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Table 1 Table of terms

From: A fully-automatic caudate nucleus segmentation of brain MRI: Application in volumetric analysis of pediatric attention-deficit/hyperactivity disorder

Ω(L p , L q )

Pulse function.

δ

Trade off coefficient between U and B.

k

Substraction of graylevel for a pair of bins in C c×r .

x 2 x 2

First and second derivatives w.r.t. x.

θ {p, q}

Angle between minimum gradient variation vectors in pixel p and q.

α, σ and β

Weight parameters of boundary term.

|·|

Cardinal of a set.

C,B

Sets of caudate and background seeds.

C c×r

Correlogram structure of c circles and r radius.

d p

Correlogram descriptor for pixel p.

d(·,·)

Minimum Euclidean distance between two sets of voxels.

Dilat e k d ( . )

Dilatation function of structure element of k d pixels.

E(·), U(·), B(·)

Cost function, Unary term, and Boundary term.

Erod e k e ( . )

Erosion function of structure element of k e pixels.

G=<V,E>

Graph of nodes V and edges ε .

G and ℓ

The 2-dimensional Gaussian function and the Lindeberg parameter.

H(·)

Entropy value.

I and I p

Grayscale image and image intensity value at pixel p.

J p, γ, s

Binary edge map of pixel p at scale s and with sensitivity edge threshold γ.

L= L 1 , . . . , L p , . . . , L | P |

Binary vectors of assignments to pixels pP.

N

Set of unordered pairs {p, q} of neighboring pixels under a 4-(8-) neighborhood system.

N {p, q}, O {p, q}

Boundary terms based on first and second derivatives.

P= 1 , . . . , p , . . . , | P |

Set of indexes of I.

Pu(·), Ps(·)

Unsupervised and supervised probability function.

P(·)

General frequency-based Probability function.

{p, q}

n-link connecting a pair of neighbors p and q.

R 0

Region of Interest (ROI).

R p (s)

Neighborhood of size s × s.

S, T

Caudate and Background terminal nodes.

SVM(.)

Support Vector Machines classifier function.

T p

Atlas-based threshold over probability map.

UU(·), SU(·)

Unsupervised and supervised unary terms.

X= x 1 , . . . , x p , . . . , x | P |

Set of pixels of I.