Volume octree with an implicitly defined dual grid

Volume data are usually represented as a uniform structured grid. Nevertheless, this representation imposes large memory requirements when large volumes are stored. Hierarchical representations, can be used to reduce either memory requirements or rendering time. Their use to store the volume model make the surface extraction process more complex, as cracks may appear on the boundary of cells with different size. When they are used only as an index to the cells of the grid the memory requirements are increased. Dual cells method has been proposed to solve cracks problems, but it require to explicitly generate a dual grid, which increases the memory requirements. This paper presents a new, octree based, multirresolution representation for volumes that implicitly stores the dual grid using just one byte per leaf node. Isosurfaces are built from these implicitly stored dual cells on the fly when the voxel octree is traversed. Our proposal permits to have a volume represented by a hierchical structure without storing both structures, the grid of samples and the index tree; just the tree stores all the information. So, we can have a storage requeriment similar to a grid and a visualization time similar to a structure that uses an index tree.