Volume data can be calculated from the two- dimensional radiographic images.  This   is analogous   to   the   pixel   (picture   element) which 2D image processing sensors use to represent the local light intensity of the image in an equidistant, planar array.  The voxel (volumetric pixel) is used in X-ray tomography to describe the local radiation absorption in an equidistant, spatial array.  Dark voxels represent areas with low absorption (e.g. air), while bright voxels are areas with high absorption (e.g. metal). Analogous to the negative imaging of light intensity in black and white photography, the absorption values appear in reverse.  Voxel data are typically calculated from the 2D radiographic images (projection data) using the filtered back projection method.  Image reconstruction is essentially done in three steps:

  • Data preparation
  • Filtering
  • Back projection


Preparation includes standardizing the projection images, followed by taking the logarithm in order to obtain a linear characteristic. This replaces the exponentially decaying behavior of the beam penetrating the material (the radiation arriving in each volume element, which has already been attenuated by previous volume elements, is attenuated yet again) with a linear model. The gray-scale values in the projection images no longer correspond to the measured intensities. Rather, they are the sum of absorption or density values of the object along the beam path of the X-ray. This sum is also known as the line integral. In practice, this means that each pixel value in the X-ray sensor represents exactly the sum of all voxel values along the beam through the (still to be calculated) volume. To calculate this volume from the prepared projection data, the procedure to create these sum values is mathematically inverted. This requires filtering of the projection data.

See in image above from pixel to voxel the 2D image stack (a) the 3D image of the volume is created and represented by voxels (b).