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10. Linear Registration

10.0.0.0.1 What is Registration?

Image registration is the process of calculating realigning and warping factors that transform one image into the space of another. This allows for comparisons of corresponding regions of different images, as well as the creation of overlays. This function is important since acquisitions via different methods (MRI, SPECT, CT, etc.) result in differently sized, spaced, and oriented images. Furthermore, the comparison of images from different subjects, or a single subject before and after a morphological change, requires realignment of corresponding structures in order to extract meaningful information. The BioImage Suite software provides a variety of user-directed functions to perform these calculations, allowing you to register images in the manner most efficient and relevant to the information you are trying to obtain.

10.0.0.0.2 Transformation Types

A transformation is the result of image registration; it is simply some function that maps a point in one image to a point in another. There are many different types of functions that can be used to specify this mapping, with varying degrees of associated flexibility, reliability and computational load.

Rigid Transformations: Rigid transformations are used for the registration of images from the same patient that have no distortion, and need to be realigned to the same orientation for meaningful comparisons to be made. A rigid transformation comprises 3 rotations and 3 translations. Therefore, it is a linear operation, and can be fully expressed in a 4x4 matrix. This type of registration is most often the fastest to compute.

Affine Transformations: Affine transformations are a broader class of linear transformations than rigid transformations, in that they include parameters for stretches and shears as well as rotations and translations. Nonetheless, they can still be represented by a 4x4 matrix, and are relatively quick to compute. Thus, affine transformations are typically used as a crude approximation to nonrigid transformations, either for rough estimates of location, or as a preliminary step.

Nonrigid or Elastic Transformations: Nonrigid transformations are used for registrations between images of different subjects, or images with distortions or actual physical differences (images of a patients brain before and after an operation, for example). These transformations are non-linear, and thus have no matrix representation. In fact, they have a great many different parameterizations, the results of which get saved in a large grid file.

10.0.0.0.3 Reslicing Images

Figure 10.1: The Image Reslicing Process as implemented in vtkImageReslice

Reslicing images is at the heart of most image registration procedures. While transforming surfaces is intuitive, and can be summarized in the three steps (i) take point, (ii) transform point and (iii) store point, image reslicing is somewhat counter-intuitive.

We will explain the process with reference to figure 10.1. In a typical registration process we have a Reference image and a Target image. The registration estimates the transformation FROM the Reference image TO the target image. This transformation can then be used in an image-reslicing operation to warp the Target image BACK to the Reference image, i.e. make the target look like the reference. In this way, while the transformation is ``forward'' the image moves BACKWARDS.

The process can be described by the following recipe, once the transformation exists:

• Create an empty image (often having the same geometry as a Reference Image).
• For each point (voxel) $r$ in the empty image:
  1. Compute its corresponding point in the Target image $r'$, $T:r\mapsto r'$.
  2. Interpolate the target image to find the image intensity $I$ at position $r'$ - which rarely corresponds to an exact voxel.
  3. Set the voxel $r$ in the empty reference image to have intensity $I$.
• Repeat for all voxels.

Figure 10.2: The Brain Register application. This is a dual-viewer application, where the viewer on the left is termed the ``Reference Viewer'' and image on the right is called the ``Transform Viewer''. All estimated registrations go from the ``Image'' in the Reference Viewer to the ``Image'' in the Transform Viewer.
Figure: Menu options for the main Brain Register application.Viewers menu (left) provides access to the three viewers, the Reference, Transform and Simple Viewer. The Simple Viewer is a Mosaic Viewer and can be used to view images from either the other two viewers. The Transfer menu can be used to move images from the Reference to the Transform viewer and vice-versa. The Registration menu brings up the options for performing linear and non-linear registrations as well as examining the registrations and other useful functions

10.1 Accessing the Registration Tools

Image registration functionality in BioImage Suite is available through the Brain Register or Mouse Register applications, as well as through the Data Tree Manager Tool. In both cases, the GUI consists of two viewers (the ``Reference Viewer'' and the ``Transform Viewer'') and a floating menu bar (Figure 10.2) that is linked to both viewers and mediates registrations across them.

