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Automatic Localization of Anatomical Point Landmarks for Brain

Image Processing Algorithms

Scott C. Neu and Arthur W. Toga

Department of Neurology, UCLA Laboratory of Neuro Imaging, David Geffen School of Medicine,

Suite 225, 635 Charles Young Drive South, Los Angeles, CA 90095-7334, USA

Arthur W. Toga: toga@loni.ucla.edu

Abstract

Many brain image processing algorithms require one or more well-chosen seed points because

they need to be initialized close to an optimal solution. Anatomical point landmarks are useful for

constructing initial conditions for these algorithms because they tend to be highly-visible and

predictably-located points in brain image scans. We introduce an empirical training procedure that

locates user-selected anatomical point landmarks within well-defined precisions using image data

with different resolutions and MRI weightings. Our approach makes no assumptions on the

structural or intensity characteristics of the images and produces results that have no tunable run-

time parameters. We demonstrate the procedure using a Java GUI application (LONI ICE) to

determine the MRI weighting of brain scans and to locate features in T1-weighted and T2-

weighted scans.

Keywords

Anatomical point landmark; Automation; Singular value decomposition; Least-squares; Neural

network; Multi-resolution; Seed points

Introduction

For many brain image processing algorithms, determining a good seed point is crucial. Such

algorithms include snakes and active contours (Kass et al. 1987; Daneels et al. 1993;

McInerney and Dehmeshki 2003), level sets (Sethian 1999), and others (Cox et al. 1996)

which often produce different results when started with different initial conditions. This

occurs because these algorithms typically search out and find local-minima solutions; that is,

in their solution-spaces they evolve towards the minimum that is closest to their starting

point. Software programs that utilize these algorithms must then either require users to

manually select starting points (Meyer and Beucher 1990; MacDonald et al. 1994;

Yushkevich et al. 2006) or incorporate manual interaction into their implementations

(Barrett and Mortensen 1997; Mortensen and Barrett 1995; Falco et al. 1998; Boykov and

Jolly 2001). There are currently many software packages available for brain image

processing that require user intervention to perform image registration, 1 fiber tracking in

diffusion tensor images,2 interactive labeling of sulci,3 image segmentation,4 and visual

© Humana Press 2008

Correspondence to: Arthur W. Toga, toga@loni.ucla.edu.

1http://www.imaging.robarts.ca/Software/register_tutorial/register.html.

2http://www.ia.unc.edu/dev/download/fibertracking/index.htm

3http://www.bic.mni.mcgill.ca/~georges/Seal_Reference/seal_howto.html

NIH Public Access

Author Manuscript

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Published in final edited form as:

Neuroinformatics. 2008 ; 6(2): 135–148. doi:10.1007/s12021-008-9018-x.

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image processing tasks.5 Unfortunately, for large-scale brain studies these semi-automatic

approaches become extremely time-consuming.

Anatomical point landmarks (Rohr 2001) are useful for constructing initial conditions

because they tend to be highly-visible and predictably-located points in image scans. This is

particularly true for brain structures, which appear roughly regular in shape, size, and

location. Current approaches that report on the detection of anatomical point landmarks are

limited to a few well-defined brain landmarks or specific modality, make restrictive

assumptions about image intensity distributions or image structures, and/or require intensive

computational time to execute. In this paper, we describe a method that requires no prior

knowledge of brain structures or assumptions on intensity distributions, and uses an example

set of manually selected anatomical point landmarks to calculate fitting parameters using

singular value decomposition (Kalman 1996). Singular value decomposition is a widely-

used technique in image analysis and has been used in areas such as image compression

(O’Leary and Peleg 1983), digital signal processing (Hansen and Jensen 1998;

Konstantinides and Yovanof 1995; Konstantinides et al. 1997), facial recognition (Sirovich

and Kirby 1987; Turk and Pentland 1991), texture analysis (Chen and Pavlidis 1983; Davis

et al. 1979), image restoration (Huang and Narendra 1974), and watermarking (Gorodetski

et al. 2001; Chandra 2002).

In previous work, differential operators have been applied (Le Briquer et al. 1993; Rohr

1997; Hartkens et al. 2002) to images of the brain to locate prominent points where

anatomical structures are strongly curved. Because this produces multiple points, a

manually-adjusted threshold is usually required to reduce the number of points that do not

coincide with neurologically-recognized point landmarks. The computation of partial

derivatives makes this approach relatively sensitive to image noise and small intensity

variations. Deformable and parametric intensity models have been used to detect tip- and

saddle-like structures in images of the head (Frantz et al. 2000; Alker et al. 2001; Wörz et al.

