## 3 Results and Discussion
### Impact of Decalcification on the Hard Tissue Microstructure
The similarities between tissue morphology from the non-decalcified and the decalcified bone, together with landmark anchoring, form the basis for the non-rigid registration procedure. Registration accuracy was evaluated based on 50 landmark pairs from an expert (LM2). The mean Euclidean distance between these landmark pairs improved from (361 \(\pm\) 218) \(\upmu\)m (purely rigid), via (119 \(\pm\) 75) \(\upmu\)m (rigid and isotropic scaling) to (83 \(\pm\) 62) \(\upmu\)m (non-rigid). Note that this result compares favorably to the voxel sizes of the images, namely 20.7 and 27.8 \(\upmu\)m. The non-decalcified tissue required a global shrinkage by 21.7% due to isotropic  
Figure 6: Turquoise- or orange-colored tomography data obtained before decalcification was registered, rigid and non-rigid, respectively, to the synchrotron radiation-based tomography data, grayscale image, and shown in the three orthogonal directions. Contour lines overlayed on the decalcified image show correspondence. The two middle columns demonstrate the need for the application of non-rigid registration procedures. scaling in rigid registration and a mean shrinkage of 20.0% for non-rigid alignment to fit the decalcified tissue. From visual inspection and registration accuracy, we can conclude that non-rigid registration yielded the desired correspondence between tomographic data obtained before and after decalcification. This correspondence is a prerequisite to generate a bi-variate histogram, which is shown in Figure 7. A bi-variate histogram is a useful means for evaluating the relationship between gray values of corresponding voxels in the two three-dimensional datasets. Therefore, such a diagram is also termed a joint histogram. In this study, the laboratory-based \(\mu\)CT data only allow for visualizing bone. The calcium content varies widely within the distracted jaw, as demonstrated by the histogram in Figure 7. Note that the greyscale bars in Figure 7 correspond to the greyscales used for the virtual slices in the following figures. The highest X-ray attenuation values were found for dense mature bone, while less attenuation was noted for bone formed during the consolidation phase of distraction osteogenesis. Some voxels were only partly filled by bone and thus gave rise to partial volume phenomena. The highest frequency, of about 2 \(\times\) 10\({}^{7}\), was found for the first bin, which relates to surrounding media but also includes soft tissue components, which hardly show attenuation of the X-ray photons used. Figure 7: Bi-variate histogram of the common volume measured before decalcification using conventional \(\mu\)CT (nanotom m), and after decalcification using the synchrotron radiation facility (SR\(\mu\)CT). The projection of these logarithmically presented bi-variate data to the axes yield the univariate histograms of the individual tomographic datasets. Note that the soft tissues are almost transparent for the nanotom study, and hence the first bin reaches a value greater than 10\({}^{7}\). The univariate histograms shown in lighter colors and with about two orders of magnitude lower frequencies capture the distribution of the virtual slice corresponding to the histological section, see below. The orange-colored histogram in Figure 7 is derived from SR\(\upmu\)CT data and exhibits three peaks. The sharpest peak at an X-ray absorption slightly above 1 cm\({}^{-1}\) corresponds to paraffin employed for embedding after decalcification. The peak slightly below an X-ray absorption of 2 cm\({}^{-1}\) originates from the soft tissues, as illustrated in the subsequent images. The third peak at an X-ray absorption of about 2.5 cm\({}^{-1}\) can be associated with newly formed and old bone. The grayscale bar shows X-ray absorption values as represented in the related slices in Figures 5 and 6 and the figures below. The bi-variate histogram supported a direct comparison between the two tomography datasets regarding the decalcification process, but it is limited for further conclusions.