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Research into two-dimensional phase unwrapping has uncovered interesting and troublesome inconsistencies that cause path-dependent results. Cellular automata, which are simple, discrete mathematical systems, offered promise of computation in a nondirectional, parallel manner. A cellular automaton was discovered that can unwrap consistent phase data in n dimensions in a path-independent manner and can automatically accommodate noise-induced (pointlike) inconsistencies and arbitrary boundary conditions (region partitioning). For data with regional (nonpointlike) inconsistencies, no phase-unwrapping algorithm will converge, including the cellular-automata approach. However, the automata method permits more simple visualization of the regional inconsistencies. Examples of its behavior on one- and two-dimensional data are presented.
Ghiglia et al. (1987) studied this question.