2003) by fitting model parameters to the image data through optimization of edge-based

measures. But these approaches have not been extended to other brain structure types. Other

methods rely more heavily on assumptions of brain geometry and intensity characteristics

(Han and Park 2004) and apply image intensity models to compute probability maps

(Fitzpatrick and Reinhardt 2005) that must be reduced for computational reasons. Linear

registration approaches (Woods et al. 1998) and algorithms (Pohl et al. 2002; Fischl et al.

2002) that aim to label entire anatomical structures in the brain can be used to produce point

landmarks, but their execution times are typically larger (20–30 min) than those algorithms

specifically designed to locate anatomical point landmarks (10–20 s).

In the field of image registration (Toga 1999), there are landmark-based methods that bring

image volumes from different imaging devices into spatial alignment for image-guided

neurosurgery (Peters et al. 1996) and therapy planning, as well as for visualization and

quantitative analysis. The anatomical point landmarks are usually identified by the user

interactively (Hill et al. 1991; Ende et al. 1992; Fang et al. 1996; Strasters et al. 1997), but

there are approaches that create surfaces from brain image volumes and then use differential

geometry to automatically extract extremal points (Thirion 1994; Pennec et al. 2000). These

methods usually minimize the distances between corresponding point landmarks with a

least-squares approach (Arun et al. 1987) or an iterative transformation application (Besl and

McKay 1992).

4http://www.itk.org/ItkSoftwareGuide.pdf

5http://rsb.info.nih.gov/ij/docs/intro.html

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The detection of anatomical point landmarks can be of particular use in the removal of facial

features from brain images. A subject’s identity can sometimes be discovered from a three-

dimensional surface reconstruction of the subject’s head, which may lead to violations of

HIPAA (Health Insurance Portability and Accountability Act) regulations and IRB

(Institutional Review Board) requirements that protect subject confidentiality. To address

these concerns, applications have been developed that black-out (i.e., replace with black

voxels) (Bischoff-Grethe et al. 2004) or warp (Shattuck et al. 2003) facial features in MRI

image volumes. Currently these applications require significant processing time, can only be

directly applied to T1-weighted images, and run the risk (Shattuck et al. 2003) of altering the

imaged brain anatomy.

Methods

Our methodology consists of constructing a series of functions that sequentially locates a

user-selected anatomical point landmark on a two-dimensional image slice or three-

dimensional image volume. Starting at the image/volume center, each function in the series

takes as input the output point of the previous function. The output point is closer to the

anatomical point landmark than the input point and is known with finer precision. The last

function in the series is constructed when the addition of another function yields no

improvement in the precision of locating the anatomical point landmark.

Data

Data used in this paper were obtained from the Alzheimer’s Disease Neuroimaging Initiative

(ADNI) database. ADNI is the result of efforts of many co-investigators from a broad range

of academic institutions and private corporations, and subjects have been recruited from

over 50 sites across the U.S. and Canada. The initial goal of ADNI was to recruit 800 adults,

ages 55 to 90, to participate in the research-approximately 200 cognitively normal older

individuals to be followed for 3 years, 400 people with MCI to be followed for 3 years, and

200 people with early AD to be followed for 2 years.

The different scanner manufacturers and models, pulse sequences, and spatial sizes and

resolutions of the MRI (magnetic resonance imaging) data we obtained from the ADNI

database are shown in Table 1. Because of the heterogeneousness of these acquisition

properties, we list only the most prevalent combinations. The subjects that were scanned

were between the ages of 60 and 90 (average age 73) and about 60% were female. Image

slices were acquired in both the axial (ax) and sagittal (sag) planes using different pulse

sequences [gradient echo (GR), spin echo (SE), inversion recovery (IR), and propeller MRI

(RM)] and different magnetic field strengths (1.5 and 3 Tesla). No structural abnormalities

(e.g., brain tumors) were present. We reoriented the image volumes so that the subjects are

facing the same direction and spatially normalized them into volumes of 256 × 256 × 256

voxels with 1 × 1 × 1 mm3 voxel spacings.

Terminology

We empirically determine the values of unknown constants in our functions using a training

set of image data. A testing set is then used to evaluate the trained functions using image

data that was not present during training. We typically use training sets that are two to ten

times larger than the testing sets.

As is illustrated in Fig. 1, a lattice and grid are used to extract data from each image slice/

volume in the training set. The grid contains grid cells and the intensities of all the image

pixels/voxels inside each grid cell are averaged together and normalized across all the cells.

Training data is extracted by placing the center of the grid at each equally-spaced lattice

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point and then averaging the image intensities inside the grid cells. We typically use a lattice

with a 5–7 pixel/voxel spacing and have not observed better results using smaller spacings.