The idea behind the two viewer style of display is to show the relationship between two images, as defined by the transformation between the two. Thus, when the ``x-hairs'' box is checked in both viewers, if you move the crosshairs in any view style in either viewer, the crosshairs in the other viewer move as well, to reflect the corresponding point in its image, according to the current transformation matrix that has been loaded, as described here. (Unchecking the ``x-hairs'' box in either viewer disables the movement of the crosshairs in that viewer, allowing you to lock them in place, while you navigate in the other viewer. This will be useful in manually defining crude initial transformations; more on this below.) The main menu of these applications has four submenus, as shown in Figure 10.3.

• Viewers - opens either the reference or transform viewer, both of which are orthogonal viewers by default but provides access to the Simple Viewer (an instance of the Mosaic Viewer) which can display multiple identically oriented slices. See the viewers page for more details on individual viewer functionality. Both the Reference and the Transform Viewer also have the full complement of Image Processing and Segmentation functionality.
• Transfer - commands for moving images from the reference to the transform viewer and vice versa or to swap them.
• Registration - provides access to the Registration/Overlay tool and the Point Based Registration controls.
• Multisubject - a dedicated Multisubject control that has functionality for generating composite functional maps. (The pxitcldualmultisubject app has a second multisubject control that facilitates group comparisons).

10.2 Registration | Transformation

10.2.0.0.1 Loading and Saving Transformations:

In the menu bar shown in Figure 10.2, choose (Registration | Transformation) to bring up the Registration/Overlay Tool. The Registration/Overlay Tool window contains the tools needed to register and compare a pair of images. All transformation and registration operations use the Reference/Transform convention described in the box above. Transformations are generated FROM the Reference image TO the Transform image, and when loading a transformation, you should remember this scheme. The top section of the Transformation window in Figure 10.4, above, is a simple file load/save mechanism which allows you to save the transformation that is currently defined between the reference image and the transformation image. The 4x4 matrix below the filename reflects the transformation, if it's linear. The Load button brings up a file selection dialog box that lets you load a previously saved transformation file of types Matrix (*.matr), Grid/Combo (*.grd), Thin Plate Spline Transforms (*.tps), and Old Matrix Files (*.mat).^10.1 When you load a transformation, the info box showing the transformation matrix changes to reflect the parameters of the transformation. If the loaded file contains a linear transformation matrix, this is shown; if the loaded file is a Grid or Combo file, specifying a non-linear transformation (*.grd) , then the box shows the Grid Dimensions and Spacing, as well as the linear transform matrix dimensions for Combo transformations.

Figure 10.4: The Transformation Control Window. This window, a tab in the Registration/Overlay Tool, contains functions related to the loading, saving, and verification of transformations, as well as reslicing and stitching functions. It can be accessed directly from the (Registration | Transformation) menu command in the pxitclbrainregister menu bar.

Transformation List

The listbox at the left side of the ``Transformation'' tool space is a holding space for multiple transformations, which can be loaded into memory simultaneously, but applied one at a time to the images in the viewers. When a new transformation is calculated, it will appear here. You can manually add a transformation (using the Add button), or delete a transformation (using the Delete button) to/from memory.

Clear

Hitting the Clear button removes whatever transformation is currently selected in the Transformation List, and replaces it with the identity transform. This is reflected in the matrix display.

Inverse

With a transformation in memory (i.e. selected in the Transformation List), hitting the Inverse button computes the inverse transformation, and replaces the current transformation with it.

Manual Transformation Control

You can use this tool to manually change translation, rotation, and scaling factors in all three dimensions. The tool can be accessed by clicking the Manual button underneath the matrix display in the transformation control window (See Fig 10.4) which will bring up the small manual control popup (Fig 10.5) containing input fields for the above parameters in each dimension. The fields will contain the current values for these parameters, which you can edit freely. The X-, Y- and Z- shift parameters are in the native scale of the reference image; the rotation parameters are in degrees; the scaling parameters are percentages. After inputting the desired values, hit the Set Xformation button to compute a 4x4 linear transformation matrix from your values, and send it to the transformation control. The transformation matrix will update to show your changes. This will not affect the images, however. To apply the transformation, you must hit the Copy Results to Image in the transformation control window. Equivalently, and as a shortcut, you can hit the Set & Apply button in the manual transformation control popup, which will directly apply your changes to the transformation and apply the result to the image.

