Volume reconstruction

Due to the representation of complex objects using point samples it is very likely that some information is lost. One could consider small details, for example hair on the skin of a patient, which are smaller than the sampling distance and therefore inevitably lost. From a visualization point of view it would be easy to say that this is the problem of sampling, that is, the problem of these people who devise and build the modalities which produce the data sets. If the information is not in the data set it cannot be visualized.

However, this would be much of a simplification. A visualization algorithm often consists of several steps, which are described by a so-called volume visualization (or rendering) pipeline. This pipeline describes the steps necessary starting from a raw data set to the rendering of the final image which often involves several sampling and reconstruction processes.

Figure: The volume rendering pipeline as suggested by Levoy for his classic ray casting algorithm (image taken from the paper [26]).

Let us take a look at the volume rendering pipeline as proposed by Levoy for his classic ray casting algorithm [26]. This pipeline is depicted in Fig. 1.1 (taken from the original paper [26]). It starts with a three-dimensional array of acquired scalar data values, for example from CT or MRI. The first step is then data preparation, which can be, e.g., resampling on a regular grid if the original grid was not, correction for patient motion, contrast enhancement, or sampling of additional slices. These reworked values then are shaded and classified, producing one array of voxel colors and one of voxel opacities, which then again are resampled along rays casted through every pixel on the image plane. These samples then are composited to produce the final image. Of course, the visualization pipeline looks different for different algorithms. So would the pipeline for an algorithm which fits geometrical primitives into the data (like the marching cubes algorithm [29]) contain steps for the fitting and rendering of the primitives.

So starting from the initial sampling procedure by the modality, like CT or MRI, several resampling and reconstruction steps follow during a visualization algorithm. Not yet mentioned is the final resampling, performed by the finite number of rods and cones in our eyes, and reconstruction step, by our brain. However, this issue is far beyond the scope of this work.

Nevertheless, this short review shows the importance of having a deeper understanding of what happens during sampling and reconstruction when dealing with volumetric data and it motivates to take a closer look at this subject.