As long as the size of each grid cell is much larger than the lattice spacing, we expect results

close to those that use all the points between the lattice points.

Although a subject’s head is normally well-centered in a brain scan, it is usually not true that

the same image voxel from two different scans will correspond to the same anatomical

point. However, in general the image voxels will be close to some common anatomical

point. If one draws a box large enough around each image voxel, that common anatomical

point will be contained by both boxes. The boxes in this case represent the initial precision;

i.e., how well the anatomical point is known in both scans. The initial precision of the input

point is a required input parameter for the first function in the series and is dependent upon

the scale on which dissimilarities occur between images. The final precision of the output

point of the last function is always limited by structural variations between subjects and

noise artifacts in the image data.

Mathematical Model

We train each function in the series by defining a lattice that fills the space that represents

the precision of the input to that function. For the first function, the center of the lattice is

placed at the center of each image/volume, and is large enough to cover the initial precision.

For the next functions in the series, the center of the lattice is placed at the user-selected

anatomical point landmark (for example, the center of the subject’s right eye) and the lattice

is given a size equal to the precision of the output from the previous function.

Our objective is to train the function to move every lattice point closer to the user-selected

anatomical point landmark on each image/volume of the training set. The space into which

the lattice points are moved represents the output precision of the function. The grid is

centered at each lattice point and the image intensities inside each grid cell are computed for

training. We assume that the horizontal and vertical distances from each lattice point to the

anatomical point landmark are linearly correlated with the image intensities (see the

Appendix) through

(1)

where m is the total number of lattice points in the training set, n is the number of grid cells,

Iij is the average of the image intensities in the jth grid cell at the ith lattice point, and the

are unknown coefficients that are to be solved for. Each

kth dimension from the ith lattice point to the anatomical point landmark. In Fig. 2, there is

one set of Eq. 1 for the horizontal distances

represents the distance along the

and one set for the vertical distances .

Equations 1 can also be written in matrix form as

(2)

where I is an m × n matrix and Ak and Dk are vectors of size n and m, respectively. Since we

choose the total number of lattice points to be greater than the number of grid cells (m > n),

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Eq. 1 is an overdetermined set of linear equations. This being the case, we can use singular

value decomposition (Press et al. 1995) to obtain a least-squares solution to Eq. 2. The

singular value decomposition of the matrix I yields6

(3)

where U is an m × n column-orthogonal matrix with UT · U = 1, V is an n × n orthogonal

matrix with V·VT = 1, andWis an n × n matrix whose off-diagonal elements are zero and

whose diagonal elements (the singular values wj) are non-negative:

(4)

The inverse of W is simply a matrix with the reciprocals of the singular values,

(5)

for which any diagonal element may be set to zero if it is numerically ill-conditioned (Press

et al. 1995). Substituting Eq. 3 into Eq. 2 and using the orthogonality relations for U and V

and Eqs. 4 and 5 gives the least-squares solution for the unknown coefficients

(6)

It is only necessary to calculate the generalized inverse matrix I−1 once; the same matrix is

used to compute the coefficients for each dimension. Note that Eq. 6 is not an exact solution

of Eq. 2 but is a solution only in the least-squares sense; I is a non-square matrix and

although I−1 · I = 1, in general I · I−1 ≠ 1.

Two-Dimensional Results

We illustrate our approach in two-dimensions by training a sequence of functions to locate

the center of each subject’s right eye in a two-dimensional image set. Each image slice in the

two-dimensional set is a T1-weighted MRI image that shows the subject’s right eye. We

used a training set of 64 image slices and a testing set of 32 image slices (each image slice

from a different subject). The center of each subject’s right eye (the white square in the

lower-right corner of Fig. 1) was manually located in each image in the training and testing

sets.

Figure 3 and Figure 4 illustrate the new locations of the lattice points on an image in the

testing set when the lattice points are moved in accordance with Eqs. 1 and 6. A 5 × 5 grid

of cells equal to the image size was used to compute the intensities Iij. Most of the points in

Fig. 4 fit inside a rectangle that is about one half of the lattice size. Many of the points that

fall outside the rectangle were originally located near the edges of the lattice. We can

6The superscript T denotes the transpose of a matrix.

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determine the quality of the solution by substituting the coefficients

and comparing the left-hand side of each equation with its right-hand side. We define the

error at the ith lattice point for the kth dimension as

from Eq. 6 into Eq. 1

(7)

Figure 5 shows the histograms of the errors calculated at the lattice points in each dimension

using Eq. 7. An error of zero in both dimensions refers to the case where a lattice point was

moved exactly to the subject’s right eye. The tails of the histograms show that a small

number of lattice points are not moved as close to the subject’s right eye. We note here that

the shapes of the error histograms appear to be consistent with the linear least-squares

assumption that the errors form a normal Gaussian distribution (Press et al. 1995). Since in

our observations the error histograms are normally bell-shaped, we define the error of the

solution obtained from Eq. 6 for each dimension by integrating the histogram curve area

from zero in both the positive and negative directions until the sum reaches 95% of the total

curve area. This 4σ-error is then the distance between the two stopping points (about four

standard deviations); for example, in Fig. 5 the 4σ-error in the horizontal dimension is 32

pixels and the error in the vertical dimension is 40 pixels.