Figure 10.5: The Manual Transformation Control Popup. This box contains tools for manually altering the translation, rotation, and scale parameters of a transformation matrix.

The Extract! button lets you grab the shift, rotation, and scale parameters from the transformation matrix currently loaded in the transformation control. This way, you can load a transformation as described above, and alter it manually. To reset all values to their defaults (0 translation, 0 rotation, 100% scale), press the Clear Values button.

Auto Crosshairs: Sometimes it is easier to define a translation by placing cursors than by estimating numbers. The Auto Crosshairs button gives you this capability. If you can locate the same point in both of your images, you can use it to direct the manual setting of the translation parameter. In the viewers, simply place the cross hairs over the point in one image, uncheck the ``x-hairs'' checkbox in that viewer to lock them in place at that point, and place the crosshairs over the same point in the other image. Then, back in the manual transformation control popup, click the Auto Cross Hairs button, and the X-, Y- and Z- translation parameters will be updated to specify a translation that maps the two cross hair locations together (i.e. maps the crosshair point in the Transformation Viewer onto the point in the Reference Viewer. This technique is often easier than guessing at translation parameters and then navigating in the image to confirm them.

The manual transformation control popup is most often used as a rough alignment tool, as a preprocessing step to automatic registration. Besides reducing subsequent registration processing time, it also makes the registration more reliable, since corresponding regions are in closer relative proximity, increasing the likelihood of their overlap, and helping the registration algorithm to converge properly. It is strongly advised that you make an attempt to line your images up using the manual control if they are in radically different orientations or scales.

10.2.0.0.2 Reslicing:

Once you have registered two images, you can put the resulting transformation information to work by ``Reslicing''. Reslicing takes the loaded transformation matrix or grid and applies it to the Transformation Image, so that it ``looks like'' the Reference image. That is, it places the Transformation Image into the space of the Reference Image. This means that the Transformation Image gets diced up, analyzed, and rebuilt using voxels that are the same size as those of the Reference Image, and occupy an equally sized and shaped image volume. This process is wholly dependent on the transformation matrix that links the two images. To do it, simply hit the Reslice! button in the transformation control window. The image in the transformation viewer will be resliced into the space of the image in the reference viewer, and the output will be displayed (saved in the ``Results'' display of the transformation viewer).

Figure 10.6: The Reslice Options Section in the Transformation Control.

This section contains the functions for reslicing images into other images' spaces, and various options that relate to this operation. See also Figure 10.6.

10.2.0.0.3 Reslice Options:

There are a few options that apply to the Reslicing function, which you can control in the ``Reslice Options'' section of the transformation control: Interpolation Choose the method for calculating values between those values that coincide in spatial location with the original values. Since the new image comprises differently sized voxels that occupy a new overall space, some method of interpolation must be employed. You may choose Nearest Neighbor, Linear, or Cubic.

Wrapping: If the ``Wrap'' checkbox is checked, the image will be allowed to wrap around the volume (i.e. anything that falls off the left side will appear back on the right side, etc.).

10.2.0.0.4 Computing Measures of Registration Quality:

The other three buttons in the ``Reslice Options'' section are functions that compute measures of quality after a registration has been computed. Thus, after a transformation is loaded in the transformation control (either by clicking the Load button, or by having just completed a registration), these functions will yield a number of different numerical parameters that describe your registration. All operations are comparisons between two images. Similarity Clicking the Compute Similarity! button brings up a console window that contains values for a number of measures of registration quality: Joint Entropy, Correlation, Normalized Mutual Information, Sum of Squared Differences, and Difference Entropy. These provide a quick diagnostic of how reliable the transformation loaded is.

ROI Stats: ROI stats give information about mean and standard deviations within discrete regions defined by a Region Of Interest image, which is a mask image that is registered to the reference image. Thus, you should load your ROI definition image into the Transform Viewer, your reference image in the Reference Viewer, and register them. Then click the Compute ROI stats button to get statistical measures out for each region in the ROI definition image.

