Efficient and Robust Path Openings using the Scale-Invariant Rank Operator

Some basic properties of a slightly generalized version of the scale-invariant rank operator are given, and it is shown how this operator can be used to create a nearly scale-invariant generalization of path openings that is robust to noise. Efficient algorithms are given for sequences and directed acyclic graphs with binary values, as well as sequences with real (greyscale) values. An algorithm is also given for directed acyclic graphs with real weights. It is shown that the given algorithms might be extended even further by allowing for scores based on a totally ordered semigroup.