Tarjan Union-Find algorithm and connected operators

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Abstract

Tarjan Union-Find algorithm (TUFA) aims to build, given an image, a tree representation modeling the equivalence classes following a given relation. It can be derived to define filters on those tree representations. TUFA is currently used in Milena, our image processing library, to implement connected filters. For example, closing and opening related to area, volume, or height which are useful to clean an image while preserving contours. This important property provides a nice advantage in comparison to the classical opening and closing based on erosion and dilation. Another advantage of TUFA is that it can be used for algorithms which feature the domain disjointness property. This document presents how new connected filtersin particular self-dual, have been introduced into Milena.