Chapter 4 Voxels and Cells

Volumes of data are usually treated as either an array of voxels or an array of cells. These two approaches stem from the need to resample the volume between grid points during the rendering process. Resampling, requiring interpolation, occurs in almost every volume visualization algorithm. Since the underlying function is not usually known, and it is not known whether the function was sampled above the Nyquist frequency, it is impossible to check the reliability of the interpolation used to find data values between discrete grid points. It must be assumed that common interpolation techniques are valid for an image to be considered valid.

Figure 1.2:Voxels. Each grid point has a sample value. Data values do not vary within voxels

The voxel approach dictates that the area around a grid point has the same value as the grid point (Figure 1.2). A voxel is, therefore, an area of non-varying value surrounding a central grid point. The voxel approach has the advantage that no assumptions are made about the behavior of data between grid points, only known data values are used for generating an image.

Figure 1.3: Cells. Data values do vary within cells. It is assumed that values between grid points can be estimated. Interpolation is used

The cell approach views a volume as a collection of hexahedra whose corners are grid points and whose value varies between the grid points (Figure 1.3). This technique attempts to estimate values inside the cell by interpolating between the values at the corners of the cell. Trilinear and tricubic are the most commonly used interpolation functions. Images generated using the cell approach, appear smoother than those images created with the voxel approach. However, the validity of the cell-based images cannot be verified [16].