# Three-Dimensional Anatomical Analysis of Muscle-Skeletal Districts
## 3 Geometrical and Texture-Based Features of Anatomical Districts
### Integrated Approach  
We now describe the integration of geometrical and texture-based features considered to obtain a unique and complete evaluation of both the follow-up and the single exams. In the case of a _single exam_, we have a 3D surface textured with the original volume grey levels, meaning that each vertex of the triangulation is associated with the grey-level values extracted from the image. As a geometrical feature, we considered the geometrical property that classifies each vertex in its functional region; as texture information, we considered the mean grey level of each functional region. This means that we can associate with the geometrical property the relative mean grey-level value of the region that it identifies on the surface, to visualise both properties in a unique analysis. We then compared how this association distributes over all the bones of the district of different subjects.  
For the analysis of _follow-ups_, we present two approaches that integrate the information extracted from the geometry and texture information. The distance distribution (geometrical information) is associated with each bone vertex at follow-up time and expresses the value of the distance between the bone at follow-up with the corresponding bone at baseline. From the texture analysis, each vertex of the follow-up district is associated with the value of the difference between the image grey levels at baseline and follow-up. In this way, each vertex composing the segmented surface in the follow-up is associated with a feature vector, composed of geometrical and texture information. In particular, the texture information presents intensities from \(-1\) to \(1\), since they are obtained from the difference of grey levels between \(0\) and \(1\). A value near \(1\) indicates a major change in the intensity of the  
Figure 3: Texture extraction through the application of the mapping method to the vertebral surface model in the three different criteria: (**a**) internal, (**b**) Euclidean, and (**c**) external. The difference in texture reflects the differences in tissue composition.  
image voxels, i.e., a radical change in tissue composition over time. A value of texture near \(-1\) might indicate a healing process, where the extension of an existing erosion has been reduced due to a specific therapy [19].  
The value of the distance, instead, varies from 0 to 1 depending on the entity of the geometrical deformation. The first option is to multiply the geometry and the texture values for each vertex. In this way, if a variation in geometry is associated with a high variation in texture (a value near 1), then the result has a higher total value. If a geometry change is close to zero, then the influence of the geometry has an impact on the total value lower than the grey levels in the texture. In this way, the pathological change will be highlighted only if the texture and geometry show a major variation, thus confirming that the bone has developed both a change in the morphology and tissue composition. As a second option, we considered a linear combination of geometrical and texture information. Calling \(d_{2}\) the distribution of the distances obtained by the geometry analysis and \(d_{1}\) the distribution of the texture changes in the grey levels analysis, the combined distribution is defined \(d_{1}+\varepsilon d_{2}\) with \(\varepsilon>0\). Varying the value of \(\varepsilon\), it is possible to emphasise geometrical or texture information.