Figure 6 shows how the 4σ-errors of the testing set vary when the lattice size changes using

four different grids. Each grid has a different number of grid cells (3 × 3, 5 × 5, 7 × 7, and 9

× 9) and is the same size as the image slices. The 4σ-errors from the error histograms are

combined into one measurement by taking the square root of their product. It can be seen

from Fig. 6 that for small lattice sizes (<10% of the image size), the test error is equal to or

greater than the lattice size. In these cases, the subject’s right eye is known with a certainty

less than or equal to the initial precision. But for larger lattice sizes (>20% of the image

size), the test error is about half the lattice size. This is true even as the number of grid cells

is increased from 9 to 81; in fact, we have noticed only slight differences when increasing

the number of grid cells up to 361 (a 19 × 19 grid).

As Fig. 3 and Fig 4 illustrate, when the lattice size is large enough the lattice points of each

image will be moved into a smaller area around the subject’s right eye. This area represents

a new precision (how well we know where the subject’s right eye is) that is higher than the

initial precision. In order to improve the precision even more, we define a new lattice of

points inside the area around each subject’s right eye and repeat the above approach. The top

graph in Fig. 7 shows the results when the sizes of four different grids (3 × 3, 7 × 7, 11 × 11,

and 19 × 19 grid cells) are varied using the new smaller lattice (about 16% of the image

size). The lowest test errors occur when the grid size is about one half the image size and the

test error decreases to about one half the lattice size. The bottom graph in Fig. 7 shows the

results obtained by repeating our approach once again, this time using a lattice that is 8% of

the image size. Here the lowest test errors occur when the grid size is about 35% of the

image size. Note that in each application of our approach as the size of the lattice decreases,

the size of the grid that results in the lowest test errors gets smaller as well. Figure 8

illustrates how the precision increases as our approach is repeated. The size of the lattice at

each application is represented by a white rectangle, with the largest rectangle representing

the earliest iteration and the smaller rectangles representing later applications. The precision

increases until the smallest rectangle is reached and no further improvement is achieved.

This is because structural variations between subjects and image noise inhibit functional

relationships at that resolution.

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LONI ICE

LONI ICE7 (It’s Close Enuf) is a Java application that has been developed to assist users in

training solutions using the above approach. It offers a visual interface for manually

choosing training points and for changing lattice and grid parameters (Fig. 9). Each

progressive application of our approach is represented as a rectangular module, and the

modules are connected together to illustrate how the modules relate to one another. LONI

ICE provides the means to train and test a sequence of ICE modules, and the errors at each

iteration are displayed on the graphical interface. Trained modules can be saved, reloaded,

and applied to new image volumes. In addition to modules that use singular value

decomposition to solve Eq. 6, there are also modules that use neural networks to divide

classes of images apart. Since the former modules work best when there are small structural

variations between subjects, this can be useful when the training and testing sets have

markedly different characteristics. We use the JAMA8 software package to calculate the

singular value decompositions of our matrices and the JOONE9 software package to train

the neural networks.

Three-Dimensional Results

We have used LONI ICE to locate the left and right eyes, nose, ventricles, central sulcus,

and anterior and posterior commissures in three-dimensional MRI brain image volumes.

After locating the ventricles, we also use LONI ICE to determine the MRI weighting of the

image volume. The training and testing data sets for each anatomical landmark are listed in

Table 2.

The ICE network shown in Fig. 10a is trained to locate the subject’s right eye, and the ICE

network shown in Fig. 10b is trained to determine the MRI weighting (PD, T1, T2) of an

image volume. We also trained two other ICE networks similar to Fig. 10a that locate the

subject’s left eye and the bridge of the subject’s nose. Each gray box in Fig. 10 represents a

trained ICE module and each white box displays the value of a three-dimensional coordinate

(X, Y, or Z) when the ICE network is run. The input point (in both ICE networks it is the

center of a 256 × 256 × 256 cube) at the top of each ICE network is processed downwards

through the ICE modules and an output point is returned at the bottom. The first two rows of

text on each ICE module display the grid size and grid cell size used to average voxel

intensities. ICE modules that use singular value decomposition to solve Eq. 6 display the

calculated precision with a third row of text, and those without a third row of text use neural

networks to separate image volumes into different classes.

