# Three-Dimensional Anatomical Analysis of Muscle-Skeletal Districts
## 4 Results
### Follow-Up Evaluation: Erosion Sites' Identification for the Wrist District  
The dataset used for the analysis of the carpal district is composed of the 3D MRIs of the carpus associated with their segmentation. The MRIs were obtained from a 0.2 T extremity-dedicated machine (Esaote-Artoscan) using 3D T1-weighted sequences with reconstruction on the axial and sagittal plane. The voxel intensities were normalised between 0 and 1, 0 being black and 1 being white. The clinical experts performed the semi-automatic segmentation of the bones with a region-growing method [3] supported by the CAD system RheumatSCORE [46]. Since the segmentation was performed by medical doctors, the segmented surfaces were considered the ground truth without applying further processing, such as smoothing and re-meshing. The subjects suffer from degenerative rheumatoid illnesses at different stages. The carpus is one of the most indicated for diagnosing and monitoring rheumatic diseases since it is one of the first to show symptoms and damages linked to the pathology. For our analysis, we were interested in the five subjects that underwent follow-up exams, to analyse the pathology progression. For each of those subjects, two exams were present: one at baseline time (\(t_{1}\)) and one at follow-up time (\(t_{2}\)). The physicians or radiologists can visualise either the single bone or the overall district based on his/her necessity, but the changes in each bone over time are analysed separately. We included also the hand bones and the distal segment of the forearm bones; thus, we compared how 125 bones changed over time. The integrated method merges the information provided by the geometrical analysis and texture analysis. Considering only the geometrical or the texture information, the result could present false positives, i.e., areas identified as erosion, but that are healthy [1]. In Figure 4c, false positives are not present in the results of the integrated approach, where only the areas with erosion show higher integration values. The overall result is more homogeneous, thus indicating that geometry and texture information compensate for each other, discarding misleading classifications due to low image resolution or registration inaccuracies. Nevertheless, the integration result could miss some newly developed and small erosions. The red circles in Figure 4 indicate the small erosion correctly localised by the geometrical information, but missed by texture analysis. This suggests that the erosion could be at its beginning, implying a minor change in geometry and a small change in the cortical bone tissue, which could be still partly intact. The integration approach, which considers the linear combination of texture and geometry, is more flexible compared to the multiplication approach. Varying the value of \(\epsilon\), it is possible to tune the analysis concerning the type of search that the physician is carrying out. Figure 5 shows three different integration results according to the variation of the \(\epsilon\) value. Reducing the relevance of the geometrical information (\(\epsilon=0.5\), \(\epsilon=0.2\)), the resulting values lead to a more homogeneous result. This means that the false positive areas decrease in number along with the reduction of the geometrical information. However, an excessive reduction of the geometrical information brings also the presence of false negatives, that is the misclassification of erosion regions as healthy areas. Overall, the linear combination approach allows us to adjust the focus of the search and reach the desired trade-off between false negatives and false positives. The possibility to manually change the parameter \(\epsilon\) allows physicians and rheumatologists to adjust the visualisation according to their knowledge of the patient. If the physician analyses a patient at the early stages of pathology, then higher values of \(\epsilon\) will help to localise an early erosion.