Ultimate opening: invariants, anamorphoses, and filtering

Abstract. This work is focused on the robustness of the ultimate opening (UO) and its associated function (AFUO) related to illumination changes and marker detection. It is well known that morphological filters commute to anamorphoses. This property ensures the robustness of the morphological filters to the lighting changes. However, the supremum of residues of these filters requires some conditions to commute to anamorphoses. Therefore, initially, a study of the robustness to anamorphoses is carried out. We demonstrate that the UO is invariant to linear anamorphoses and it is robust to power anamorphoses. On the other hand, related to marker detection, a study of the UO and AFUO is carried out. It is detected that small pieces of discs corrupt the UO, complicating use in marker detection. This behavior occurs because opening residues are not idempotent, so a modified UO is introduced to attenuate this inconvenience enabling a better selection of markers. Likewise, an example of a better selection of markers is carried out from images previously filtered and enhanced. Finally, the use of these transformations in image segmentation is illustrated.

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