1. Ki-Chang Kwak

2. Average Brain Templates Used for Registration

3. Introduction Registration consists of determining the transformation that best maps corresponding features from on data set into another. This transformation can be used to align them geometrically so that corresponding morphological features of both scenes are assigned to the same spatial location. In general, intrasubject image matching is nontrivial because of different volume imaging parameters and different patient positioning during the separate scanning sessions. The problem is even more difficult, both to define and to solve, for intersubject registration because of dissimilarity in brain size and shapes. This article addresses a problem common to studies that involve intersubject comparisons between large numbers of data sets, where it is necessary to use a standard coordinate space in which many subjects can be compared, regardless of the size, position, or orientation of the original volumetric.

4. Introduction Rigid-body (6 degrees of freedom) - translation, rotation only Similarity (7 DOF) - translation, rotation, single global scaling Affine (9 or 12 DOF) - translation, rotation, scale, (skew)

5. Stereotaxic Coordinate System (Talairach) Our model was defined in a brain-based coordinate system very similar to that proposed by Talairach et al, since it is a well circulated published atlas and provides a common anatomically standardized coordinate system for precise and unambiguous reporting of the location of points of interest within the human brain.

6. Stereotaxic Coordinate System (Talairach) The extent of the standard space is defined by the smallest bounding box that completely contains the cortex. Talairach’s normalized proportional grid is established on the gibed brain within the bounding box. It is divided into 12 subvolumes : - 2 divisions laterally (left, right) - 2 vertically (above and below the AC-PC line) - 3 in the anterior-posterior direction (from posterior limit to PC, from PC to AC, from AC to anterior limit) This piecewise linear transformation is an attempt to model nonlinear differences between brains that would not be adequately handled by simple linear rescaling along the orthogonal axes.

7. Stereotaxic Coordinate System (MNI) There are three areas of discrepancy between our implementation of the stereotaxic coordinate system and the original Talairach model : specification of the AC-PC line, definition of the brain limits, and number of transformations used to map the space 1. Our group uses a similar technique to identify this baseline on MR images coregistered with a PET volume of the same subject. 2. In our technique, the extents of the brain in the lateral and vertical directions are assumed to lie on the perpendicular bisectors of the AC-PC line. 3. We have previously implemented the nonlinear mapping. The present nine parameter linear transformation we have implemented for the automatic registration described here can be separated into translation, rigid body rotation, and anisotropic scaling along preselected axes (the AC-PC line, the VAC line and the lateral line)

8. Stereotaxic Coordinate System (MNI)

9. Stereotaxic Space Model Since there is significant morphometric variability between individuals, we have established a model from > 300 MRI data sets from young normals rather use the brain from a single subject. For the results quoted herein, we used the following coordinate system convention : x-axis in the (LR) direction (positive toward the right), y-axis in the (PA) direction (positive anteriorly), z-axis in the caudocranial direction (positive superiorly), and the origin was located at the intersection of the center of the AC with the interhemispheric plane.

10. Registration In our method, registration is achieved by identifying the transformation that maximizes the cross-correlation between characteristics from the current and target volumes, estimated at each voxel position. We used two features, image intensity and 3D gradient magnitude, stored at each voxel location for both volumes. In practice, we found that the algorithm required only the intensity feature at two scales (σ=8 and σ=4mm ; FWHM= 18.8 and 9.4mm). Figure shows the two features at the σ=4mm scale. To provide an initial estimate of the transformation, a weighted principal axis method is employed to calculate the covariance matrix and the center of gravity using the intensity features from volumes with an imposed Gaussian blur with an FWHM=18.8mm(σ=8mm).

11. Registration The rotation angles are extracted from the principal axis vectors to establish the initial transformation. This is used as the starting point for the optimization procedure in 9 parameters where we maximize the correlation of image intensity in the blurred volumes at σ=8mm scale. Since we are interested only in the optimal overlap of corresponding brain voxels, we defined a brain mask in stereotaxic space and added on step to the multiresolution correation procedure described. The second improvement makes the algorithm more robust when dealing with data sets where image sensitivity is not constant across the entire object due to RF inhomogeneity. One last step is added to further refine the transformation with the 3D gradient magnitude of the MRI intensity as the feature to be used in the optimization. This feature emphasizes boundaries between tissue types and is less sensitive to low frequency variations in absolute intensities.

12. Registration To summarize the registration process, the optimal solution obtained at each step is used as input to the next, where it is refined : 1. principal axis transformation; 2. optimization on σ = 8 mm blurred volumes; 3. optimization on σ = 4 mm blurred volumes; 4.optimization on σ = 4 mm blurred volumes with brain mask; - We found that the correlation technique described identified the best transformation for brain plus scalp, which will sometimes bias the overall scale in the resulting transformation when a subject has a thicker or thinner skull than the average. 5.optimization on σ = 4 mm gradient volumes with brain mask. - due to RF inhomogeneity

13. Experiments and results Gradient Magnitude versus Voxel Intensity - Automatic intrasubject registration (16 subjects) in stereotaxic space : comparison of full volume intensity correlation (head) versus brain-masked intensity correlation (brain) versus brain-masked gradient correlation (edge) based on registration residuals of symmetrically disposed landmark points. When the registration parameters for T man and T auto are compared for each data set, rms rotation : 2.1, 0.75 and 1.48° around the x-, y-, and z-axes rms translation : 0.49, 0.95 and 1.0mm in the x-, y-, and z-directions rms scales : < 2.5% along the x- and y-axes and 4.8% along the z-axis.

14. Experiments and results Mapping differences - We estimated the difference in mapping through T man and T auto into stereotaxic space by measuring the average distance between landmark points mapped forward by the two transformations. Average rms difference Average rms misregistration

15. Experiments and results Plot of correlation value and z-score versus parameter error for 8mm gradient magnitude data. Twenty data sets were deliberately misregistered varying one parameter at a time. The solid line corresponds to the z-score, the dashed line to the correlation measure.

16. Experiments and results Plot of misregistration error versus slice missing. Solid line cooresponds to slices removed from the top, dashed line to slices removed from the top and bottom, and dash-dot line to slices removed from the bottom.

17. Discussion When compared with manual landmark-based methods, there was no bias in the registration parameters recovered by the automatic technique. - it was more stable than the manual registration method (smaller S.D for correlation) We have shown that the algorithm was robust to missing data. Because the final fit is edge-driven by the gradient magnitude, it is important that the input data contain robust, reliable edges to be registered with the model. A large amount of data could be missing from the bottom (below line c), since the ventricles along with superior aspect of the cortex will fix the caudocranial position and scale. The same is true when slices are missing from the top(above line b), as the ventricles and the floor of the cerebral volume serve to fix the parameters.