Overlap: The Compute Overlap button thresholds both loaded images at 50% of their maximum value, and then computes the percentage of overlap between the resulting regions. This is very useful with binary valued images, but can also be a good diagnostic of registration quality in other images.

10.2.0.0.5 Stitching:

The stitching function allows you to combine two adjacent images, provided that you are able to register them first. Thus you need a region of overlap between the two images. The result is a single image. The x, y, and z radio buttons let you choose which dimension to stitch in. The ``Flip'' checkbutton option lets you toggle which image comes first (i.e. lies at the top, left, or front, depending on the dimension of stitching). The ``Pad'' value is editable, and lets you specify how much to grow the image by before stitching (since you need to make the image bigger to fit both pieces into it).

10.2.0.0.6 Additional Procedures:

This section contains a few extra functions that are associated with reslicing, and may be useful for evaluating the quality of registration operations. Often, the quickest way to check your registration is to create a blended or checkerboard image, and be sure that structures that cross image boundaries remain reasonably continuous. All of these operations apply the current transformation loaded into the transformation control.

Checkerboard Creating a checkerboard does just this: creates a combined image, in which alternating cube-shaped sections are contributed by each of the two images registered together. The ``Spacing'' option lets you control the size of the checkerboard spaces. The ``Normalize Images'' box should usually be left checked, since it normalizes the intensity scales of the two images, so that one set of checkerboard spaces does not appear much brighter than the other. Figure 10.7 left image shows an example of the checkerboard image.

Blended Images A blended image has contributions from both images, but they are complementary at every point. The effect is that both images become semi-transparent and get merged. Adjusting the ``Opacity'' slider button lets you adjust which image dominates in the result. A value of 0.30 means that the image is contributed to 30% by the image in the transformation viewer and 70% by the image in the reference viewer. A value of 0 would result in an image identical to that in the reference viewer. Check the ``Auto Update'' box to have the blended image result update as you move the opacity slider. Figure 10.7 right image shows an example of a blended image being used to combine a whole brain MRI with a scout slice MRI.

Figure 10.7: Combining Images as a test of Registration Quality. The combined images provide a quick diagnostic of the quality of the registration between two images. In the left: shows a checkerboard image, created by merging alternating cubic sections of two images. Areas discrepancy can be easily picked out, and areas that line up are also readily apparent (Trace the contours of the corpus callosum, for example: They are fairly continuous, even as you cross from one square in one image to the next in the other image). On the right: shows a blended image, created from a whole brain MRI and a scout slice MRI that has been resliced into the whole brain space. The image comprises 90% scout slice image and 10% whole brain image (the scout slice has no data outside the narrow band seen, thus outside this region only the whole brain image is visible). Again, by looking at the interface between the two regions, continuities and discrepancies are easily seen.

Masking Masking is the process of creating a binary image, i.e. an image that contains only two distinct values. Thus separate regions are created: those which have the value zero, and those which have the non-zero value. The Mask Image! button thresholds the image in the Transformation viewer at 50% of its maximum value, and then sets any voxels above the threshold to 100. This creates distinct regions in the image, creating a mask that can be used for region of interest definitions. The ``Dilation of Mask'' option allows you to specify how much to grow the mask image by after thresholding.

10.3 Manual Registration

Other than allowing users to manually control the parameters for registration, we also provide some visual metrics to help users pick parameters that can then be used for registration.

Figure 10.8: Manual registration tool choice in the menu.

On invoking this tool, the Transform Viewer and the Reference Viewer windows are shown to the user. On loading the appropriate images into the transform viewer and the reference viewer, the user can then select the ``Manual Registration'' option in the menu as shown in Figure 10.8. On selecting manual registration, a ``Manual Registration Tool'' window pops up that allows the user to control parameters for manual registration. Figure 10.9 shows a screenshot of the tool. The ``Show Surfaces'' checkbox toggles the display of surfaces overlaid on the images. When the ``Template in Transform Space'' checkbox is checked/selected, the transformations by changing parameters such as tx, ty, tz, rx, ry, rz and sc (scaling) are applied to the surface in the ``Reference viewer''. If the ``Template in Transform Space'' checkbox is unchecked, the transformations are applied to the surface in the ``Transform Viewer.'' The ``L'' and ``S'' buttons in the tool refer to Load and Save which allow loading and saving of transforms. The ``?'' button provides more details about the generated surface such as the Number of points and number of cells.

