Time-efficient computation of 3D topological functions

An important issue in 3D image processing is the identification of points (voxels) in the image 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 over relatively large 3D images. We report new very fast algorithms for computing functions which identify 3D simple points and related topological conditions using table-based methods which use a hierarchy of relatively small tables of pointers and some function tables. We compare time-storage tradeoffs for the new table-based methods with other table-based and propagation labeling methods for these computations.