Distance Field Calcualtion & Voxelisation

This tutorial demonstrates how to generate voxelised data and calculate distance fields, originally for use with the Volume2SurfaceCNN model.

We will use the example of a liver model and intraoperative surface, but this can be applied to any 3D model and partial surface. Data used for this example can be found in the GitHub repository.

Figure 1 - Original model/surface (left) and voxelised model/surface (right)

Creating a signed distance field from a 3D model

Setup parameters:

import numpy as np
from sksurgeryvtk.models import voxelise

The input mesh is expected to be in metres. If it is in mm, as above, we pass a scale factor of 0.001. Run voxelisation function:

The voxelise function returns a vtkStructuredGrid, but it also writes the data to the file specified by output_grid, which now contains a 3D volume, and a data array preoperativeSurface, which stores the distance value for each voxel in the grid.

Negative distance values indicate that the element is inside the surface. We can use this property to visualise the voxelised model using suitable software, e.g. ParaView.

If we apply a threshold filter only showing negative values, this will show the model surface:

Creating an usigned distance field from a surface

The process for creating a distance field for a surface is similar, except we calculate the unsigned distance field, which will be stored in a data array ‘intraoperativeSurface’.

The distance field can be calculated from a file, as above, or from a numpy array:

We can visualise the intraoperative surface, by using a threshold filter between 0 and the (roughly) voxel size, which is equal to size/grid_elements

Applying a displacement field to a mesh

Once a displacement field has been calcualted (e.g. by V2SNet in scikit-surgerytorch), it can be used to displace an input mesh. This could be the orginal preoperative surface, or objects inside the surface model (e.g. vessels, tumors). Objects outside the surface of the preoperative mesh do not have a valid displacement defined.

The output mesh can optionally be saved by specifying a file name for the save_mesh argument.

Streamlined Workflow

The above examples have been reading/writing vtk data to an output mesh on disk. However, this can be inefficient if we are repeatedly calling the function, and we can get the same results by just working with the vtk grid in memory instead. The voxelise function can take a vtkStructuredGrid, instead of a file path, as the output_grid agrument.