Fundamentals of three-dimensional mathematical morphology

Three-dimensional mathematical morphology and its implementation in three-dimensional cellular automation are discussed. Automata having up to 262,144 PEs (processing elements) have been emulated using the Triakis software. Each PE in addition to its present state (either on or off) is permitted by Triakis software to store up to 20 previous states and is assigned a program word having 2^N binary locations (bits), where (N-1) is the number of neighbors to which the PE is connected. Triakis uses the FCC (face-centered cubic) tessellation, where the kernel is the tetradekahedron and N=13. The problem of embedding the tetradekahedron in the 64×64×64 array is addressed, and properties of the FCC tessellation are examined. The use of the approach for analyzing true three-dimensional binary data from CT (computer tomography) and MR (magnetic resonance) and three-dimensional binary arrays generated from column encoding gray-level imagery is reported