## 4 Discussion
### Literature Analysis
#### 4.2.2 Description of Advanced Computerized Techniques for Image Processing Pre-Processing
Therefore, any measurement may be performed automatically, since all the spatial coordinates of all the voxels (the 3D equivalent of 2D pixels) are known, with all of them having been grouped into separated voxel clouds corresponding to the individual bones. Using these data and stepping up from classical measurements, new tools have been reported on in the literature to improve visualization and our comprehension of pathological processes. We present these below:  
1. Absolute and Relative 3D Bone Measurement Reporting  
Theoretically, an infinite number of measurements are possible, hence the diversity of measurements described in this area of the literature [16; 21; 22; 26; 52; 53; 54; 55; 56; 57; 58; 59; 60; 61; 62; 63; 64]. In more practical terms, considering there are on average 28 bones in the foot and ankle, each with a center of mass that has three spatial coordinates and three inertial vectors each, with each having three spatial coordinates, each bone may be described by a set of 12 'absolute' coordinates, which are calculated within the WBCT frame of reference (Figure 8). This frame is referenced by the floor plane for the two vertical (sagittal and coronal) planes. There is no consensus on how to set the rotation in the axial plane, but the most commonly used is traditionally the second metatarsal or the bisector of the forefoot in 3D biometrics papers [48]. However, the possibility of relative measurements is remote, as any of the 12 absolute coordinates in each of the 28 bones can be described relative to any of the 12 absolute coordinates of the 27 other bones, which equates to \(12^{27}\) possibilities. This huge number explains why there has always been a quest to discover new measurements in the realm of musculoskeletal research. Things were easier with 2D radiography, which results in dimensional reduction, thus reducing the possible number of measurements, albeit with a non-negligible loss of information. After the introduction of WBCT, a need has arisen to find and promote a standardized methodology for describing bone orientations in space, which is among the tasks of the International WBCT society mentioned above. However, the industry has anticipated this and is already proposing different off-the-shelf software solutions to provide systematic reporting of bone and joint angles, based on the historical literature, including such widely used angles as the M1-M2 angle for hallux valgus assessment, or the hindfoot alignment angle for deformity assessment. However, even these may be defined differently depending on the software provider, hence the importance and urgency of an international consensus on this matter so that reports may be comparable across all software platforms. There are many reasons for these differences, not the least being the absence of consensus in the existing literature. Other reasons pertain to computerized techniques used to obtain absolute measurements [60]. The 3 main techniques reported are as follows [87]. 1--Principal component analysis (PCA) determines the center of mass and the three principal components or inertial axes of the bones through averaging the relative contributions of each spatial dimension, a rather common mathematical tool, but still complex to the layperson. Its advantage is that it can easily be made fully automatic. Its disadvantage is  
Figure 8: Example of a foot automatic measurement report (Disior OY/Paragon 28, Denver, CO, USA); (**a**) example of M1-M2 angle illustration; (**b**) example of forefoot measurement automated report. that it provides slightly different results depending on the volumetric shape of considered bones, which can be otherwise interpreted as increased variability in measuring anatomical axes depending on surface landmarks. 2--Statistical shape modelling averages a large number of real-life examples from pre-existing datasets of bones to create a library to which a given bone may then be compared. Once the bone has been recognized, its orientation can be derived from that of the library example.