Figure 10.9: Manual registration tool choice in the menu.

Figure 10.10: The Reference viewer and the Transform viewer with the surfaces overlaid to allow for control of registration parameters.

To use this tool, the user should first click the ``Auto Create Surface'' button which creates a surface around the images in both the Transform viewer as well as the Reference viewer, as shown in Figure 10.10. On obtaining surface overlays, the user can then tweak the parameters using the controls in the Manual Registration tool. The ``Update Main Application'' button will take the user to the main registration tab and fills in the transformation matrix based on the user's choices of rotation, translation and scaling transforms. Figure 10.11 shows a screenshot of the main registration tab with the transformation matrix filled in based on the transformations selected by the user in the Manual Registration Tool in Figure 10.9.

Figure 10.11: The transforms from the Manual Registration Tool such as translation, rotation and scaling are transmitted to the Registration/Overlay tool, which generates the transformation matrix based on the user selected transforms. Here we can see ``Trans.1'' shows the transformation matrix as per the selected transformations in Figure 10.9.

10.4 Linear Registration (Intensity Based)

Figure 10.12: The Linear Registration Controls. Left: the most common options under the Simple tab. Right: advanced options.

Linear registration enables the computation of a transformation between two images that can be captured in terms of a 4x4 matrix (hence the term linear). The most common types are ``Rigid'' - simple translation and rotation which is useful in mapping images of the same subject that have no underlying distortion (both inter- and intra-modality, i.e. MRI to MRI or MRI to CT) and ``Affine'' which adds additional flexibility in terms of scaling/shearing of the image and is useful both as a crude distortion correction registration or for crude inter-subject registrations.

To perform a linear registration, first load the reference image in the ``Reference'' Viewer and then the target image in the ``Transform Viewer''. The resulting transformation will map coordinates FROM the reference TO the target, and when it is applied for image reslicing will move the target image to the space of the reference - the overall goal of all registration being to move the target to look like the reference.

There are two sets of controls. In the Simple Controls (Figure 10.12 top), the user specifies the resolution (as a multiple of the native resolution of the reference image), as well as whether to automatically save and overwrite the resulting transformation. If the ``Use Current'' transformation checkbutton is enabled then the currently selected transformation in the Transformation List is used to initialize the registration parameters. If not then the transformation is initialized by mapping the ``centers'' of the two images. Three default operations are provided:

Rigid - compute a full 3D rigid mapping.
Rigid2D - compute a 2D rigid mapping.
Affine - compute a 12-parameter affine mapping.

Figure 10.13: Methods used to manually transform an image to create a new starting point for the registration.

Under the Advanced tab (Figure 8 bottom) the user can set additional parameters such as the similarity metric (default=Normalized Mutual Information), the optimization method etc. Key parameters are the number of levels (for multiresolution optimization = 3) and the number of steps (different step sizes for computing the gradient etc. = 1). The ``Old Style'' optimization method is that used in the original paper by Studholme et al [108]. If this is selected it is advisable to set the number of steps to 4 (default = 1).

10.5 Functional Overlay

Figure 10.14: The Functional Overlay Control.

The functional overlay control enables the overlaying of functional images onto anatomical images, to enable the combined display of structure and function. The anatomical image in this case is the Image (i.e. not results) of the Reference Viewer and the functional image is the Image of the Transform Viewer - the later is first resliced to match the anatomical image using the current transformation.

The basic principle used for the overlay is that the users sets a threshold for what constitutes significant function using the Low Threshold slider and then saturates the functional data at the level set by the High Threshold slider.

