Digital morphological curvature flow
Résumé
Morphological filters are defined as increasing and idempotent filters. Openings, being anti-extensive and closings, being extensive, are extremal such filters. Other filters are combinations of openings and closings. In order to obtain a graceful filtering effect, one uses alternate sequential filters, based on a sequence of alternating openings and closings of increasing size. A disk of radius ro cannot enter into a convex part of a particle with a curvature higher than ro. For this reason, an opening by disks will suppress convex zones of high curvature ; in a dual way closings by disk suppress concave zones of high curvature. This is not the sole effect of an opening, as a disk of radius ro also cannot enter particles or parts of particles smaller than ro. Similarly a closing by such a disk will suppress thin channels between particles. This dual behavior of openings and closings, acting simultaneously on convex and concave zones but also suppressing narrow particles and filling narrow channels between particles constitutes a drawback. Curvature flow filters overcome this drawback as they locally modify the boundaries so that only convex or concave zones are smoothed out. They are not influenced by the thickness of the particles or the channels between particles. The talk is organized as follows: • Definition of digital distances and digital geodesics on a grid • Definition of zones of high curvature as overlapping zones between geodesics • Presentation of two algorithms working on the level lines of a grey tone image • Presentation of an algorithm working on all grey tones simultaneously • Introduction of “anisotropy filters”, better designated as filters whose effect is inhibited by high gradient zones • Illustration of the filtering effect
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