Efficient and Robust Path Openings Using the Scale-Invariant Rank Operator
Path openings and closings are efficient morphological operators that use flexible oriented paths as structuring elements. They are employed in a similar way to operators with rotated line segments as structuring elements, but are more effective at detecting linear structures that are not necessarily locally perfectly straight. While their theory has always allowed paths in arbitrary dimensions, de facto implementations were only proposed in 2D. Recently, a new implementation was proposed enabling the computation of efficient <i>d</i> -dimensional path operators. However this implementation is limited in the sense that it is not robust to noise. Indeed, in practical applications, for path operators to be effective, structuring elements must be sufficiently long so that they correspond to the length of the desired features to be detected. Yet, path operators are increasingly sensitive to noise as their length parameter <i>L</i> increases. To cope with this limitation, we propose an efficient <i>d</i>-dimensional algorithm, the Robust Path Operator, which uses a larger and more flexible family of flexible structuring elements. Given an arbitrary length parameter G, path propagation is allowed if disconnections between two pixels belonging to a path is less or equal to G and so, render it independent of <i>L</i> . This simple assumption leads to constant memory bookkeeping and results in a low complexity.