Fast opening functions and morphological granulometries
Luc M. Vincent · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1994
In this paper, a comprehensive set of fast algorithms for computing granulometries in binary images is first proposed: linear granulometries (i.e., granulometries based on openings with line segments) constitute the easiest case, and are computed using image `run-length'. The 2D case (granulometries with square or `diamond'-shaped structuring elements, or granulometries with unions of line-segments at different orientations) involves the determination of opening functions or granulometry functions. The grayscale case is then addressed, and a new algorithm for computing grayscale linear granulometries is introduced. This algorithm is orders of magnitude faster than any previously available technique. The techniques introduced in this paper open up a new range of applications for granulometries, examples of which are described in the paper.