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- A fast algorithm for auto-dual trees + (For the last few years, connected operator … For the last few years, connected operators have gained a certain popularity in image processing field, they have been widely used for filtering, image segmentation, object detection...However, they encountered several issuesthe most important being contrast dependence, one can only retrieve either dark or bright objects. Auto-dual operators allow computation on dark and bright components in the same time and as a consequence, do not suffer from the drawback of classical connected operators. Howeverauto-dual operators are more difficult to implement and current algorithms are computationally expensive. We propose a new algorithm to compute auto-dual operators based on Tarjan's union-find which is faster that current state-of-the-art contour tree algorithms. state-of-the-art contour tree algorithms.)