Computing Scalar and Vector Fields

Scalar-based maps and vector fields of anisotropy, as well as scalar-based maps of volume fraction, can be computed from bone segmentations within the area defined by a Box shape (see Scalar and Vector Fields). Visualizations of vector-based maps are available in the 3D views in the workspace, while the mapped scalar values can be examined in both 2D and 3D views.

Vector fields of anisotropy magnitude (left) and orientation (middle) of a proximal femur and scalar-based map of volume fraction (right)

The inputs for computing scalar and vector fields can be any region of interest, while the outputs of anisotropy and volume fraction mapping include the following:

Anisotropy of… Scalar-based map of anisotropy, as computed with the MIL or Surface normals algorithm(channelAnisotropyMapping).

Eigenvector max of… Orientation field of the eigenvector associated to the highest eigenvalue (vectorFieldEigenvectorMax).

Volume fraction of… Scalar-based map of volume fraction (channelVolumeFractionMapping).

1. Advance to the Compute Scalar and Vector Fields page of the Bone Analysis Wizard.
2. Select a mapping method — MIL, Surface normals, or Volume fraction — in the Algorithm drop-down menu (see Scalar and Vector Fields for a description of these algorithms).

   

3. Select the region of interest that you want to map in the Bone drop-down menu.

   

4. Select the Box shape that will define the region within which you want to compute the mapping in the Area box drop-down menu, as required.

   

   Note You can choose the 'Default mapping box' or any other available box (see Adding and Editing Shapes). You can add multiple boxes to compute anisotropy and volume fraction maps in different orientations.

5. Adjust the size and position of the area box, as follows and as required.
   • Make the shape visible by clicking its associated Eye and 3D icons in the Data Properties and Settings panel.
   • Adjust the size and position of the shape, as required (see Editing Shapes for information about resizing, rotating, and repositioning shapes).

     

     Note In cases in which you need very precise measurements and plan to use a small spacing value, you should reduce the box as much as possible.

   • Lock the shape by checking the Locked option in the Visual effects box, recommended.

     

6. Enter the required spacing value in the Spacing edit box (see Global Settings for Computing Scalar and Vector Fields).

   Note If you are computing anisotropy for a large region, you may consider increasing spacing or the radius of influence from the lowest value to reduce processing times. If you computing maps within a smaller sub-volume, you can decrease sampling spacing or the radius of influence.

   Note For faster computations, and to obtain orientation fields that are easier to observe, you can select the Use single voxel in direction with smaller box length option. In this case, computations will limited to a single voxel in the direction of the smallest length of the selected area box.

7. Enter the required settings for the selected algorithm.
   • If you are computing scalar and vector fields of anisotropy, refer to the topic Settings for Computing Anisotropy.
   • If you are computing volume fraction, refer to the topic Settings for Computing Volume Fraction.
8. Click the Compute Scalar and Vector Fields button to start the computation.

   This will map the anisotropy of 3D surfaces — their preferred orientation and the direction of that preferred orientation with respect to the Cartesian coordinates — or the volume fraction.

   At the end of the process, the requested vector field and/or generated dataset with scalar values will appear in the Data Properties and Settings panel.

   

   Note Refer to the topic Visualizing Vector Fields of Anisotropy for information about visualizing vector fields of anisotropy and Visualizing Scalar-Based Maps for information about visualizing scalar-based maps of volume fraction.