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Component trees are important data structures for computation of connected attribute filters. Though some of the available algorithms are suitable for high-dynamic range, and in particular floating point data, none are suitable for computation of component trees for so-called second-generation, and mask-based connectivity. The latter allow generalization of the traditional notion of connected components, to allow considering e.g. a star cluster as a single entity. This paper provides an O(N log N) algorithm for component trees, suitable for standard and mask-based connectivity. At 24 bits per pixel, the new algorithm outperforms the existing by a factor of 20 to 77 in cpu-time, on 3 megapixel images, depending on the image content.