A pyramid is a hierarchical multilevel and multiresolution data representation, where every level contains a different resolution version of the whole volume data. The level increases with decreasing resolution. In order to generate a pyramid every level is constructed depending on the level below, where normally the original volume data is the base level. In order to construct one level in general n1xn2xn3 voxels (data points) are replaced by one data point in the next level. Normally n1, n2 and n3 are equal 2, so every time 8 voxels are replaced. All approaches introduced here proceed in this way.
 

There are several functions used, in order to get a value for this new point, like the order, the minimum, the maximum, the average and so on. Either the function is only applied to the replaced voxels or also to some of the surrounding cells. In the nodes of a pyramid can be stored data points, colors, opacities and some additional informations like the error which is associated with representing a section of the volume with a lower resolution, instead of with the full possible resolution.