Material transitions are important for some of the anatomical models. There are ba- sically two kind of transitions in the medical models of interest to my client. One is along the object, and the other is through the object. To obtain this transition for the models, a thresholding scheme is applied to the values in the X2U map.
Figure 4.2: Along-object material transition field for the scm. Left: the X2U map on the model. The red channel encodes u, the green channel encodes v, and the blue channel encodesτ. Right: the material transition field along the model. The red channel encodes the first region, the green channel encodes the second region, and the yellow channel encodes the transition region between the first region and the second region.
according to the depth (e.g., bone), a thresholding scheme is applied on the depth information that is provided by the parameterτ. Using the fact that τ is zero at the medial sheet and 1 on the boundary, the regions are classified by the user by setting threshold values forτ (e.g., 0< τ <0.5 is the marrow region, 0.5< τ <0.7 is the interior bone region, and 0.7< τ <1 is the exterior bone region).
2. Transition along the model: For the models in which the material changes along the model (e.g., muscles), a thresholding scheme is applied based on user selection on the along-object coordinate that is provided by the parameteru (Figure 4.2).
After regions are classified using the model-based thresholding scheme, this informa- tion is used to compute a smooth transition field,st, for each voxel inside the model. The main advantage of this approach is that it gives consistent transition fields for different instances of the same anatomical organ.
4.3.1
Adding randomness to the transition regions
Although the thresholding scheme works well for obtaining uniform transitions along the desired directions, in Frank Netter, MD’s illustrations, the transition is more random along that transition region. For example, in Figure 4.3 there is a randomness in transition field in addition to the distinction between the regions.
Figure 4.3: An illustration of the scm from Netter (2009). The transition between the red and white regions on the scm is not smooth. (@2011 Elsevier)
Figure 4.4: Along-object material fields can be modified by adding randomness around the thresholds via the sketch-based interface presented in Takayama et al. (2008a). (Left) two lines drawn on the model; (left-middle) part of the model between the lines; (right-middle) an example of regions specified for the model; (right) another example of regions specified for the same model.
To obtain randomness in the transition regions on the models, the sketch-based interface proposed in Takayama et al. (2008a) is adapted. In Takayama et al. (2008a)’s approach, the user is allowed to put colored points on the 3D model by clicking the mouse on the surfaces. The user has the ability to cut off the model, if s/he wants to place the points on the inner regions of the model. After assigning the points on and inside the model, the system computes a smooth material transition field inside the model. In this dissertation the position and colors of these points are obtained from medial-coordinates and the lines drawn by the user. The steps of the proposed approach in this dissertation are as follows:
1. Load the model with its medial representation: This step consists of loading both the 3D mesh of the model and the model-based coordinates of each vertex of that model.
2. Specify model-based regions along and through the object: This step is done using ranges of u. (The method can be extended to ranges in τ as well.)
3. Assign a region label value to each specified region of the object surface: These label values will be used in step 6 as constraints to compute a smoothly varying color field across the voxels within the object. Here a fixed label value is assigned
to all vertices whose u value falls in the range specified for that region.
4. Add randomness to the boundaries between adjacent regions: This step is achieved by drawing a piecewise linear curve around the thresholded region boundaries using the sketch-based interface. These curves are applied at all depths relative to the screen (Takayama et al. (2008a)). The subdivision of the mesh into subregions is updated based on the position of the curves.
5. Update the label values of the mesh vertices if their regions are changed: If the region of a vertex is changed from region 1 to region 2, then change the label of that vertex from 1 to 2.
6. Use interpolation to find a real label value for each voxel inside the model; these will be used to interpolate the textures between the regions . Here, thin plate spline interpolation (Turk & O’Brien (1999)) from the object surface vertex coordinates is used to find a smoothly varying scalar field in the 3D space.
Using this approach, different region boundaries can be obtained near the same thresholded region boundaries. Figure 4.4 illustrates some transition fields obtained using this technique.