal

or gyral labels are more likely to occur in the direction of

highest surface curvature.

Learning the Likelihood

In Section ‘Mixture Models,’ the parameters y of the likelihoodp(yn|Ln,y) were estimated from the target subjects. When pre-

viously labeled subjects are available, it may be advantageous

to estimate y from these subjects. If p(yn|Ln,y) is a Gaussian

distribution and yk is the mean and variance of the k-th Gauss-

ian distribution, we can estimate yk by the sample mean and

variance of the training subjects.

One major advantage of estimating the likelihood from

training subjects is the possible increase in power to learn a

more complex likelihood p(yn|Ln,y). For example, suppose the

feature yn is the T1-relaxation parameter at the voxel n, then it

mm

qL

L

(a) (b)

Figure 2 Graphical models summarizing approaches in this article. (a) Mod‘Registration-Based Labeling’). (b) Model corresponding to the mixture modto the MRF approach (Section ‘Fusion of Registration-Based Labeling and Mobserved. The arrows indicate conditional dependencies. For example, in (b) aHowever, L and y are no longer independent when conditioned on y.


may be advantageous to learn a spatially varying likelihood

(yn|Ln,y) (Fischl et al., 2002) because T1 relaxation is not

uniform over the gray matter. For example, T1 -relaxation in

the central sulcus is less than the rest of the cortex (Steen,

Reddick, & Ogg, 2000).

As another example, labeling cortical folds using a spatially

constant likelihood of mean curvature feature is ineffective

because the intrasulcal variation in mean curvature is much

larger than between sulci. Consequently, Fischl et al. (2004)

and Yeo et al. (2008) utilized a spatially varying likelihood for

labeling cortical folds.

Inference and Applications to Cortical Labeling

Depending on the applications, the MRF priors (Section

‘Spatially Dependent Priors: Markov Random Fields’) can

be mixed and matched with different priors (Section

‘Spatially Varying, Spatially Independent Priors’) and likeli-

hoods (Section ‘Learning the Likelihood’). Exact inference of

a model that includes an MRF is generally computationally

infeasible. However, approximate inference can be accom-

plished via general classes of approximation algorithms,

including Markov chain Monte Carlo (Robert & Casella,

2004), variational inference (Wainwright & Jordan, 2008),

and graph cuts (Kolmogorov & Zabin, 2004).

The MRF strategy has been applied to labeling cortical folds

(Desikan et al., 2006; Destrieux, Fischl, Anders, & Halgren,

2010; Fischl et al., 2002; Klein & Tourville, 2012; Yeo et al.,

2008) and obtaining cortical labels based on resting-state

fMRI (Ryali, Chen, Supekar, & Menon, 2012) or task-based

fMRI (Rajapakse & Piyaratna, 2001; Svensen, Kruggel, & von

Cramon, 2000; Woolrich & Behrens, 2006).

Summary

The different approaches in this article can be summarized

using graphical models (Figure 2). The conventions follow

that of Wainwright and Jordan (2008). The registration-based

approach (Section ‘Registration-Based Labeling’) has the sim-

plest model (Figure 2(a)), where the labels L only depend on

the prior probabilities m specified by the atlas. Registration is

assumed to be already accomplished so the (implicit) depen-

dency on image features used for registration is not shown. The

mixture modeling approach (Section ‘Mixture Models’) has a

more complex model (Figure 2(b)). The labels L are generated

from the prior m. The features y are then generated conditioned

q

LY

Y

W

V

(c)

el corresponding to the registration-based approach (Sectioneling approach (Section ‘Mixture Models’). (c) Model correspondingixture Models’). The shaded circles indicate that the features Y arend (c), y is conditionally dependent on y and L. L and y are independent.

ce, (2015), vol. 1, pp. 357-363



on the labels L and the likelihood parameters y. Finally, theMRF approach (Section ‘Fusion of Registration-Based Label-

ing and Mixture Models’) can be represented by the model in

Figure 2(c). Here, the local potentials W replace m and the

labels L also depend on the clique potentials V.

The approaches mentioned earlier have been especially

successful for cortical labeling based on macroanatomy, con-

nectivity (diffusion and resting state), architectonics, and func-

tion (meta-analysis of activation coordinates). They are less

popular in task-based fMRI, which generally employs general

linear modeling of the hemodynamic response, and in visuo-

topic mapping, which generally employs spectral or Fourier

techniques.

Other approaches not covered in this article include inde-

pendent component analysis; morphological approaches, such

as edge detection (Cohen et al., 2008; Nelson et al., 2010) and

watershed (Lohmann & von Cramon, 2000; Rettmann, Han,

Xu, & Prince, 2002); and machine learning techniques, such

as discriminative models (Tu et al., 2008), neural networks

(Mangin et al., 2004; Riviere et al., 2002), and label fusion

(Heckemann et al., 2006; Sabuncu, Yeo, Van Leemput, Fischl,

& Golland, 2010).

See also: INTRODUCTION TO ANATOMY AND PHYSIOLOGY:Cytoarchitectonics, Receptorarchitectonics, and Network Topology ofLanguage; Cytoarchitecture and Maps of the Human Cerebral Cortex;Functional Connectivity; Functional Organization of the Primary VisualCortex; Gyrification in the Human Brain; Sulci as Landmarks;Transmitter Receptor Distribution in the Human Brain;INTRODUCTION TO METHODS AND MODELING: Analysis ofVariance (ANOVA); Bayesian Multiple Atlas Deformable Templates;Computational Modeling of Responses in Human Visual Cortex;Contrasts and Inferences; Convolution Models for FMRI; DiffeomorphicImage Registration; Diffusion Tensor Imaging; Effective Connectivity;Fiber Tracking with DWI; Nonlinear Registration Via DisplacementFields; Probability Distribution Functions in Diffusion MRI; Q-SpaceModeling in Diffusion-Weighted MRI; Resting-State FunctionalConnectivity; Reverse Inference; Rigid-Body Registration; SulcusIdentification and Labeling; Surface-Based Morphometry; The GeneralLinear Model; Tissue Classification; Tract Clustering, Labeling, andQuantitative Analysis; INTRODUCTION TO SYSTEMS: FacePerception; Hubs and Pathways; Large-Scale Functional BrainOrganization; Motion Perception; Neural Codes for Shape Perception;Primate Color Vision.

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