An Algorithm for Fast Voxel Scene Traversal

Abstract

Together with improvement of tomographic method of scanning 3D data, residing in an increase of distinguishing ability of the scanners, the quality of final 3D reconstruction of the data comes into foreground. An inevitable condition for visualization of small details, comparable with the voxel size is application of such algorithms, which enable to define a surface of the scanned object on subvoxel level. Comong out from paper published at previous year of Winter School on Computer Graphics and CAD Systems we present an algorithm for fast traversal of the voxel scene, which enables to find a nearest intersection of a ray with the object surface defined in such way. High speed of the algorithm utilizes object coherency of the scene, which means that voxels belonging to the object are usually grouped in connected regions.

The algorithm consists from two steps : preprocessing and scene traversal. In the preprocessing phase we assign to each background voxel of the segmented scene a value equal to its chessboard distance from the nearest object voxel, which defines a cubic macro region with no voxels inside. While generating a discrete ray, we can jump over this region, which results in up to 6-fold speed up of the traversal. The algorithm has no additional demands on memory, since the distance is stored in originally "empty" background voxels.