Consider, for example, the case where the functional map has range -3000 to 3000 the anatomical image has range 0 to 256 and the F1 colormap is used. The F1 Colormap maps the anatomical image in the range 0 to 55, the negative functional data (if selected) in the range 56-59 (56 is the most significant) and the positive functional data in the range 60-63 (with 63 being the most significant). If the thresholds are set to 2000 and 2500 respectively, then the output of the overlay tool will be:

1. The anatomical image if functional image $<$ 2000 and functional image $>$ -2000 (i.e. insignificant activations), or if the anatomical image intensity (scaled in the range 0.55) is less than Inten Threshold. This last step masks spurious activations outside the brain or in the ventricles.
2. Otherwise
   • If function is positive and over 2000 then 2000-$\mapsto$60, 2500 -$\mapsto$ 63 and anything over 2500 will saturate to 63.
   • If function is negative and under 2000 then -2000-$\mapsto$59,-2500-$\mapsto$56 and anything less than -2500 will saturate to -56.

Additional Options: The Overlay Type drop menu selects whether positive, negative or both positive and negative function is overlaid. The colormap is selected using the Colormap drop menu. Colormaps F2 and F4 perform similar mappings but use greater numbers of colors giving a higher fidelity overlay. The default colormap can be set in the User Preferences dialog. The Normalize Anatomical checkbox automatically windows the anatomical image prior to creating the overlay to improve its contrast.

The Clustering slider performs a cluster filter operation on the functional image. Only clusters greater than the selected size in voxels will be overlaid on the anatomy. By default, the number of voxels is in the space (and resolution of the reference image. Enable ``Orig Voxels'' to scale this to the original resolution of the functional data.

If the input functional image is four-dimensional, i.e. there are multiple frames/tasks in it, the user can select to overlay only one frame by enabling the Single Component checkbox. The frame (component) is selected using the Select Component slider.

If all goes well the overlay is created using the CreateOverlay button. The Reslice button can be used to reslice and display the functional image only, if this is desired. The ``Toggle Colorbar'' button can be used to show a colorscale at the bottom of the viewer.

The t-dist distribution tool - see Figure 10.15 can be used to help set thresholds etc.

Figure 10.15: The T-distribution Tool. This is accessed under the Help menu of the main Brain Register application and can be used to convert from ``t-values'' to ``p-values'' and vice-versa. The T-value is entered into the box marked as T. This may be an actual t-value or one scaled by 1000 (if the checkbutton G is enabled). It can also be set from the current position of the viewer cross hairs using the C or D buttons respectively. The number of degrees of freedom is specified in the entry marked as F. To convert to P-value press the button marked as A. The reverse conversion is accomplished by the button marked as B. (The control can also do z to p conversions - in this case enable the checkbox marked as E).

10.6 Image Compare

Figure 10.16: The Image Compare Control.

The Image Compare control can be used to either perform a straight image addition, subtraction and %change operations or compute a two-group t-test. It has four image controls labeled Mean1, Mean2, Standard Deviation 1 and Standard Deviation 2, where the images to be used for the comparison must be loaded.

There are three standard operations that only utilize the mean images namely:

• Mean1+Mean2
• Mean1-Mean2
• Intersection Threshold.

which result in an image placed in the Transform Viewer. Naturally, this operations can also be used to compare standard images (i.e. not means) provided that they have the same size!

Intersection Threshold performs a logical AND of the two images after first thresholding their values using the Intersection Threshold. When both images are above this, the output images has value equal to the average of the images, otherwise it is set to zero.

For the t-test computation, the standard deviation images and the size of the two groups must be also defined. The size of the two groups can be specified in the textboxes labeled N1 and N2 respectively at the bottom of the control. Invoking the Compute Tmap button will result in the computation of a voxelwise t-test between the groups represented by their mean and standard deviation images. The output image, which is equal to the t-score * 1000 is displayed in the Transform Viewer. Conversion of these t-scores to p-values can be performed using the T-distribution table tool that is accessible under the Help menu of the main Brain Register application - Figure 10.15.

10.7 EXAMPLE: Interactive Registration Tools

The following instructions are for using the interactive graphical interface (GUI) to accomplish registrations between two brain images.

10.7.1 Co-register 2D conventional thick slice anatomicals to individual 3D

Figure 10.17: Methods used to Co-register a 2D conventional thick slice anatomical with a 3D wholebrain anatomical.