We used 64 T1-weighted and 64 T2-weighted image volumes to train the eyes and nose ICE

networks and 16 T1-weighted and 16 T2-weighted image volumes for testing. The results

for a T1-weighted (top) and a T2-weighted (bottom) image volume from the testing set are

illustrated in Fig. 11. The solid white squares graphically depict how precisely the bridge of

the nose and the right and left eyes are determined. Each eye is detected within a rectangular

volume of (10, 10, 10) voxels and each nose bridge is located within a rectangular volume of

(10, 12, 16) voxels. Even though the image volumes have different resolutions and the

subject’s nose is cut off in the T1-weighted image volume, the anatomical point landmarks

are still well-determined. In order to verify the accuracy of the right eye ICE network, we

computed a histogram of the errors determined from 144 T1-weighted and 92 T2-weighted

image volumes. The errors are defined as the differences in each dimension between the

7http://www.loni.ucla.edu/Software

8http://math.nist.gov/javanumerics/jama

9http://www.jooneworld.com

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manually selected points and the points output by the ICE network. As Fig. 12 illustrates,

the output points are correctly localized to the error bounds [(−5, 5) in each dimension]

computed by our approach.

As Fig. 10b illustrates, our strategy for determining MRI weighting starts with two ICE

modules that locate the center of the subject’s ventricles, and are followed by an ICE

module that classifies the image volume as either PD-/T1-weighted or T2-weighted. When

the image volume is classified as PD-/T1-weighted, an additional ICE module is used to

further classify it as PD-weighted or T1-weighted. We use the subject’s ventricles for

classification because the intensities of the voxels in that region are different for the three

MRI weighting types. The MRI weighting ICE network was trained using 76 PD-weighted,

62 T1-weighted, and 72 T2-weighted image volumes and was tested using 20 PD-weighted,

20 T1-weighted, and 20 T2-weighted image volumes. Figure 13 shows the results for a PD-

weighted (top), T1-weighted (middle), and T2-weighted (bottom) image volume from the

testing set. The solid white squares show the center of each subject’s ventricles as output by

the second ICE module in Fig. 10b. All the image volumes from the training and testing sets

were correctly classified.

Table 3 summarizes how well the trained LONI ICE networks can locate anatomical

landmarks in MRI image volumes of adult heads. Included in this table are results for the

anterior and posterior commissures. Only T1-weighted images were used for training and

testing because of the difficulty in manually finding the commissures in T2-weighted

images. There are also results for the lateral termination of the central sulcus (defined as the

extrapolated intersection of the central sulcus with the Sylvian fissure on the surface of the

right hemisphere). The central sulcus point was determined by manually removing the skull

in each image volume and then generating a brain surface. Each point was chosen by

viewing and manipulating each surface in a three-dimensional display.

Discussion

Applications

The LONI ICE networks that locate a subject’s eyes and nose bridge are pertinent to the

removal of facial features from MRI brain images. We anticipate that by blacking-out image

voxels around the output points of the ICE networks, one can develop a relatively quick and

accurate application that performs facial deidentification. Since the ICE networks can locate

facial features in T1-weighted and T2-weighted images, it will be applicable for both types

of images, unlike current approaches (Shattuck et al. 2003; Bischoff-Grethe et al. 2004). The

LONI ICE network that determines the MRI weighting of an image volume has a practical

value because in our experience there does not exist a formula that can reliably return the

MRI weighting from common scanner acquisition parameters (i.e., echo time, repetition

time, etc.) alone. Further, it is often the case that the file format (e.g., ANALYZE10 or

MINC11) used to store image voxels does not contain information about the MRI weighting

or the acquisition parameters of the scan. An automatic method for determining the MRI

weighting is particularly useful when, for example, archiving a large set of image files and

populating a database that can be queried over MRI weighting type. We have noticed that

this ICE network does sometimes misclassify T1-weighted image volumes as PD-weighted

image volumes when the subject’s ventricles are very small. Although the center of the

ventricles are located properly, the neural network that is trained to classify the images as

PD-weighted or T1-weighted can give incorrect results. But we have consistently found that

10http://www.mayo.edu/bir/PDF/ANALYZE75.pdf

11http://www.bic.mni.mcgill.ca/software/minc/minc.html

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when we add these problematic images to the training set and retrain the ICE network, it

correctly classifies these images.

