We present a hybrid three-dimensional (3D) unwrapping algorithm that combines the strengths of two other fast and robust existing techniques. In particular, a branch-cut surface algorithm and a path- following method have been integrated in a symbiotic way, still keeping execution times within a range that permits their use in real-time applications that need a relatively fast solution to the problem. First, branch-cut surfaces are calculated, disregarding partial residue loops that end at the boundary of the 3D phase volume. These partial loops are then used to define a quality for each image voxel. Finally, unwrapping proceeds along a path determined by a minimum spanning tree (MST). The MST is built according to the quality of the voxels and avoids crossing the branch-cut surfaces determined at the first step. The resulting technique shows a higher robustness than any of the two methods used in isolation. On the one hand, the 3D MST algorithm benefits from the branch-cut surfaces, which endows it with a higher robustness to noise and open-ended wraps. On the other hand, incorrectly placed surfaces due to open loops at the boundaries in the branch-cut surface approach disappear.
© 2009 Optical Society of America
Original Manuscript: July 13, 2009
Revised Manuscript: August 25, 2009
Manuscript Accepted: September 15, 2009
Published: November 6, 2009
Miguel Arevalillo-Herráez, Munther A. Gdeisat, and David R. Burton, "Hybrid robust and fast algorithm for three-dimensional phase unwrapping," Appl. Opt. 48, 6313-6323 (2009)