Time-efficient computations for topological functions in 3D images

An important issue in 3D image processing is the identification of points (voxels) which could be altered while leaving the topology unchanged-such points are referred to as simple points. We need time-efficient algorithms for identifying such points, since such computations are typically evoked over many iterations on large 3D images. We report new very fast algorithms for computing functions which identify 3D simple points and related topological conditions using “table-based” approaches which use a hierarchy of small tables of pointers. We also demonstrate time-storage tradeoffs which can be achieved by mixing table-based algorithms with more traditional techniques