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. They have been used as index to the cell grid, but this increases memory requirements, as both the tree and the grid must be stored. They have also been used as a direct representation of the volume model, but this makes the surface extraction process more complex, as cracks may appear on the boundaries of different-sized cells. A dual cell method has been proposed to solve the problems of cracks, but this approach requires the explicit generation of a dual grid, which also increases memory requirements.This paper presents a new, octree based, multi-resolution representation for volumes that do not need to store the dual cell grid, while generating high-quality crack-free isosurfaces. Our proposal utilizes a dual cell grid that is implicitly stored in the tree using just one byte per leaf node. Isosurfaces are built on the fly from these implicitly stored dual cells when the voxel octree is traversed.