The step-by-step instructions, with reference to Figure 10.17 are:

1. Choose brainregister from the BioImageSuite main menu. Three windows will appear: a transform viewer, a reference window and a brainregister menu bar. In the Reference Window choose (File | Load)
2. Choose the filename that refers to the stripped whole brain acquisition from the brain extraction steps explained above and click Open.
3. In the Transform Window choose (File | Load)
4. Choose the conventional 2D thick slice anatomical image and click Open
5. On the BrainRegister menu bar, choose (Registration | Linear Registration). A new Registration/OverlayTool window will appear.
6. In the new Registration/OverlayTool window click Rigid. This will compute a Linear Registration between the two loaded images. If the Auto Save Results box is red, BioImageSuite will automatically save the resulting .matr transformation file in the current working directory.
7. While the registration is running a PXTkConsole window will appear showing the status of the registration.
8. When the registration is complete a ``For Your Information'' window will appear telling you the name of the saved registration file. If the filename already exists the window will ask if you want to overwrite the existing file. Click OK.
9. Check the registration by clicking around in the 2D brain image (Transform Viewer) and seeing if the crosshairs match the same anatomical position in the 3D brain image (Reference Viewer). Three examples are shown - the gyral patterns should match on both images.
   1. Superior Frontal Gyrus
   2. Supramarginal Gyrus
   3. Middle Occipital Gyrus
10. Optionally in a unix window rename the newly generated .matr file to [studynum]_2Dto3D.matr e.g.: % mv tr3567_3D_stripped.hdr_tr3567_PIname_stack3d_S003.matr tr3567_2Dto3D.matr

Figure 10.18: Methods used to Co-register a 4D echoplanar image with a 2D conventional thick slice anatomical. Part I.

10.7.2 Co-register 4D echoplanar images to 2D conventional thick slice anatomicals

Figure 10.19: Methods used to Co-register a 4D echoplanar image with a 2D conventional thick slice anatomical. Parts II and III.

The step by step instructions with reference to Figures 10.18 and 10.19 are:

1. Choose brainregister from the BioImageSuite main menu. Three windows will appear: a transform viewer, a reference window and a brainregister menu bar. In the Reference Window choose (File | Load)
2. Choose the filename that refers to the conventional 2D thick slice anatomical image and click Open.
3. In the Transform Window choose (File | Load)
4. Choose the middle trial of all echoplanar image files and click Open
5. In the Transform Window choose (Image Processing | ReOrient/Crop Image)
6. Choose a range t that will only be one image - this will increase the registration speed.
7. Click Crop
8. Click Copy Results to Image
9. There is a choice to be made as to which registration method should be used for the echoplanar to 2D registration. One can either choose to do a Linear Registration (LR), or because of the distortion found in echoplanar (i.e. functional) images once can choose to do a Linear Registration with Distortion Correction (LRDC). Both methods are described here.
   1. LR: On the BrainRegister menu bar, choose (Registration | Linear Registration).
   2. LRDC: On the BrainRegister menu bar, choose (Registration | Distortion Correction).

10. A new Registration/OverlayTool window will appear. If the Auto Save Results box is red, BioImageSuite will automatically save the resulting .matr or .grd transformation file in the current working directory
    1. LR: Click Rigid to compute the linear registration (a .matr file will be generated).
    2. LRDC: Click Compute Linear and Distortion Correction to compute the registration (a .grd file will be generated).

11. While the registration is running a PXTkConsole window will appear showing the status of the registration. When the registration is complete a ``For Your Information'' window will appear telling you the name of the saved registration file. If the filename already exists the window will ask if you want to overwrite the existing file.
    1. LR: Click OK
    2. LRDC: Click OK

12. In a unix window, rename the newly generated registration file. The six images at the bottom of Figure 7B were created using (Registration | Jacobian) and clicking Create. Comparing these two sets of images illustrates the difference between the two transformation methods.
    1. LR: ex: % mv tr3567_PIname_stack3d_S003.hdr_Crop_tr3567_PIname_stack4d_S708.matr tr3567_FCTto2D.matr
    2. LRDC: ex: % mv tr3567_PIname_stack3d_S003.hdr_Crop_tr3567_PIname_stack4d_S708.grd tr3567_FCTto2D.grd

13. Check the registration by clicking around in the echoplanar brain image (Transform Viewer) and seeing if the crosshairs match the same anatomical position in the 2D anatomical image (Reference Viewer).
    1. LR: click around on different gyri to check if gyral patterns match on both images.
    2. LRDC: click around on different gyri to check if gyral patterns match on both images.

