The Hierarchical Splatting ([4]) group as large as possible homogeneous sections in the volume and consider it as one large cell. Such a cell is approximated with one large splat, which is projected on the image plane. Every node of the pyramid contains the average RGB and alpha of its children and the associated average error if you approximate this region with one average splat, instead of using the original volume data. For adjusting progressive refinement you choose an error which is a measure for the wanted homogeneity. With the user-specified error you determine the traversal through the pyramid. You move down the pyramid until the error in a node is less equal than the desired error or homogeneity. Now the whole volume data is decomposed in cubes of different sizes depending on their homogeneity.
 

If you select a large error the volume is decomposed in fewer subvolumes, the number increases with decreasing error. For every level of the pyramid are calculated proper sized footprint tables, which are used for projecting and compositing cells of this level. Further the splats are approximated with Gouraud shaded RGBA polygons, so you can use hardware for compositing and drawing.