Structural variations between subjects primarily determine the precisions of the LONI ICE

modules that use singular value decomposition to solve Eq. 6. For example, in Table 3 the

lateral termination of the subject’s right central sulcus is known with less precision than the

subject’s right eye because cortical landmarks are more variable in location than eye

landmarks. Also, in Fig. 11 the bridge of the subject’s nose is known with less certainty

sagittally (16 voxels) than the subject’s eyes (10 voxels). This is because the eyes normally

appear as predictable ellipsoids across subjects whereas the region around the nose tends to

have higher variance. In contrast, the ICE modules that use neural networks yield the best

results when the differences between subjects can be separated into distinct classes.

Variations in intensity (e.g., between T1-weighted and T2-weighted images) are less

important than structural variations because one can find least-squares coefficients that

provide a good fit to different intensity correlations. Since we spatially average voxel

intensities using grids, our approach will produce the best results when structural variations

are smaller than the sizes of the grid cells.

Computational Considerations

The training process used by LONI ICE is divided into two main computational steps. The

first step calculates the average voxel intensities at each lattice point in the training set, and

the second step uses the results of the first step to construct the matrices in Eq. 2 and

performs the singular value decompositions. Using an image volume with dimensions 205 ×

240 × 240, completion of the first step requires about 8 min on a computer with a 3.2 GHz

CPU and 2G of RAM. Since each image volume in the training set can be processed

separately, we usually perform the computations in parallel on our grid computing

architecture. The singular value decomposition calculations needed for the four module ICE

network shown in Fig. 10a take about 10 min to finish using a training set of 128 image

volumes. Although the singular value decompositions can be performed in parallel as well,

the current version of the LONI ICE application performs them serially. Executing a trained

ICE network requires about 6 s to read in and reformat the image volume and about 2 s to

run the actual ICE network.

Although our approach can be applied to any number of dimensions, memory limitations

practically impede the singular value decomposition computations for higher dimensions,

which are performed entirely in computer memory. This is because the size of the intensity

matrix I grows geometrically with the number of dimensions; for example, in two-

dimensions a 9 × 9 grid has m = 81 elements but in three-dimensions a 9 × 9 × 9 grid jumps

to m = 729 elements (effectively increasing the size of I by an order of magnitude).

Fortunately, as is illustrated in Fig. 7, we have empirically found that grids with a low

number of cells (e.g., 7 × 7) yield test errors comparable to grids with a high number of cells

(e.g., 19 × 19). In practice, we rarely need to use grids with more than 5 × 5 × 5 cells in

three-dimensions.

It should be noted that the output point of a trained LONI ICE module is not guaranteed to

lie within the error ranges shown on the module. As Fig. 5 illustrates, there are tails to the

error histograms that indicate there is a small chance that the output point will fall outside

the error bounds. We have found that these points typically originate near, but are not

entirely constrained to, the edges of the lattice. Increasing the size of the lattice will help

reduce the possibility of an errant output point, but it will also decrease the trained module’s

precision, which may then require the addition of more ICE modules to a network.

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Comparison with Linear Registration

We have compared a standard linear registration technique with our method and have found

the accuracies of both approaches to be the same. The linear registration technique deduces

anatomical point landmarks by transforming an image volume into an “atlas” space. We

created such an atlas using the Automated Image Registration (AIR) package (Woods et al.

1998) and a set of 64 resampled T1-weighted image volumes. The first image volume was

chosen to be the target, and affine transforms were computed to best map each image

volume into the target space. These transforms were combined into an “averaged”

transform, and a preliminary atlas was created by combining all the image volumes in the

averaged space. After computing a second set of affine transforms that mapped each image

volume into the preliminary atlas space, the final atlas was created by combining the image

volumes in the preliminary atlas space. An anatomical point landmark was found by locating

the point landmark on the atlas, computing the affine transform that maps an image volume

to the atlas, and then transforming the point landmark from the atlas to the image volume.

Although the accuracies of both approaches are the same, we have found that it typically

takes minutes to compute the affine transform to the atlas space whereas our method

requires only several seconds of CPU time. This makes our method preferrable when only a

few anatomical point landmarks are desired in a relatively short amount of time.

Information Sharing Statement

Data used in the preparation of this paper were obtained from the Alzheimer’s Disease

Neuroimaging Initiative (ADNI) database.12 The ADNI was launched in 2003 by the

National Institute on Aging (NIA), the National Institute of Biomedical Imaging and

Bioengineering (NIBIB), the Food and Drug Administration (FDA), private pharmaceutical

companies and non-profit organizations, as a $60 million, 5-year public-private partnership.

The primary goal of ADNI has been to test whether serial magnetic resonance imaging

(MRI), positron emission tomography (PET), other biological markers, and clinical and

neuropsychological assessment can be combined to measure the progression of mild

cognitive impairment (MCI) and early Alzheimer’s disease (AD). Determination of sensitive

and specific markers of very early AD progression is intended to aid researchers and

clinicians to develop new treatments and monitor their effectiveness, as well as lessen the

time and cost of clinical trials.

