Ultimate Opening and Gradual Transitions

Ultimate Opening (UO) is a powerful operator based on numerical residues. In a multi-scale framework, it analyzes an image under a series of increasing openings. Contrasted objects are detected when they are filtered out by an opening, generating an important residue. Gradual transitions make this operator underestimate the contrast of blurred objects. In this paper we propose a solution to this problem, integrating series of non-null residues. The resulting operator handles correctly blurred boundaries, without modifying the behavior on sharp transitions. keywords Numerical residues, ultimate opening, attribute opening, image segmentation, mathematical morphology.