# Measurement-Driven Synthesis of Female Digital Mannequin Using Convex Sub-Volumes
## 3 Materials and Methods
### Cleaning of Reference Mannequin Geometries  
Since the Reference Mannequins \(RM\) constructed in Section 3.3 are manually built, the reference coordinate system on which each model is created may be different. In addition, the models may not be symmetric with respect to sagittal plane, and the orientations (local coordinate system) of **corresponding ellipsoids** may posses high morphing. Consider \"corresponding ellipsoids\" as the ellipsoids that are the same topological entity (e.g., 13.a Rectus Abdominalis) and belong to different mannequins from \(RM\). All of the mentioned factors, if not corrected, will lead to an erroneous creation of \(F\) and, as a consequence, to the incorrect synthesis of mannequins. Hence, the geometric data of all mannequins in \(RM\) are sequentially processed and corrected to ensure consistency in the set. The process for correcting the geometric data is as follow:  
1. A common SO(3) coordinate system (WCS) is defined;
2. The position of each model is corrected according to WCS to ensure common placement;
3. The orientations of the sets of corresponding ellipsoids are corrected to ensure minimum variation between analogous axes;
4. The ellipsoids in the right hemisphere are omitted and replaced by reflections (with respect to the sagittal plane) of the ellipsoids in the left hemisphere to obtain symmetry;
5. Central ellipsoids are corrected in order to posses symmetry with respect to themselves along the sagittal plane. **Correction of Mannequins Position**  
A registration process is performed to define a common placement for the Reference Mannequins. This process consists of defining a set of landmarks and a common coordinate system (WCS), and placing the Reference Mannequins in the same position with respect to the WCS. These landmarks are based on **anatomical planes**(see Figure 10) that are widely used in medical fields. Such anatomical planes represent an infinite set of planes perpendicular to the axis in which they are defined:  
1. **Coronal plane:** Perpendicular to the ground. Separates front from back. 2. **Transverse plane:** Parallel to the ground. Separates head from feet. 3. **Sagittal plane:** Perpendicular to the ground. Separates left from right. Now that the directions of the axes \(\overrightarrow{X}\), \(\overrightarrow{Y}\), \(\overrightarrow{Z}\) of WCS are given by the normals of the coronal, sagittal, and transverse planes, respectively, the origin (position) of WCS is defined. Such an origin is defined for each Reference Mannequin as follows [40] (see Figure 11):  
1. In the \(\overrightarrow{Z}\) direction, the origin is set in the lowest coordinate of the feet;
2. In the \(\overrightarrow{X}\) direction, the origin is set in the centroid of the shoulder ellipsoids (10.a Trapezius) from the lateral view;
3. In the \(\overrightarrow{Y}\) direction, the origin is set in the middle point between shoulders (viewed from the front). Figure 9: Set \(RM\) of Reference Mannequins as ellipsoid mannequins (no cushions) of extreme and average models. From left to right: Small Chubby, Small Slim, Average, Tall Slim, and Tall Chubby. **Processing of Ellipsoid Orientation**  
Now that a common global coordinate system is defined for all mannequins, sets of corresponding ellipsoids should also have a similar coordinate system orientation. Knowing that corresponding ellipsoids differ in geometry (dimensions, position, and orientation), the goal is to obtain smooth morphing or minimal variation (see Figure 12) rather than equal orientation. Take, for instance, the example in Figure 12a; it shows that analogous axes (e.g., \(X_{1}\)'s) of corresponding ellipsoids may posses large variation in their orientations. Averaging orientations (applying \(F\)) with such morphing (variation) will lead to erroneous results. In order to make up for the large variation between analogous axes, two processes are performed.