Finding minimum spanning trees more efficiently for tile-based phase unwrapping.

Abstract

The tile-based phase unwrapping method employs an algorithm for finding the minimum spanning tree (MST) in each tile. We first examine the properties of a tile's representation from a graph theory viewpoint, observing that it is possible to make use of a more efficient class of MST algorithms. We then describe a novel linear time algorithm which reduces the size of the MST problem by half at the least, and solves it completely at best. We also show how this algorithm can be applied to a tile using a sliding window technique. Finally, we show how the reduction algorithm can be combined with any other standard MST algorithm to achieve a more efficient hybrid, using Prim's algorithm for empirical comparison and noting that the reduction algorithm takes only 0.1% of the time taken by the overall hybrid.