Fast fuzzy connected filter implementation using max-tree updates

Connected filters are widely used filters in image processing, and their implementation highly benefits from tree representations of images, called max-trees. Extending these filters to fuzzy sets, which may be used to represent imprecision on gray levels in fuzzy gray-level images, requires frequent manipulations of these trees. In this paper we propose efficient algorithms to update tree representations of fuzzy sets according to modifications of the membership values. We show that any modification can be reduced to a series of simple changes, where only one pixel is modified at each step.