LONI ICE is freely available (http://www.loni.ucla.edu/Software) under the UCLA

Laboratory of Neuro Imaging’s terms and conditions of use license.

Acknowledgments

This work was supported by the National Institutes of Health through the NIH Roadmap for Medical Research,

grant U54 RR021813 entitled Center for Computational Biology (CCB). Information on the National Centers for

Biomedical Computing can be obtained from http://nihroadmap.nih.gov/bioinformatics. Additional support was

provided by the NIH research grants R01 MH071940 and P01 EB001955, the NIH/NCRR resource grant P41

RR013642, and the Biomedical Informatics Research Network (BIRN, http://www.nbirn.net).

The authors thank Edward Lau for manually producing brain surfaces from our image volumes and Cornelius

Hojatkashani for directing the effort.

12http://www.loni.ucla.edu/ADNI

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Appendix: Relation to Cross-Correlation

Cross-correlation (Russ 2006) is a well-known method in image processing that is

commonly used to find features within images. The shift required to align a target image

with another image is determined by sliding the target image along the latter image and

summing the products of all overlaid pixel values at each location. The sum is a maximum

where the images are best matched.

In this Appendix we relate cross-correlation to the method described in this paper in one-

dimension; it is straight-forward to extend this relation to two and three dimensions. If I is a

one-dimensional image intensity function and is displaced a distance x relative to another

function A, the cross-correlation is defined as

(8)

In the limit of small x, we approximate I(g + x) as I(g) + xI′ (g) and note that Eq. 8 has the

form

(9)

where D and C are constants. In particular, if we choose C = −1, then in this limit the

integral is equal to the distance between I and A (with D defined as the distance between

them at x = 0).

In our case, we are choosing a function for the cross-correlation integral and solving for A

(as opposed to being given I and A and computing the integral). We are then interested in

finding a function A that makes

(10)

approximately true. The integral can be approximated by evaluating the integrand at n

locations that are a distance δ apart

(11)

and if the range of x is evaluated in m steps of length Δ, we have the system of equations

given in Eq. 1 where Aj = A(jδ), Iij = I(jδ + iΔ), and Di = D − iΔ. The coefficients Aj are

determined using least-squares to minimize the differences between both sides of Eq. 10.

One advantage of using least-squares is that the solution is insensitive to constant changes in

intensity. For example, let I1(x) and I2(x) be image intensities where I2(x) = I1(x) + I0 and I0

is a constant. Then the function A that minimizes the differences between both sides of the

equations

(12)

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is also the function that minimizes the differences between both sides of the equations

(13)

(14)

by subtracting the two equations. Equation 14 states that the contributions of constant

intensity terms are minimized.

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Fig. 1.

Terminology. Training data is extracted at each lattice point by centering the grid at the

point and averaging all the image intensities inside each grid cell. The solid white square at

the lower-right shows the location of the center of the subject’s right eye

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Fig. 2.

Training parameters. At the ith lattice point (black circle), a grid is used to compute the

average image intensity inside each grid cell (Ii1, Ii2,…Ii9). The horizontal and vertical

distances from the ith lattice point to the center of the subject’s right eye (black square) are

labeled , respectively

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Fig. 3.

Initial locations of the lattice points. Each white square represents a lattice point and the

lattice size is 38% of the image size

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Fig. 4.

Final locations of the lattice points. The lattice points shown in Fig. 3 are moved in

accordance with Eqs. 1 and 6. The lattice points are clustered around the subject’s right eye

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Fig. 5.

Error histograms in two-dimensions. The histograms were constructed using Eq. 7 at each

lattice point. The 4σ-error (full width at four standard deviations) in the horizontal and

vertical dimensions are 32 pixels and 40 pixels, respectively

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Fig. 6.

Test error versus lattice size for four equally-sized grids. Small lattice sizes (< 10% of the

image size) are associated with test errors that are equal to or larger than the lattice size.

Larger lattice sizes (> 20% of the image size) correspond to test errors that are about half the

lattice size

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Fig. 7.

Test error versus grid size for two different lattice sizes. In the top graph the lattice size is

16% of the image size, and in the bottom graph it is 8%. As the lattice size decreases, the

grid size that results in the lowest test error also decreases

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Fig. 8.

Improvement in precision. Each white rectangle has dimensions equal to the 4σ-errors

computed from the error histograms at each application of our approach. The precision

improves after each iteration, as is illustrated by the smaller rectangles

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Fig. 9.

LONI ICE. The Java application contains a viewer for manually selecting training points

and visualizing the quality of results. It also has a graphical interface for building, training,

and testing modular networks

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Fig. 10.

