Data set description

This section describes both the synthetically generated data and the clinical data used for the image registration assessment.

Random synthetic data generation

The synthetic data set consists of the synthetically generated reference images, and the ground truth deformation fields (velocity fields) warping the reference images to

Figure 4.1: Example of the synthetically generated data: (from left to right) - fixed image, fixed image warped by the deformation field, and the grid warped by synthetically generated deformation field.

obtain the moving image.

The reference images were generated from a random zero-mean and unit variance Gaussian image process defined for all points of a two-dimensional regular grid of size 64x64. Then, the generated image is smoothed by a low-pass filter, scaled into the range r0.0, 1.0s, and padded with a black border to avoid the edge artifacts during image registration. The sample of the synthetically generated image is shown in Figure 4.1.

The known velocity fields were generated from two independent random zero- mean and a three pixel standard deviation Gaussian velocity process defined on the selected knots of the sparse two-dimensional regular grid of size 12x12. Then, for both components of the velocity field the repeatable low-pass filtering procedure was applied to obtain a desirable smoothness (the determinant of the Jacobian matrix has to be positive). Finally, velocity fields were interpolated to the finer grid resolution (64x64) with cubic spline interpolation and then scaled and exponentiated to get a wide range magnitudes of diffeomorphic deformation fields. This procedure of generating deformation field is similar to the state-of-the-art method described in [17] that was used to validate the Baker-Campbell-Hausdorff formula for calculation of the velocity fields. The sample of the synthetically generated deformation field is shown in Figure 4.1 and in Figure 4.2.

Real data

The real data used for the validation consist of two public available data sets and one available at the University of Central Lancashire.

The data sets include:

• POPI (POPI stands for the Point-validated Pixel-based Breathing Thorax Model) computed tomography of lungs with the landmarks manually selected

Figure 4.2: Example of the partially synthetically generated data: (from left to right) fixed image - the axial slice from MRI brain volume, fixed image warped by the deformation field, and the grid warped by synthetically generated deformation field.

by the medical experts for assessment of the image registration quality. The data were obtained by the Léon Bérard Cancer Center & CREATIS Laboratory in Lyon, France and are freely available to download from the Internet. For the data, the set of the landmarks is attached thereby the target registration error (T RE) can be calculated as a quantitative measure and compared to other method published on the aforementioned web page. Further details of the data sets can be found in [141]. The data set consists of ten volumes with the size of 482 x 360 x 141 and the resolution is 0.976562mm x 0.976562mm with a slice thickness of 2.0mm. This particular set was used for validation of the registration method by [43]. Thus far, various in-house data sets of the lungs were usually used for the validation [159, 73, 75, 74, 36]. The example of CT lung data are shown in Figure 4.4.

• BrainWeb data set consists of 20 anatomical models of 20 normal brains [8]. Each anatomical model is labelled thus each tissue class (each brain structure) can be found in the volume. The structure of brains is divided into 12 classes: Background, CSF, Gray Matter, White Matter, Fat, Muscle, Muscle/Skin, Skull, Blood vessels, Connective (region around fat), dura mater and bone marrow. Therefore, the registration quality can be assessed by the segmenta- tion accuracy. With one of the models used as a reference and the remaining models registered to it, the ground truth labelling of the reference image is compared with the labelling achieved by the warping labels of the registered images. The segmentation accuracy is calculated based on the region overlap- ping (RO) of the different structures. The data set consists of 20 volumes of size 256 x 256 x 181 with the spatial resolution of 1.0mm x 1.0mm x 1.0mm. In this comparison work, the first ten volumes was used only. The reason

Figure 4.3: Example of MRI brain data (left) and their ground truth (manual) labelling (right) used in the experimental validation.

for selecting the brain image data set is motivated by the literature findings, where the brain annotation is most often used as a quantitative measure of the image registration algorithms [27, 162, 4, 143, 144, 145, 136, 68]. The example of MRI brain data are shown in Figure 4.3.

• Data set of the MRI images of the pelvic-area organs. The data exhibit sig- nificant changes of the bladder size and shape. The quality of the registration can be assessed in a similar manner as in the case of the brain data due to the labelling provided for the anatomical structures such as the prostate and the bladder. The data set consists of five volumes of size 240 x 320 x 30 with the spatial resolution of 1.0mm x 1.0mm x 3.0mm representing one subject with shape changes of bladder, rectum, and prostate. The pelvic-area image registration is also very common issue as the potential benefits of the accurate registration can be entirely applied to the radiotherapy of the prostate cancer. The example of MRI brain data are shown in Figure 4.5.