Simplification of color images using semi-flat morphological operators and statistical metrics
ICIP'09 Proceedings of the 16th IEEE international conference on Image processing
General adaptive neighborhood viscous mathematical morphology
ISMM'11 Proceedings of the 10th international conference on Mathematical morphology and its applications to image and signal processing
General Adaptive Neighborhood-Based Pretopological Image Filtering
Journal of Mathematical Imaging and Vision
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Morphological operators designed for grey-scale functions process every points of the space identically whatever their luminance. In many situations however, it is interesting to modulate the amount of processing according to the local grey-level. This leads to the idea of intensity-adaptive morphological operators. A simple way to construct such operators is to threshold the function at every grey-value, then to apply set operators to the level sets obtained in this way, and finally to reconstruct a new transformed function from the transformed level sets. The reconstruction's step is not straightforward since the transformed level sets are not obligatorily nested. Two schemes of stacking reinvestigated in the present paper that lead to two kinds of intensity-adaptive operators: the upper and lower adaptive operators. Those operators are complementary in the sense that, by coupling, one defines adjunctions and consequently, by composition, one defines intensity-adaptive morphological openings and closings. The theoretical study of grey-level adaptive morphological operators is supplemented of some examples that illustrate the potential of the investigated operators in image filtering applications.