10.7.3 More Advanced Technique when Registrations are not Accurate

Sometimes if an image is quite rotated from the target, the automatic registration will not be accurate. The user can manipulate the transform image to approximate the target image using a Manual Transformation Control box. This approximation can then be used as an input starting point for the registration.

The step-by-step instructions, with reference to Figure 10.13, are:

1. Choose brainregister from the BioImageSuite main menu. Three windows will appear: a transform viewer, a reference window and a brainregister menu bar. In the Reference Window choose (File | Load)
2. Choose the filename that refers to the stripped whole brain acquisition from the brain extraction steps explained above and click Open.
3. In the Transform Window choose (File | Load)
4. Choose the conventional 2D thick slice anatomical image and click Open
5. On the BrainRegister menu bar Choose (Registration | Transformation). A new Registration/OverlayTool window will appear.
6. Under the Transformation block Click Manual. A separate Manual Transformation Control window will appear.
7. On the Manual Transformation Control window, with all values set to zero, click the Set&Apply button. This will center both images. Check the crosshairs in one window to see how different they are on the other.
8. Manually input shifts and rotations into the Manual Transformation Control window and click Set&Apply button to manipulate Transform window image. Repeat until the image in the Transform window approximates the image in the Reference window.
9. On the BrainRegister menu bar, choose (Registration | Linear Registration). A new Registration/OverlayTool window will appear.
10. Click Use Current Transform for Initialization, the box will turn red.
11. In the new Registration/OverlayTool window click Rigid. This will compute a Linear Registration between the two loaded images. If the Auto Save Results box is red, BioImageSuite will automatically save the resulting .matr transformation file in the current working directory.
12. While the registration is running a PXTkConsole window will appear showing the status of the registration.
13. When the registration is complete a ``For Your Information'' window will appear telling you the name of the saved registration file. If the filename already exists the window will ask if you want to overwrite the existing file.
14. Check the registration by clicking around in the 2D brain image (Transform Viewer) and seeing if the crosshairs match the same anatomical position in the 3D brain image (Reference Viewer).
15. Optionally, in a unix window rename the newly generated .matr file to [studynum]_2Dto3D.matr

    ex:  \%  mv  tr3567\_3D\_stripped.hdr\_tr3567\_PIname\_stack3d\_S003.matr   tr3567\_2Dto3D.matr
    

10.8 Linear Transformations Theory:

Transformations are maps which implement the following equation: $x \mapsto y, \mbox{ or } y= T(x)$, where $x$ is the input point and $y$ is the output point. Linear transformations are represented as $4\times4$ matrices. This enables the use of a single operation to capture both a translation as well as a combination of rotation/shear/scale. Ordinarily, we would write such a transformation in two parts as:

$$y = Ax + b$$ (10.1)

where $A$ is a $3\times3$ matrix that performs a combinations of rotation, scale and shear and $b$ is a $3\times1$ vector specifying the translation. A more compact representation is to use homogeneous coordinates. To accomplish this, we write each point as a 4-vector $(x_1,x_2,x_3,1)$, and apply the transformation as follows:

$$\left[\begin{array}{c} y_1\\ y_2\\ y_3\\ 1 \end{array}\r... ...egin{array}{c} x_1 \\ x_2 \\ x_3 \\ 1 \end{array} \right ]$$ (10.2)

This method can be used to transform all linear transformations into linear algebra operations on $4\times4$ matrices. This enables easy concatenation (matrix multiplication) and inversion (matrix inversion). Note also that a linear transformation can have at most 12-free parameters. There are 3 general types of linear transformations as follows:

1. Rigid - these have six parameters (3 rotations and 3 translations)
2. Similarity - these have seven parameters, rigid + overall scale factor
3. Affine - this is the general linear transformation group and has 12 parameters.

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