Two networks of LONI ICE modules. a An ICE network trained to locate the subject’s right

eye. b An ICE network trained to identify the weighting (PD, T1, or T2) of an MRI image

volume

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Fig. 11.

Automatic detection of the eyes and bridge of the nose in a T1-weighted (top) and a T2-

weighted (bottom) image volume. The axial and sagittal view planes intersect the bridge of

the subject’s nose. The solid white squares show how precisely the anatomical point

landmarks are determined

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Fig. 12.

Error histograms for the right eye ICE network. The errors in all three dimensions are

localized within the calculated error bounds of (−5, 5) voxels

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Fig. 13.

Automatic detection of the ventricles in a PD-weighted (top), T1-weighted (middle), and T2-

weighted (bottom) image volume. Both the axial and sagittal views for each image volume

are shown. The solid white squares show how precisely the center of the ventricles are

determined

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Table 1

Acquisition properties of the image volumes

ImagesScanner Type

Size (voxels3) Spacing (mm3)

T1[20%] Philips-InteraGR-sag256 × 256 × 1720.94 × 0.94 × 1.2

T1[18%]GE-Signa-Excite GR-sag256 × 256 × 1680.94 × 0.94 × 1.2

T1[16%]Siemens-SymphonyIR-sag 192 × 192 × 1601.25 × 1.25 × 1.2

T1[14%]GE-Signa-ExciteRM-sag 256 × 256 × 194 0.94 × 0.94 × 1.2

T1[14%] Siemens-SymphonyGR-sag 192 × 192 × 1601.25 × 1.25 × 1.2

PD[40%] Siemens-SymphonyGR-sag 192 × 192 × 1601.25 × 1.25 × 1.2

PD[17%] GE-Signa-ExciteSE-ax 256 × 256 × 480.94 × 0.94 × 3.0

PD[16%]GE-Signa-ExciteGR-sag 256 × 256 × 1660.94 × 0.94 × 1.2

PD[14%]Siemens-TrioGR-sag 240 × 256 × 160 1.00 × 1.00 × 1.2

PD[13%] Philips-Intera GR-sag 256 × 256 × 1600.94 × 0.94 × 1.2

T2[31%] GE-Signa-ExciteSE-ax256 × 256 × 52 0.94 × 0.94 × 3.0

T2[30%]Siemens-Symphony SE-ax 448 × 512 × 360.47 × 0.47 × 3.0

T2[18%]Siemens-Allegra/Trio SE-ax 226 × 256 × 40 0.94 × 0.94 × 3.0

T2[14%] GE-Signa-ExciteSE-ax 256 × 256 × 480.94 × 0.94 × 3.0

Combinations of the scanner manufacturer and model, type (pulse sequence and acquisition plane), volume size, and volume spacings are listed by

percentage for each MRI weighting (T1, PD, T2). The percentages for each MRI weighting sum to less than 100% because only the largest

combinations are shown. The first row of the table indicates that 20% of the T1-weighted image volumes were acquired from Intera Philips

Medical Systems scanners using a gradient echo (GR) pulse sequence. Each image volume was acquired in the sagittal plane (sag), consists of 172

images, and has a slice spacing of 1.2 mm. Each image width and height is 256 pixels with pixel spacings of 0.94 mm.

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Table 2

Image volumes in the training and testing sets

Anatomical landmarkTraining setTesting set

Right eye64T1 + 64T2 16T1 + 16T2

Left eye 64T1 + 64T2 16T1 + 16T2

Bridge of nose64T1 + 64T2 16T1 + 16T2

Ventricles 76PD + 62T1 + 72T2 20PD + 20T1 + 20T2

Anterior commissure64T1 16T1

Posterior commissure64T1 16T1

Lateral termination of the central sulcus 64T1 16T1

The terms “PD,” “T1,” and “T2” refer to a PD-weighted, T1-weighted, and T2-weighted MRI image volume, respectively. The number preceding

each term gives the number of image volumes of that type; for example, “64T1 + 64T2” refers to 64 T1-weighted and 64 T2-weighted image

volumes or 128 image volumes in the set

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Table 3

Precisions of trained LONI ICE networks that locate anatomical landmarks in MRI images of adult heads

Anatomical landmark Precision (X) (mm)Precision (Y) (mm)Precision (Z) (mm)

Right eye±5±5 ±5

Left eye±5 ±5±5

Bridge of nose ±5 ±6 ±8

Ventricles±3±5 ±6

Anterior commissure ±3±5±6

Posterior commissure ±3 ±5 ±5

Lateral termination of the central sulcus±6±8 ±6

The networks were trained using the training and testing sets in Table 2.

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