  This paper deals with computing topological invariants such as connected
components, boundary surface genus, and homology groups. For each input data
set, we have designed or implemented algorithms to calculate connected
components, boundary surfaces and their genus, and homology groups. Due to the
fact that genus calculation dominates the entire task for 3D object in 3D
space, in this paper, we mainly discuss the calculation of the genus. The new
algorithms designed in this paper will perform:
  (1) pathological cases detection and deletion, (2) raster space to point
space (dual space) transformation, (3) the linear time algorithm for boundary
point classification, and (4) genus calculation.
